Valid-only Modus Ponens is essentially circular [Archive]

John Powell

March 4th 2003, 04:29 PM

Gavin:

You could have fooled me!:teeth:

I am fairly certain it is my intellectual obtusity that is the problem.

POWELL:
Given your responses, I am fairly certain that it is merely because you haven't thought about it enough yet.

GAVIN:
That being said, I have re-read everything you have written in this thread and I am fairly certain that I understand your position better now (though this does not mean that I will be able to dialogue with it at any significant comprehensive level).

Your claim is essentially that MP, when claimed to be valid (not sound), is circular. Correct?

POWELL:
Yes.

GAVIN:
Questions:

First, why would the same not be true then concerning when MP is claimed to sound? Since validity is a necessary criterion for soundness, and the more basic, initial, step, would not circularity in validity lead to circularity in soundness?

POWELL:
You are thinking very well, I think, Gavin. I also initially believed that if the valid form were circular than the sound form would also be circular for reasons essentially the same as those you gave, but Tim Holt brought up some things that I had to concede to based upon his persuasive arguments. Tim does not necessarily agree with my "M.P valid form is essentially circular" argument.

Let me quote what I said in the argument and elaborate.

POWELL:
Modus Ponens as a sound argument:

1) if p then q
2) p
3) therefore, q

This looks the same as the merely valid form, but it has a different meaning.

Expanded:
The conditional "if p then q" is true and "p" is true therefore because this is a valid argument form and the premises are true, "q" is true.

POWELL:
When one claims that an argument of the M.P. form is sound they are NOT saying

If the conditional "if p then q" is true and if "p" is true then "q" is true.

as is done when claiming mere validity, rather they are saying

The conditional "if p then q" is true and "p" is true therefore "q" is true.

When M.P. is treated as sound it doesn't have the various "if" parts possibly necessary to successfully argue that the form is circular.

Maybe the sound form is circular too, but I haven't been able to come up with a persuasive argument for that yet.

Is that more clear now?

GAVIN:
Maybe it is the concept of "circularity" that I need you to explain more fully before I can decide about the relative relations of validity and soundness to it.

POWELL:
Perhaps.

I have struggled with claiming M.P. is circular or claiming that it is essentially circular because of definitional concerns. I have opted for the weaker claim for now.

If one defines "circular" such that the conclusion is identically the same as one of the premises or something close enough to that then my argument probably fails. I might have complaints about that definition. I am trying to get at the "spirit" of the meaning of circularity rather than the strict definition before I tackle whether that kind of definition for circularity is advisable.

GAVIN:
And secondly, if MP is circular, aren't all argument forms? Don't all argument forms require you to start with the truth of something, that A=A? I think using a relatively simple example might help me here, John.

POWELL:
I don't think inductive arguments are circular.

1. Every day of my life the sun has risen.
2. Therefore, the sun will rise tomorrow.

There is an implied "probably" in the conclusion.

Also, I don't think statistical arguments are circular.

1. All men are mortal.
2. Socrates is a man.
3. Therefore, Socrates is probably mortal.

One of my soap-box complaints is that too many philosophers have criticized science and its use of inductive statistical arguments as inferior to their deductive certain arguments. I am trying to "put them in their place" below science by arguing that their much-vaunted M.P. valid form is a circular argument. In other words, I'm saying, "What's so big about your M.P. valid form? It's true by definition. A = A. That's no big deal. Inductive arguments, on the other hand, go beyond the premises to provide new information, powerful new insights."

I have more attacks up my sleeve, Gavin. If you think my circularity argument is a revolutionary attack of a scientist against non-science philosophers, wait until you see my validity-smashing arguments.

GAVIN:
Finally, in specific reference to your last thread, regarding MT. In the argument:

POWELL:
1) If M.P. and M.T. are both valid deductive arguments then "if p then q" is equivalent to or means "if not q then not p."

2) If the "if p then q" in M.T. is replaced with "if not q then not p" then M.T. becomes (i.e. is) "M.T. converted into M.P."

3) If M.P. is circular then "M.T. converted into M.P." is circular.

4) If "M.T. converted into M.P." is circular then M.T. is circular.

GAVIN:
It seems to me that the onus lies on proving 1, and the argument hinges on it. Your thoughts?

POWELL:
Yes.

I think statement 1 is the big problem. There may be some problems with the "A = B, B = C, therefore A = C" kind of presentation I used. Perhaps that could be made less awkward.

GAVIN
Thanks John.

POWELL:
No, thank you Gavin for giving me a chance to discuss this "discovery" of mine. Surely others have discovered it before me (realizing that it still might be wrong), but it was still something I came up with much on my own.

If one can't look forward to a life of eternal bliss, little joys in this life will have to suffice.

John Powell

Gavin

March 4th 2003, 05:45 PM

POWELL:
You are thinking very well, I think, Gavin. I also initially believed that if the valid form were circular than the sound form would also be circular for reasons essentially the same as those you gave, but Tim Holt brought up some things that I had to concede to based upon his persuasive arguments. Tim does not necessarily agree with my "M.P valid form is essentially circular" argument.

Let me quote what I said in the argument and elaborate.

quote:
--------------------------------------------------------------------------------
POWELL:
Modus Ponens as a sound argument:

1) if p then q
2) p
3) therefore, q

This looks the same as the merely valid form, but it has a different meaning.

Expanded:
The conditional "if p then q" is true and "p" is true therefore because this is a valid argument form and the premises are true, "q" is true.

--------------------------------------------------------------------------------

POWELL:
When one claims that an argument of the M.P. form is sound they are NOT saying

If the conditional "if p then q" is true and if "p" is true then "q" is true.

as is done when claiming mere validity, rather they are saying

The conditional "if p then q" is true and "p" is true therefore "q" is true.

When M.P. is treated as sound it doesn't have the various "if" parts possibly necessary to successfully argue that the form is circular.

Maybe the sound form is circular too, but I haven't been able to come up with a persuasive argument for that yet.

Is that more clear now?

Ah ha! I think I finally get it. :idea:

So you are saying that MP is circular because, when claiming to be valid, it itself uses the same type of "if-then" argument to prove its validity? Is that the idea?

Very interesting.

I have more attacks up my sleeve, Gavin. If you think my circularity argument is a revolutionary attack of a scientist against non-science philosophers, wait until you see my validity-smashing arguments.
I am all ears.

POWELL:
No, thank you Gavin for giving me a chance to discuss this "discovery" of mine. Surely others have discovered it before me (realizing that it still might be wrong), but it was still something I came up with much on my own.

If one can't look forward to a life of eternal bliss, little joys in this life will have to suffice.
IMO, intellectual joys (though real) don't even compare to the joys of eternal life in Christ.

And I would argue all intellectual joys ultimately stem from God, the author of good and perfect gift, as well.

I have struggled with claiming M.P. is circular or claiming that it is essentially circular because of definitional concerns. I have opted for the weaker claim for now.
Very interesting thread, John!

John Powell

March 4th 2003, 06:13 PM

mattbballman19:

In response to your first post,

Your discussion of the Modus Ponens is quite intriguing. And I share in your conclusion that atheistic arguments are not persuasive. But I must protest this idea that Modus Ponens is essentially question-begging.

POWELL:
We agree that some atheist arguments are not persuasive.

MATT19:
The M.P. form is intended to go from a hypothetical conditional to a matter of fact which will result in the condition being satisfied.

Think of an example:

(1) If you are a student at USC then you are attending a college in California.
(2) You are a student of USC.
(C) Therefore, you are attending a college in California.

POWELL:
Are you claiming this argument to be sound or merely valid, Matt19?

MATT19:
If the form of the argument were truly circular, then the conclusion must be found explicitly in the premises (conclusions of deductive-type arguments attempt to make explicit what is implicit in the premises). But it is not.

POWELL:
Sneaky, aren't those philosophers? They take a circular valid argument, put it into a syllogism that is ambiguous whether it's being claimed to be sound or merely valid which obscures that all they really are doing is switching some quotes around and calling what was part of the conclusion part of the premise and, presto, you have what appears to be a non-circular argument.

If your opponent accepts the conditional as true, Matt19, why do you need the rest of the argument? The conditional "If p then q" linguistically means "if you have p then you'll have q," doesn't it?

Why don't you show me which specific parts of my posted argument are wrong, Matt?

MATT19:
The first premise (1) only establishes a "What if . . .?" scenario and does not require that there be any existential matters to consider. The second premise does just the opposite. We are informed by (2) that there is a matter of fact to consider (an existential claim) that is not hypothetical like (1). As a result, the conclusion becomes manifestly existential (as it comes into being when (2) is true).

POWELL:
Interesting. Are you saying, Matt, that if the M.P. form argument is claimed to be sound that you are NOT claiming that the conditional is true, but you are ONLY claiming that the antecedent and the consequent are true? What about the correctness of the inference?

What is your definition of a sound deductive argument, Matt?

MATT19:
To see how (2 and (C) do not relate to (1) existentially, consider that USC might have no students at all. This would make (2) false but not (1). This is curious if the argument is circular because the premises must be identical in some sense to the conclusion (or, in your analysis, (1) must be a restatement of (2) - (C)).

POWELL:
My argument is that 2 and C essentially go together if the argument is claimed to be merely valid. Things are different if the argument is claimed to be sound.

Please go through my argument and show me the step(s) where my reasoning is flawed and explain why.

MATT19:
Instead, if (2) were false, we would actually have:

(1) If you are a student at USC then you are attending a college in California.
(2*) You are not a student of USC.
(C*) Therefore, you are attending a college in California or you are not attending a College in California.

Keep in mind that denying the antecedent (which (2*) does) does not establish the original conclusion or its negation for it is now invalid.

POWELL:
Yes, your second argument is invalid. If you deny the antecedent then you cannot say for sure what is true about the consequent.

MATT19:
But this is odd if (1) is supposed to be a re-statement of (2*) - (C*). Clearly, it must not be circular. It is a step from a hypothetical to an actual fact which work in concert to establish the conclusion.

POWELL:
It may be clear to you that it's not circular, but I have not yet been persuaded to agree with you. It would help if you would avoid the syllogism form because it is ambiguous whether you're claiming the argument is valid or sound and, consequently, whether you are claiming "if true" or "is true."

Would you please point to the specific part(s) of my argument that fail to persuade you and explain why?

MATT19:
Now, the atheist argument you presented would be false for reasons other than badgering the Modus Ponens.

POWELL:
Propositions (premises and conclusions) are true or false. Deductive arguments are things like valid, invalid, sound, or unsound.

MATT19:
You state:

1) If God knows the future then there is no free will.
2) God knows the future
3) therefore, there is no free will.

What the theist would do is contest the conditional statement (1) without denying (2).

POWELL:
I think that effort could stall if this argument was claimed by the atheist to be merely valid. If this is merely claimed to be valid by the atheist then she is saying

IF the conditional "If God knows the future then there is no free will" were true then . . . The atheist is not claiming the conditional is true, only that if it were true other things would follow.

Do you deny that my argument is valid? Doesn't it match the M.P. form if you replace "p" with "God knows the future" and "q" with "there is no free will"? Are you saying that arguments of the M.P. form are not always valid, that it depends upon what you substitute in for "p" and "q"?

What is your definition of a valid deductive argument, Matt?

MATT19:
It is the hypothetical statement itself that is to be questioned, not the form of the argument.

POWELL:
That would be true if the argument were claimed to be sound, but the atheist isn't claiming the argument is sound, but merely valid.

MATT19:
Premise 1 assumes that foreknowledge is logically exclusive to free will, which it clearly is not.

POWELL:
It may be clearly not to you, but it clearly is to me. Are you willing to go through my free-will scenario that purports to demonstrate this?

MATT19:
So, the soundness issue would be the level of critique here without presuming that a tautology is in play (and think of how many things would be critiqued if you were correct!).

matt

POWELL:
The atheist can play a sneaky dance of jumping between valid and sound forms because the syllogism form doesn't distinguish between these.

The atheist is claiming the argument is merely valid so all she has to do is show that it follows the M.P. form which she and the theist agree produces a valid argument. The sneaky atheist then claims that the theist must prove or demonstrate at least one of the premises are false or accept that the conclusion is true, because if the premises are not false, but are true, then because of validity the argument will be sound.

The theist needs to remember that just because he can't prove or demonstrate something false doesn't mean it's true. Furthermore, the burden of proof is upon the atheist to demonstrate that the premises are true if she claims the argument is sound, not upon the atheist to demonstrate that the premises are false.

When the atheist claims the argument is valid, the theist can reply "Yes, but so what? Just because an argument is valid, doesn't mean the conclusion is true, only that if the premises were true then the conclusion must be true. Are you claiming the argument is sound? No? Ok, then what's your point? Surely you don't expect me to prove false to you something you already think is false, do you?" The atheist might reply, "Yes, but you might believe those premises. You need to demonstrate to yourself that those premises are false or accept the conclusion." Theist: "Perhaps, but I didn't propose the argument. You did."

If, on the other hand, the theist replies, "The conditional is false," the atheist might reply with, "the conditional is only a hypothetical, it's not claiming to be true." This might confuse the theist. Perhaps without the theist noticing, the atheist just jumped back onto the safe ground of validity when the theist tried to argue against soundness as the atheist had insisted.

This dance trick can be more easily avoided if the syllogism is avoided in this kind of an exchange. Usually syllogisms are helpful, but they can produce problems when there's uncertainty about whether the syllogism is claimed to be sound or merely valid.

Debater beware.

John Powell

John Powell

March 4th 2003, 07:40 PM

Gavin:
Ah ha! I think I finally get it. :idea:

So you are saying that MP is circular because, when claiming to be valid, it itself uses the same type of "if-then" argument to prove its validity? Is that the idea?

Very interesting.

POWELL:
That's so close to what I'm saying, Gavin, I think you do understand the argument! :yipee:

POWELL:
I have more attacks up my sleeve, Gavin. If you think my circularity argument is a revolutionary attack of a scientist against non-science philosophers, wait until you see my validity-smashing arguments.

GAVIN:
I am all ears.

POWELL:
I would like to improve the arguments before I present them here, but you can see the current form of the arguments at www.topica.com at the forum II Errancy Annex. You don't have to be a member to read them. They are titled "Invalidating Validity-X." I added a few corrections in later posts.

Doug Krueger, the heavy weight philosopher at II Errancy, discounted them with what I considered to be an argument by assertion, appeal to ignorance, and appeal to authority, because he probably had not even read them at that time.

Andre Artus, another of the heavy weights at II Errancy versed in both science and philosophy, said he had looked at them, but was not impressed, and that he would post rebuttals if he could find the time. I haven't seen any rebuttal from anyone yet.

Tim Holt, my best correspondent on philosophical logic, may have looked through them, but hasn't posted rebuttals.

If you want to join the Annex, you just need to join II Errancy (Farrell Till's forum) and then remind Jim Java, the owner of the Annex, to sign you up to the Annex.

Farrell kicked me off of II Errancy, I think because he didn't like me criticizing the way he and other skeptics at II Errancy operated. Dissension in the ranks can't be tolerated, I guess. Jim did not kick me off of the Annex.

POWELL:
No, thank you Gavin for giving me a chance to discuss this "discovery" of mine. Surely others have discovered it before me (realizing that it still might be wrong), but it was still something I came up with much on my own.

If one can't look forward to a life of eternal bliss, little joys in this life will have to suffice.

GAVIN:
IMO, intellectual joys (though real) don't even compare to the joys of eternal life in Christ.

And I would argue all intellectual joys ultimately stem from God, the author of good and perfect gift, as well.

Very interesting thread, John!

POWELL:
Perhaps God loves me a lot more and thinks I'm a lot less foolish and less evil than some Biblical writers apparently thought.

John Powell

Gavin

March 4th 2003, 09:26 PM

Perhaps God loves me a lot more and thinks I'm a lot less foolish and less evil than some Biblical writers apparently thought.
Perhaps God knows my wickedness and folly searchingly , but still loves me a lot more?

mattbballman19

March 6th 2003, 11:55 PM

John,

I do think you have misunderstood my objections. I explained that a modus ponens is not circular reasoning because the first premise is merely a hypothetical conditional that can be true regardless of what actually occurs in the world. The second premise is some actual state of affairs coming about (in this case, that the antecedent occurs). The conclusion simply tells us that now the consequent must also be actualized. My contention is that one can contest the second premise without doing any damage to the first premise. But this would be impossible to do if premise 1 was a mere re-statement of premise 2 and the conclusion. And I don't believe that a valid argument = a sound argument. I only said that one contests a valid argument by analyzing the truth values of each premise.

Regarding the atheist argument from foreknowledge, I believe (in agreement with what you aptly noted) that the atheist has to show how "God has foreknowledge" contradicts "I have free will." There has to be some hidden premise that would make this supposed contradiction real. As it stands, they do not contradict each other.

matt

John Powell

March 7th 2003, 05:19 AM

MATTBALLMAN19:
John,

I do think you have misunderstood my objections.

POWELL:
That can happen.

MATTBALLMAN19:
I explained that a modus ponens is not circular reasoning because the first premise is merely a hypothetical conditional that can be true regardless of what actually occurs in the world. The second premise is some actual state of affairs coming about (in this case, that the antecedent occurs). The conclusion simply tells us that now the consequent must also be actualized. My contention is that one can contest the second premise without doing any damage to the first premise.

POWELL:
If you're contesting the truth value of the second premise then you must be dealing with an argument claimed to be sound. I'm only arguing that merely valid deductive arguments are circular. I am not arguing that sound deductive arguments are circular.

MATTBALLMAN19:
But this would be impossible to do if premise 1 was a mere re-statement of premise 2 and the conclusion. And I don't believe that a valid argument = a sound argument. I only said that one contests a valid argument by analyzing the truth values of each premise.

POWELL:
I think you're confusing sound and valid.

A sound argument is a valid argument with true premises. A valid argument is one for which the conclusion would be true, could not be false if the premises were true.

You don't contest a valid deductive argument by challenging the truth value of the premises, you may not even know what "p" and "q" correspond to in the real world. You challenge a valid deductive argument by determining whether the form of the argument matches recognized valid forms such as Modus Ponens or Modus Tollens or it otherwise satisfies the definition that the conclusion would have to be true, could not be false if the premises happened to be true.

Challenging the truth values of premises is a way you can challenge an argument claimed to be sound.

A valid argument of the M.P. form says

IF the conditional "if p then q" were true and IF "p" were true THEN "q" would have to be true, could not be false.

It does not say that the conditional "if p then q" is true nor does it claim that "p" is true. It merely claims that if they were both true then q would have to be true.

A sound argument, on the other hand, does claim that the premises are true. A sound argument of the M.P. form would be claiming:

The conditional "if p then q" is true and "p" is true and, because the argument is valid, "q" must be true, cannot be false.

MATTBALLMAN19:
Regarding the atheist argument from foreknowledge, I believe (in agreement with what you aptly noted) that the atheist has to show how "God has foreknowledge" contradicts "I have free will." There has to be some hidden premise that would make this supposed contradiction real. As it stands, they do not contradict each other.

matt

POWELL:
Then please consider the following scenario that I've posted elsewhere.

Informal foreknowledge-free-will Scenario:
Imagine a theist named Peter with free will who is skeptical of God's foreknowledge. He has a choice of A or B. He asks God, "Since people claim you know the future, God, please tell me, will I pick A or B? Let me warn you that whatever you tell me, I'm going to do the opposite."

God says . . .

If God says "A" then Peter does B and God is wrong.

However, if God says "B" then Peter does A and God is wrong.

Regardless whether God says "A" or "B" God will be wrong if Peter does the opposite. Therefore, God could not know whether Peter would do A or B if Peter has free will. Therefore, in at least this case, God could not know the future. At most God could predict what Peter might do. What do you think, Matt? Are you persuaded to accept that God cannot know the future if we have free will?

More Formal foreknowledge-free-will Argument:
1. If P has free will then P can choose A or B despite what G foretells.
2. If G knows the future and if G honestly foretells A or B then G will be right.
3. If G foretells B and P chooses A then G will not be right.
4. If G foretells A and P chooses B then G will not be right.
5. Therefore, G either does not know the future or G is not honest or P does not have free will.

More symbolically:
1. If FW then A or B
2. If NF and HF then R
3. If A then not R
4. If B then not R
5. therefore, not NF or not HF or not FW

What do you think, Matt? Are you persuaded to accept that God cannot know the future if we have free will?

John Powell

mattbballman19

March 11th 2003, 03:26 PM

John,

I still think you are confusing my approach here. I'm not suggesting that to be valid is to be sound. I'm only suggesting that if a modus ponens is circular then it must be such that premise 1 = premise 2 & conclusion or P1 = (P2 & C) which per my analysis does not. The truth value of any of its constituent variables is left out of account. Circular arguments must be either explicitly tautological or implicitly tautological and neither is the case here.

Now, your presentation of God's foreknowledge being incompatible with free will is even more dubious. You write:

1. If P has free will then P can choose A or B despite what G foretells.
2. If G knows the future and if G honestly foretells A or B then G will be right.
3. If G foretells B and P chooses A then G will not be right.
4. If G foretells A and P chooses B then G will not be right.
5. Therefore, G either does not know the future or G is not honest or P does not have free will.
[6. Not (G does not know the future or G is not honest)] -- hidden premise assumption
[7. Therefore, P does not have free will] -- hidden second conclusion assumption

What this presentation amounts to is that God will necessarily not be right if an only if He is right. And this amounts to P's defiance leading to a self-contradiction. It is a self-contradiction because it suggests that God foreknows what P will do and that P will do what God does not foreknow. So:

1' G knows A if and only if P does A.
2' G knows ~A if and only if P does ~A.
3' G knows A.
4' So, P does ~A.
5' Therefore, ?

The problem is now apparent for it cannot be the case that the first half of the first biconditional (P does A) be false (see premise 4) if the second part of that biconditional is true (God knows A -- see premise 3). The problem is that the foreknowing some action is not the sufficient cause that brings the action about. This is backwards for it confuses the logical priority of some action obtaining with God's foreknowing it. It is not that God's foreknowing some action that makes P choose but, rather, that some action P chooses will be foreknown by God. And if P makes his stubborn plea that he will not choose anything until he is made privy to God's foreknowledge about it, then the following counterfactual is known by God:

If P will not choose A or B without knowing what God knows then P will not choose A or B.

What your argument amounts to, basically, is (i) it is self-contradictory as implied by 1' - 5'. Or (ii), even if one gets beyond the contradiction, the best we are left with is that although P has free will, and that he has the ability to choose A or B, he simply will refrain from choosing A or B. There is nothing here that makes one conclude that free will does not exist.

matt

John Powell

March 13th 2003, 05:33 AM

mattbballman19:
John,

I still think you are confusing my approach here.

POWELL:
That's discouraging. I usually understand after the first elaboration.

MATTBALLMAN19:
I'm not suggesting that to be valid is to be sound. I'm only suggesting that if a modus ponens is circular then it must be such that premise 1 = premise 2 & conclusion or P1 = (P2 & C) which per my analysis does not. The truth value of any of its constituent variables is left out of account. Circular arguments must be either explicitly tautological or implicitly tautological and neither is the case here.

POWELL:
I thought circular just meant they concluded what they assumed.

I'm arguing that M.P. is "essentially" circular. The second premise and conclusion is merely a linguistic restatement of the original conditional. I recognize that neither "if p then q" nor "p" is identically the same as "q." My argument is that M.P. as a valid deductive argument says:

If "if p then q" then (or "and') if "p" then "q"

which, with a simple rearrangement of quote marks, is essentially the same as

If "if p then q" then "if p then q"

What they've done apparently is split the "if p" from the "then q" in the conclusion, called the "if p" a premise and "then q" as the conclusion and then put the "if" in front of "if p" and the "then" in front of "then q" into the inference. This might be a useful rearrangement if the argument is claimed to be sound. If it is only claimed to be valid, however, it looks to be essentially circular to me. Once you accept "if p then q" to be true then the rest of valid-only M.P. is a superfluous restatement.

Is the following argument circular?

1. If p then q
- - - - therefore
2. if you have p then you have q.

Isn't the phrase "if you have p then you have q" essentially the same thing as the second premise and conclusion of M.P.?

MATTBALLMAN19:
Now, your presentation of God's foreknowledge being incompatible with free will is even more dubious. You write:

1. If P has free will then P can choose A or B despite what G foretells.
2. If G knows the future and if G honestly foretells A or B then G will be right.
3. If G foretells B and P chooses A then G will not be right.
4. If G foretells A and P chooses B then G will not be right.
5. Therefore, G either does not know the future or G is not honest or P does not have free will.
[6. Not (G does not know the future or G is not honest)] -- hidden premise assumption
[7. Therefore, P does not have free will] -- hidden second conclusion assumption

POWELL:
Why do I need 6? I don't want to argue that G knows the future or that G is honest, only that If this were the case then certain things would result 7 is only true if "G knows the future" is true and I haven't claimed that to be true. I only want to claim if God knows the future then . . .

Although I don't think your suggestions are appropriate, I may need to reword the argument anyways.

MATTBALLMAN19:
What this presentation amounts to is that God will necessarily not be right if an only if He is right.

POWELL:
I don't like that. I wanted to conclude that God could only be right if P did not have free will.

MATTBALLMAN19:
And this amounts to P's defiance leading to a self-contradiction. It is a self-contradiction because it suggests that God foreknows what P will do and that P will do what God does not foreknow.

POWELL:
Sort of, I think, if both G knows the future AND P has free will, consequently both can't be true. P MIGHT POSSIBLY do what G does not foreknow.

MATTBALLMAN19:
So:

1' G knows A if and only if P does A.
2' G knows ~A if and only if P does ~A.
3' G knows A.
4' So, P does ~A.
5' Therefore, ?

The problem is now apparent for it cannot be the case that the first half of the first biconditional (P does A) be false (see premise 4) if the second part of that biconditional is true (God knows A -- see premise 3).

POWELL:
Ok. So, perhaps G does not know the future.

MATTBALLMAN19:
The problem is that the foreknowing some action is not the sufficient cause that brings the action about.

POWELL:
I think knowledge of that future prevents P from doing otherwise which contradicts free will.

MATTBALLMAN19:
This is backwards for it confuses the logical priority of some action obtaining with God's foreknowing it. It is not that God's foreknowing some action that makes P choose but, rather, that some action P chooses will be foreknown by God. And if P makes his stubborn plea that he will not choose anything until he is made privy to God's foreknowledge about it, then the following counterfactual is known by God:

If P will not choose A or B without knowing what God knows then P will not choose A or B.

What your argument amounts to, basically, is (i) it is self-contradictory as implied by 1' - 5'. Or (ii), even if one gets beyond the contradiction, the best we are left with is that although P has free will, and that he has the ability to choose A or B, he simply will refrain from choosing A or B. There is nothing here that makes one conclude that free will does not exist.

matt

POWELL:
Perhaps I'll need to work on the argument.

Have you gone through the scenario in my debate with Jaltus?

John Powell

mattbballman19

March 14th 2003, 02:23 AM

John,

Let me look at your comments so far:
"I thought circular just meant they concluded what they assumed."

I don't think this is a precise definition of petitio principii only because this is also the definition of determining unstated text just in case it is the conclusion. But this, even on a conventional understanding, is not removed from what I clarified -- that if a tautology exists, it is begging the question. And a tautology can exist in any number of ways. For example:

1. If A then B.

C: ~(A and ~B)

Although the token statements are different, they are saying exactly the same thing.

Regarding your re-wording of the Modus Ponens, only if you keep supplying an implicit "if" before premise 2 and an implicit "then" in front of the conclusion will your case be true -- that Modus Ponens is circular. However, I think that "if" and "then" in front of p2 & C are implied. As I originally noted, only the first premise is hypothetical. But the second premise is a statement of something being actualy, namely, that A has really occurred. And now that A has actually occurred, it satisifies the antecedent of the hypothetical thereby making the conclusion (B) actually true as well.

Regarding the foreknowledge argument, you write:

"I wanted to conclude that God could only be right if P did not have free will . . . if both G knows the future AND P has free will, consequently both can't be true. P MIGHT POSSIBLY do what G does not foreknow."

I understand what you are wanting to conclude, but one cannot make such a case by presuming a contradiction. It is just like the village atheist who wants to say that "God cannot make a rock so big that he can't lift it." He argues the same way. He says, God MIGHT POSSIBLY create something that He can't lift. And this makes no sense either for it also enacts a self-contradiction. In order to be successful in your approach, you would have to prove that some action necessarily results on the basis of God's foreknowledge. But I don't think one can do this because this inevitably commits a standard modal fallacy. It is fallacious in this circumstance because it ignores possible subjunctive counterfactuals:

If P were to choose X instead of ~X then God would have known that.

and this amounts to

God knows either X or ~X.

and nothing P does can make God's foreknowledge false.

matt

John Powell

March 14th 2003, 04:28 AM

mattbballman19:
John,

Let me look at your comments so far:
"I thought circular just meant they concluded what they assumed."

I don't think this is a precise definition of petitio principii only because this is also the definition of determining unstated text just in case it is the conclusion. But this, even on a conventional understanding, is not removed from what I clarified -- that if a tautology exists, it is begging the question. And a tautology can exist in any number of ways. For example:

1. If A then B.

C: ~(A and ~B)

Although the token statements are different, they are saying exactly the same thing.

POWELL:
I'm reading about this right now in my logic text, but this appears to be false.

It is my understanding that the English phrase "if A then B" is NOT constrained to satisfy the conditions of the truth table of the horseshoe which is the same truth table as ~(A and ~B). If the phrase "if A then B" CAN be so translated then the power of truth-table analysis can be brought to bear on the logical problem.

Counter examples are where "if A then B" is causal such as "If I drop this rock then it will fall with an acceleration of 9.8 m/s^2" and decisional "If Bush wins again then I'm going to eat my hat." Someone might agree that both these conditionals are true, yet even if the antecedent were true the consequent might not be. The consequent does not HAVE to follow logically if the antecedent is true in these two cases. At least that's the way it looks to me right now.

MATTBALLMAN19:
Regarding your re-wording of the Modus Ponens, only if you keep supplying an implicit "if" before premise 2 and an implicit "then" in front of the conclusion will your case be true -- that Modus Ponens is circular.

POWELL:
Right.

MATTBALLMAN19:
However, I think that "if" and "then" in front of p2 & C are implied.

POWELL:
Right, if the argument is claimed to be merely valid, not sound.

MATTBALLMAN19:
As I originally noted, only the first premise is hypothetical. But the second premise is a statement of something being actualy, namely, that A has really occurred.

POWELL:
That's if the argument is claimed to be sound. A merely valid argument is NOT claiming the premises are true. A merely valid argument is only claiming that if the premises were true then the conclusion must be true, could not be false. If the argument is claimed to be sound THEN it is claimed that the premises are true.

MATTBALLMAN19:
And now that A has actually occurred, it satisifies the antecedent of the hypothetical thereby making the conclusion (B) actually true as well.

POWELL:
Again, you're right if the argument is claimed to be sound. I'm not claiming M.P. is essentially circular when it is claimed to be sound only when it is claimed to be merely valid.

MATTBALLMAN19:
Regarding the foreknowledge argument, you write:

POWELL:
I wanted to conclude that God could only be right if P did not have free will . . . if both G knows the future AND P has free will, consequently both can't be true. P MIGHT POSSIBLY do what G does not foreknow.

MATTBALLMAN19:
I understand what you are wanting to conclude, but one cannot make such a case by presuming a contradiction. It is just like the village atheist who wants to say that "God cannot make a rock so big that he can't lift it." He argues the same way. He says, God MIGHT POSSIBLY create something that He can't lift. And this makes no sense either for it also enacts a self-contradiction.

POWELL:
I don't agree.

The village atheist made his point. He won the argument, but the conclusion is not that God does not exist, but that a God who is omniscient in the way people used to claim does not exist.

If "omnipotent" means "can do anything (even what a human might think is impossible)" then God can't be omnipotent. What this "too heavy rock" argument did was pressure theists to revise the definition of "omnipotent" to indicate something like "can do anything that is logically possible." The "too heavy rock" argument served its purpose. It forced philosophical theologians to revise the meaning of "omnipotent" so it did not allow for impossible things.

MATTBALLMAN19:
In order to be successful in your approach, you would have to prove that some action necessarily results on the basis of God's foreknowledge. But I don't think one can do this because this inevitably commits a standard modal fallacy. It is fallacious in this circumstance because it ignores possible subjunctive counterfactuals:

If P were to choose X instead of ~X then God would have known that.

and this amounts to

God knows either X or ~X.

and nothing P does can make God's foreknowledge false.

matt

POWELL:
Then I would argue P does not have free will. If P can't do other than what God foretold that he would do then P does not have free will as I understand the term.

Here's a revised argument that is easier to test using truth tables. Maybe it will be a more persuasive argument.

1. IF (P has free will) THEN (it is possible for P to choose B).

2. IF (G knows the future and G foretells that P will choose A) THEN (it is not possible for P to choose B).

3. (P has free will) AND / OR (G knows the future and foretells that P will choose A).

4. It is not the case that both (it is possible for P to choose B) AND (it is not possible for P to choose B).

5. Therefore, it is not the case that both (P has free will) AND (G knows the future and foretells that P will choose A).

I believe this is a valid argument. A and B could be reversed to give the same basic result.

Premise 1 follows from the definition of free will. Premise 2 is a consequence of G knowing the future.

Which of the premises do you not agree with?

This argument can be represented more compactly by adopting the following abbreviations.
FW = "P has free will"
B = "it is possible for P to choose B."
NFF = "G knows the future and G foretells that P will choose A"

1'. If FW then B
2'. If NFF then not B
3'. FW and/or NFF
4'. not (B and not B)
5'. therefore, not (FW and NFF).

If these English words can translate to the horseshoe, curl, wedge, and dot then this becomes

1''. FW C B
2''. NFF C ~B
3''. FW V NFF
4''. ~ (B * ~B)
5''. therefore, ~ (FW * NFF).

Is this argument persuasive?

John Powell

John Powell

March 14th 2003, 04:59 PM

POWELL:
That argument is unnecessarily complicated. I put in the wedge to produce a valid truth table result since I was using the dot to translate "and". Tim correctly noted that if I use the "&" instead of the dot then the wedge is unnecessary. Consequently, let me try again.

1. IF (P has free will) THEN (it is possible for P to choose B).

2. IF (G knows the future and G foretells that P will choose A) THEN (it is not possible for P to choose B).

3. It is not the case that BOTH (it is possible for P to choose B) AND (it is not possible for P to choose B).

4. Therefore, it is not the case that BOTH (P has free will) AND (G knows the future and foretells that P will choose A).

I believe this is a valid argument. A and B could be reversed to give the same basic result.

Premise 1 follows from the definition of free will. Premise 2 is a consequence of G knowing the future.

Which of the premises do you not agree with?

This argument can be represented more compactly by adopting the following abbreviations.
FW = "P has free will"
B = "it is possible for P to choose B."
NFF = "G knows the future and G foretells that P will choose A"

1'. If FW then B.
2'. If NFF then not B.
3'. not (both B and not B).
4'. therefore, not (both FW and NFF).

If these English words can translate to the horseshoe, curl, and "&" (meaning both and) then this becomes

1''. FW C B.
2''. NFF C ~B.
3''. ~ (B & ~B).
4''. therefore, ~ (FW & NFF).

Is this argument persuasive?

That's better. Notice the conclusion is NOT that if we have free will then God can't know the future, it's that God can't know the future and REVEAL that knowledge.

I remember now realizing this weakness of the argument when I was a believing Mormon. Since becoming an atheist, I forgot about it.

It's possible that God knows the future about us according to this argument, but He apparently can't have that knowledge if He reveals it in any way to any person capable of telling us or affecting us, even perhaps to himself as verbal signals (spiritual sound waves) or thoughts (spiritual neural signals).

The belief that God has foreknowledge as long as He doesn't reveal it might provide a sense of security to the believer, but it would not support the idea that Biblical prophecies are visions of the future. Rather, Biblical prophecies would at most be highly likely predictions of the future and promises by God to make good on them.

Here is my argument against God knowing the future even if God doesn't reveal what that future act (A) will be.

5. If God knows the future then P does A.
6. If P does not A then G does not know the future.
7. It appears that P can do not A.
8. therefore, it is unlikely that God knows the future.

No person other than God, including P, can tell if P is doing opposite to what God knows will happen if God won't reveal what the future will be. If God seeks to reveal the future then He probably loses the ability to have that foreknowledge. At least that's the way it looks to me.

What do you think?

John Powell

John Powell

March 17th 2003, 05:32 AM

POWELL:
The God I'm referring to in the previous post is NOT necessarily the Christian God who reveals His will in the Bible. It would be a God who might know the future, but might not be either omnibenevolent or willing to reveal any of the future.

John Powell

mattbballman19

March 18th 2003, 02:24 AM

Hey John, sorry for the wait.

(i) My comparison of If A then B, and ~(A & ~B) is only meant to show an identical truth table -- no causal or decisional considerations are required in this analysis. But if you run a truth-table analysis of both of these statements, you will see that they have identical outcomes. And I must protest your statement that "[t]he consequent does not HAVE to follow logically if the antecedent is true in these two cases." It is necessarily the case that in a conditional statement that if the antecedent is true then the consequent MUST be true as well (it's the only point in the truth table where the conditional statement is false). Likewise, it is impossible for ~(A & ~B) to have the conjunct B false if conjunct A is true. Something else, this statement can be perceived in both a causal and decisional context:

It is not the case that where there's coffee there's also no aroma around.

This can be converted correctly into either a conditional statement or a conjunctive statement.

(ii) And your subsequent analysis of the modus ponens is still committing the same mistake (and you keep accusing me of defining my contention as an issue of soundness when, in fact, soundness is not being addressed at all). It does not matter if any truth-values are assigned to A and B (a necessary condition for analyzing soundness). The point is, it is false that there is logical equivalence between "If A then B" and "A; therefore, B." In fact, if you begin to assign arbitrary truth values to the second instance, it is possible for the premise ("A") to be true and the conclusion ("therefore, B") to be false -- a feature that makes a statement invalid. However, the statement "If A then B" CANNOT have a situation where its antecedent is true and its consequent false. So,

A

Therefore, B.

is not identical to

If A then B.

because the first situation makes no logical connection between A and B. You would first have to ASSUME that "If A then B" and that sort of assumption would make just about anything circular. For example, suppose I made the following argument:

All A are B.

Therefore, All B are A.

This is clearly invalid. However, I could use the same strategy you are making and say, "Well, I am assuming that in the premises there exists a statement that says, 'No B are non-A." So that the following results:

All A are B.

[No B are non-A]

Therefore, All B are A

Therefore, so says my new analysis, all A-Claim categorical statements are logically equivalent to their converse -- a direct contradiction of basic conversion! This is why your analysis about modus ponens is only true if you supply the "if . . . then . . . " in p2 - C to make it identical with p1.

(iii) Regarding the definition of omnipotence, the "too heavy rock" argument did not tie the hands of theists to revise the definition of omnipotence -- that's incorrect. Instead, the argument was dead on arrival because it made a logical contradiction in the premises. So, it's not that God can't create a rock so big that he can't lift it but, rather, that NO ONE can make a rock so big that they can't lift it because there is no such thing! It is evoking things such as a "round triangle" or a "married bachelor."

You then say, "Then I would argue P does not have free will. If P can't do other than what God foretold that he would do then P does not have free will as I understand the term." However, this does not follow from a set of contradictory premises. You need not make any conclusion on the basis of an unsound argument. The fact that a bad argument does not make God's foreknowledge non-existent is NOT corrected when you say that another conclusion, P does not have free will, is then suggested. Two wrongs don't make a right! The premises, apart from their conclusion, are still self-contradictory.

So, you propose another argument:

"1. IF (P has free will) THEN (it is possible for P to choose B).

2. IF (G knows the future and G foretells that P will choose A) THEN (it is not possible for P to choose B).

3. (P has free will) AND / OR (G knows the future and foretells that P will choose A).

4. It is not the case that both (it is possible for P to choose B) AND (it is not possible for P to choose B).

5. Therefore, it is not the case that both (P has free will) AND (G knows the future and foretells that P will choose A)."

The main problem, as I noted in my previous response, is the error of (2) where God's foreknowledge is seen as the causal antecedent to what P will do. And this does not take into account the subjunctive counterfactual that

God knows the future and G foretells that P will choose B.

If P were to choose B, God would have known that and his foreknowledge would have been "God knows that G will choose B." Likewise, if P were to choose A then God would have known THAT and so "God knows that G will choose A" would be true. I think the modal conditional set up in (2) is simply false. It is not necessary that God's foreknowledge leads to a decision -- quite the opposite! If the game is rigged so that P will only choose the opposite of God's foreknowledge, then you only have grounds for God's knowledge being: "God knows that P will withhold choosing until a contradiction results." It's like saying, "Okay, God; I will only pray if you say and mean 'It is true that it is impossible for Matt to pray.'" Or, P if and only if ~P. And these types of paradoxes are just that -- paradoxes.

matt

mattbballman19

March 20th 2003, 12:07 AM

John,

I responded above also,

Without getting bogged down in the logical semantics (and I don't disagree with the validity of what you set up, just its soundness), you stress:

"Notice the conclusion is NOT that if we have free will then God can't know the future, it's that God can't know the future and REVEAL that knowledge."

Now, this stipulation should actually say "God can't know the future and reveal that knowledge to someone who will specifically choose the contradictory of God's foreknowledge." This, to me, might be vacuously true. Yet a deeper incoherence is still present in the argument, namely, the modal fallacy I noted previously. But nevermind. You offer a separate argument against God having foreknowledge:

"5. If God knows the future then P does A.
6. If P does not A then G does not know the future.
7. It appears that P can do not A.
8. therefore, it is unlikely that God knows the future."

This, presumably more of an inductive argument, explicates the error of denying God's foreknowledge for it suggests that God can only know one course of action. Here is a cleaned up, valid argument that cannot be false if God can know all possibilities:

1. Either (P will do A and God knows A) or (P will do ~A and God knows ~A).
2. P will do A.
3. Therefore, God knows A.

or

2*. P will do ~A.
3*. Therefore, God knows ~A.

Know matter what course of action P freely decides, God will always know it. Therefore, I find it incredible to think that foreknowledge of some action is grounds for rejecting someone's freely doing it.

Regarding prophetic declarations, you may have to consider that it is logically possible that future contingents only ensue if and only if God reveals them. If this counterfactual is possible, your analysis here becomes flawed.

matt

Socrates

March 20th 2003, 12:27 AM

All deductive syllogisms are circular when stated in propositional calculus. But they are still vital, and could be argued to become non-circular when actual propositions are substituted for the variables. That's because they can show that a previously unknown conclusion follows from accepted premises.

John Powell

March 20th 2003, 05:28 AM

MATTBALLMAN19:
Hey John, sorry for the wait.

POWELL:
No problem. I'm happy you're still interested in discussing this with me.

MATTBALLMAN19:
(i) My comparison of If A then B, and ~(A & ~B) is only meant to show an identical truth table -- no causal or decisional considerations are required in this analysis. But if you run a truth-table analysis of both of these statements, you will see that they have identical outcomes.

POWELL:
I'm new to this, but I don't think so. If the phrase "if A then B" is true that only means that if you have A then you'll have B. It says nothing about what happens if A is false. The truth table analysis apparently works if you assume that if A is false then B can be true or false and the conditional will be true. That's not what the conditional necessarily means in English, however.

MATTBALLMAN19:
And I must protest your statement that "[t]he consequent does not HAVE to follow logically if the antecedent is true in these two cases." It is necessarily the case that in a conditional statement that if the antecedent is true then the consequent MUST be true as well (it's the only point in the truth table where the conditional statement is false).

POWELL:
I respect that, but disagree. If I claim "If I drop this apple then it will fall with an acceleration of 9.8 m/s^2" and everyone agrees that this conditional is true and I drop the apple, it is not necessarily true that the apple will fall with an acceleration of 9.8 m/s^2. Likewise, if I claim that "If Bush wins re-election then I will eat my hat" and everyone were to agree that that conditional is true, if Bush were to win the election it is not necessarily the case that I would eat my hat. What this means is that those two kinds of "if p then q" statements do NOT necessarily obey the truth-table requirements of ~(A & ~B).

MATTBALLMAN19:
Likewise, it is impossible for ~(A & ~B) to have the conjunct B false if conjunct A is true. Something else, this statement can be perceived in both a causal and decisional context:

It is not the case that where there's coffee there's also no aroma around.

This can be converted correctly into either a conditional statement or a conjunctive statement.

POWELL:
Are you claiming that it's not possible to have coffee without the aroma?

MATTBALLMAN19:
(ii) And your subsequent analysis of the modus ponens is still committing the same mistake (and you keep accusing me of defining my contention as an issue of soundness when, in fact, soundness is not being addressed at all).

POWELL:
But it is!

MATTBALLMAN19:
It does not matter if any truth-values are assigned to A and B (a necessary condition for analyzing soundness). The point is, it is false that there is logical equivalence between "If A then B" and "A; therefore, B."

POWELL:
When you say "A; therefore, B" is this translated into English as "If A is true therefore B is true" or "A is true. Therefore, B is true"? If the former, then they do mean the same thing linguistically and you are dealing with an argument claimed to be merely valid. If the latter then they do not mean the same thing and you are dealing with an argument claimed to be sound. If you were to write out all your syllogisms and symbolic logic into long English this would be more clear.

MATTBALLMAN19:
In fact, if you begin to assign arbitrary truth values to the second instance, it is possible for the premise ("A") to be true and the conclusion ("therefore, B") to be false -- a feature that makes a statement invalid. However, the statement "If A then B" CANNOT have a situation where its antecedent is true and its consequent false. So,

A

Therefore, B.

is not identical to

If A then B.

because the first situation makes no logical connection between A and B.

POWELL:
Doesn't the "therefore" provide a logical connection between A and B in "A; therefore B" like "then" provides one between A and B in "if A then B"? I need you to indicate whether you mean "If A is true therefore B is true" or "A is true. Therefore, B is true."

MATTBALLMAN19:
You would first have to ASSUME that "If A then B" and that sort of assumption would make just about anything circular. For example, suppose I made the following argument:

All A are B.

Therefore, All B are A.

This is clearly invalid.

POWELL:
Perhaps you are right if you assume "are" means something like "are members of the set of." All dogs are (members of the set of) animals, but all animals aren't (members of the set of) dogs.

On the other hand, if "are" means mathematical equality or similar equivalence then it could be valid. A = B so B = A.

Language is too vague to insist that it always fit the desires of logicians.

MATTBALLMAN19:
However, I could use the same strategy you are making and say, "Well, I am assuming that in the premises there exists a statement that says, 'No B are non-A." So that the following results:

All A are B.

[No B are non-A]

Therefore, All B are A

Therefore, so says my new analysis, all A-Claim categorical statements are logically equivalent to their converse -- a direct contradiction of basic conversion!

This is why your analysis about modus ponens is only true if you supply the "if . . . then . . . " in p2 - C to make it identical with p1.

POWELL:
Which I claim is justified if the argument is claimed to be merely valid, but is not necessarily justified if the argument is claimed to be sound.

MATTBALLMAN19:
(iii) Regarding the definition of omnipotence, the "too heavy rock" argument did not tie the hands of theists to revise the definition of omnipotence -- that's incorrect.

POWELL:
I think it did. I suspect that early Christians were blissfully claiming that "omnipotence" meant "can do anything" and they meant "anything." The "too heavy rock" type arguments pressured the more logically-minded theists to rethink things and conclude that "omnipotence" could not mean "can do anything, even that which is logically impossible" but must mean something more like "can do anything that is logically possible."

MATTBALLMAN19:
Instead, the argument was dead on arrival because it made a logical contradiction in the premises.

So, it's not that God can't create a rock so big that he can't lift it but, rather, that NO ONE can make a rock so big that they can't lift it because there is no such thing! It is evoking things such as a "round triangle" or a "married bachelor."

POWELL:
Exactly. That's why God can't do it. No one can. It's something impossible to do. Perhaps knowledge of the future falls into a similar category.

MATTBALLMAN19:
You then say, "Then I would argue P does not have free will. If P can't do other than what God foretold that he would do then P does not have free will as I understand the term." However, this does not follow from a set of contradictory premises. You need not make any conclusion on the basis of an unsound argument.

POWELL:
Are inductive or statistical arguments unsound?

MATTBALLMAN19:
The fact that a bad argument does not make God's foreknowledge non-existent is NOT corrected when you say that another conclusion, P does not have free will, is then suggested. Two wrongs don't make a right! The premises, apart from their conclusion, are still self-contradictory.

So, you propose another argument:

"1. IF (P has free will) THEN (it is possible for P to choose B).

2. IF (G knows the future and G foretells that P will choose A) THEN (it is not possible for P to choose B).

3. (P has free will) AND / OR (G knows the future and foretells that P will choose A).

4. It is not the case that both (it is possible for P to choose B) AND (it is not possible for P to choose B).

5. Therefore, it is not the case that both (P has free will) AND (G knows the future and foretells that P will choose A)."

POWELL:
I've since revised this argument to be simpler.

MATTBALLMAN19:
The main problem, as I noted in my previous response, is the error of (2) where God's foreknowledge is seen as the causal antecedent to what P will do.

POWELL:
Are you claiming that premise 2 is false?

If yes, are you saying that it is possible for P to choose B if G knows the future and G foretells that P will choose A?

MATTBALLMAN19:
And this does not take into account the subjunctive counterfactual that

God knows the future and G foretells that P will choose B.

POWELL:
A and B are interchangeable.

Valid arguments are supposed to be able to stand on their own. For example, the validity of the classical "all men are mortal, Socrates is a man, therefore Socrates is mortal" isn't supposed to depend on anything else such as ignored counterfactuals. Are you saying that it might?

MATTBALLMAN19:
If P were to choose B, God would have known that and his foreknowledge would have been "God knows that G will choose B." Likewise, if P were to choose A then God would have known THAT and so "God knows that G will choose A" would be true. I think the modal conditional set up in (2) is simply false. It is not necessary that God's foreknowledge leads to a decision -- quite the opposite! If the game is rigged so that P will only choose the opposite of God's foreknowledge, then you only have grounds for God's knowledge being: "God knows that P will withhold choosing until a contradiction results." It's like saying, "Okay, God; I will only pray if you say and mean 'It is true that it is impossible for Matt to pray.'" Or, P if and only if ~P. And these types of paradoxes are just that -- paradoxes.

matt

POWELL:
Perhaps, but it looks different to me.

By making that demand of God you are already praying, so you must be saying that you won't pray any more after the current interchange until / unless God says and means that you can't pray. It appears that you just won't pray anymore since you refuse to pray until it's impossible for you to pray. What's the paradox?

In my scenario I'm testing a being's claim to foreknowledge. I'm trying to show that any being who might claim to know the future would be mistaken if we have free will.

I see no paradox. I believe that knowledge of the future is impossible because the future doesn't exist yet. God doesn't know the future, but at most predicts it and promises to make it be a certain way.

John Powell

John Powell

March 20th 2003, 05:30 AM

Socrates:

All deductive syllogisms are circular when stated in propositional calculus. But they are still vital, and could be argued to become non-circular when actual propositions are substituted for the variables. That's because they can show that a previously unknown conclusion follows from accepted premises.

POWELL:
Does this mean you agree with my initial post in this thread?

John Powell

Socrates

March 20th 2003, 05:39 AM

Not exactly. A sound argument is a valid argument with true premise(s). But yes about the circularity of valid theorems of propositional logic, including MP and MT, and it makes no difference whether they are sound or not. However, no if circularity is considered a problem.

Pate

March 20th 2003, 03:27 PM

I've only superficially skimmed through this discussion, but I'll make a comment on this:

02-27-2003 @ 09:50 AM
John Powell:
A problem I see is that too many philosophers won't admit that their merely valid arguments of the M.P. form are essentially circular arguments. Instead they might argue that because the form is valid, which is something their opponent probably agrees to, their opponent must show one or more of the premises to be false or that opponent must conclude that the argument is sound. This would be deceptive since the burden of proof is upon the person claiming the argument is sound, not upon the other to prove it isn't. This deception is even more despicable when the proponent doesn't believe the argument is sound in the first place.

Example:

Atheist argument:

1) If God knows the future then there is no free will.
2) God knows the future
3) therefore, there is no free will.

This is a valid argument since it is in the M.P. form. If the atheist were to tell the theist that she "must prove at least one of the premises false or necessarily conclude that the argument is sound" then that atheist would be deceptive. First of all, the atheist doesn't believe the argument is sound because the atheist believes premise 2 is false. Secondly, the burden of proof is upon the person claiming the argument to be sound to prove that's the case rather than upon the other to prove it isn't.

If the theist feels a need to disprove the premises, she can choose to do so, but it's not required of her.

I don't like it when my fellow atheists "cheat" in their debate arguments.

I think that you might be mistaken as to what the philosophers are trying to accomplish with deductive arguments like the one you mentioned. Of course it would be ridiculous to claim that one has to decisively prove wrong at least one of the premises. But the argument may be constructed to demonstrate just that IF one accepts those premises, then he should also accept the conclusion. The argument may be constructed just to show an inconsistency in the opponent's position. The argument against free will that you presented, is a good example of this. Its purpose is to show the (alleged) inconsistency of belief in God who has foreknowledge and belief in human freedom.

John Powell

March 20th 2003, 08:13 PM

POWELL:
Thanks Socrates and Pate for interesting and useful comments.

John Powell.

mattbballman19

March 22nd 2003, 03:40 PM

John,

For the sake of brevity, I'm only going to concentrate on the initial features of the discussion (I think that you are compounding your error by multiplying additional ones; e.g., you say that "All A are B" can mean "A = B" which is false for "=" is a connector of identity whereas "All A are B" reflects relationship).

(i) In any conditional statement, if true, cannot have a situation where the antecedent is true and the consequent false. If you say, "Well, I have a counterexample in that if I drop an apple then it will fall at such-and-such speed, yet it is possible that I drop the apple and it not fall at that speed." But this does not contest the logical framework of the conditional but the truth value of the conditional for you are saying that "If A then B" is actually false. You have confused posing counterexamples to premises with posing counterexamples to arguments. This same sentiment applies to your question about the coffee and the aroma.

(ii) Also, you have not shown that a valid construction of modus ponens is circular despite any truth value considerations. In fact, you seem to acknowledge that you have to assume the additional statements in the argument to do that. And my response was, "Well, you can do that with other valid arguments, too." And that only leads to vacuously true statements. But if you remove the supplied assumptions you make about modus ponens and the A-Claim invalid conversion, then on a pure level of validity your accusation of circular reasoning vanishes!

(iii) Regarding omnipotence, the earliest formulations from Christian philosophers do not entail God being able to bring about logical contradictions so I think you are simply ill-informed there. But if you agree with me that "round triangles" and "married bachelors" aren't "things" then they do not participate in the rudimentary biblical definition of omnipotence that "with God all things are possible" for those aforementioned items are not "things" after all. So, no "progression" of definition of omnipotence with respect to logical possibility exists. But, alas, even if such definitions did evolve it does nothing to attack their truthfulness (after all, many "facts" about the world evolve such as our understanding of the universe, biology, archaeology, etc...). So, this is just a red herring.

(iv) Yes, inductive and statistical syllogisms are unsound. That's why they are assessed in terms of strength, not soundness.

(v) I'm not sure if you understood the issue of paradox, especially as I related it to praying if and only if one cannot pray -- a self-contradictory demand. But I certainly deny your premise 2 in that God's foreknowledge and revelation are the sufficient conditions of something coming about. The major error is in that you supplied "not possible" thereby invoking modal quantifiers. In effect, this makes God's foreknowledge the constraining cause of human action which I reject entirely. And you haven't addressed my corrective argument either where God's foreknowledge is to be better understood as:

1. Either (P will do A and God knows A) or (P will do ~A and God knows ~A).
2. P will do A.
3. Therefore, God knows A.

or

2*. P will do ~A.
3*. Therefore, God knows ~A

and you can't find anything self-contradictory or absurd about this and it is perfectly consistent with God's foreknowledge and human freedom. In fact, given the definition of validity, this is necessarily true.

matt

John Powell

March 25th 2003, 10:02 PM

POWELL:
To Mattballman19

MATTBALLMAN19:
John,

For the sake of brevity, I'm only going to concentrate on the initial features of the discussion (I think that you are compounding your error by multiplying additional ones; e.g., you say that "All A are B" can mean "A = B" which is false for "=" is a connector of identity whereas "All A are B" reflects relationship).

POWELL:
Let A = "theists" and B = "those who believe in God or gods" Could it then be true that "All A are B" and "All B are A" and "A=B" and "B=A"? As another example, consider A = "human males" and B = "humans with XY genotype."

Something you don't seem to understand, Matt, is that "language in general" is more vague than mathematics and more vague than logical language. You seem to think that logical language compels language in general to be a certain way.

MATTBALLMAN19:
(i) In any conditional statement, if true, cannot have a situation where the antecedent is true and the consequent false.

POWELL:
Your statement is true for conditional statements converted to the horseshoe logical operator. Whether this conversion is appropriate for every "if p then q" specimen from language in general is under debate. I have suggested that causal and decisional conditionals might not always be appropriate material for that conversion.

MATTBALLMAN19:
If you say, "Well, I have a counterexample in that if I drop an apple then it will fall at such-and-such speed, yet it is possible that I drop the apple and it not fall at that speed." But this does not contest the logical framework of the conditional but the truth value of the conditional for you are saying that "If A then B" is actually false.

POWELL:
But, Matt, everyone accepted that it was a true conditional before I dropped it. Were they wrong? Does the truth of a conditional depend on whether you actually do the experiment?

MATTBALLMAN19:
You have confused posing counterexamples to premises with posing counterexamples to arguments. This same sentiment applies to your question about the coffee and the aroma.

POWELL:
I'm suggesting that every case of "if p then q" in language in general does not necessarily follow the logical rules of the horseshoe logical operator. Do you claim that they do?

The problem with the coffee and aroma is the same as with dropping the apple I think.

MATTBALLMAN19:
(ii) Also, you have not shown that a valid construction of modus ponens is circular despite any truth value considerations.

POWELL:
Then please indicate in my presentation, the first post in this thread, precisely where my reasoning is flawed.

MATTBALLMAN19:
In fact, you seem to acknowledge that you have to assume the additional statements in the argument to do that. And my response was, "Well, you can do that with other valid arguments, too." And that only leads to vacuously true statements.

POWELL:
You're beginning to understand, Matt. Deductively valid arguments (at least M.P.) have true conclusions essentially by definition. You conclude essentially what you assumed to be true.

MATTBALLMAN19:
But if you remove the supplied assumptions you make about modus ponens and the A-Claim invalid conversion, then on a pure level of validity your accusation of circular reasoning vanishes!

POWELL:
If my assumptions as to what is meant by a valid-only M.P. are wrong then please supply how you would word this in long English:

if p then q
p
therefore q

What does this series of statements mean in long English if the proponent is only claiming the argument is valid, not sound?

Doesn't it mean in very long English:

If the conditional "if p then q" is true and (or then) if the statement "p" is true then (or therefore) the statement "q" is true?

Doesn't it mean in shorter English:

If "if p then q" then if "p" then "q"?

If not, Matt, then what does it mean in long English?

MATTBALLMAN19:
(iii) Regarding omnipotence, the earliest formulations from Christian philosophers do not entail God being able to bring about logical contradictions so I think you are simply ill-informed there.

POWELL:
Possibly. If you're right then I would argue the Christians prior to the earliest Christian philosophers, those who lived during the days of Paul for example, likely held to a view that ignored logical impossibility. They probably believed there was no logical restriction to God's omnipotence.

MATTBALLMAN19:
But if you agree with me that "round triangles" and "married bachelors" aren't "things" then they do not participate in the rudimentary biblical definition of omnipotence that "with God all things are possible" for those aforementioned items are not "things" after all.

POWELL:
They may not be logical things, Matt, but they are things even if only written things. Everything is a thing. Although I have trouble imagining them, I can easily write them on the page. If Mark 10:27 should be taken literally rather than as hyperbole then God can create round triangles and married bachelors and those triangles would have three straight sides and those bachelors would not be married. You're assuming that the law of non-contradiction applies to God. Perhaps it doesn't.

MATTBALLMAN19:
So, no "progression" of definition of omnipotence with respect to logical possibility exists. But, alas, even if such definitions did evolve it does nothing to attack their truthfulness (after all, many "facts" about the world evolve such as our understanding of the universe, biology, archaeology, etc...). So, this is just a red herring.

(iv) Yes, inductive and statistical syllogisms are unsound. That's why they are assessed in terms of strength, not soundness.

(v) I'm not sure if you understood the issue of paradox, especially as I related it to praying if and only if one cannot pray -- a self-contradictory demand. But I certainly deny your premise 2 in that God's foreknowledge and revelation are the sufficient conditions of something coming about. The major error is in that you supplied "not possible" thereby invoking modal quantifiers. In effect, this makes God's foreknowledge the constraining cause of human action which I reject entirely.

POWELL:
I see. Others agree with you.

The debate with Jaltus on this issue is nearing its end.

MATTBALLMAN19:
And you haven't addressed my corrective argument either where God's foreknowledge is to be better understood as:

1. Either (P will do A and God knows A) or (P will do ~A and God knows ~A).
2. P will do A.
3. Therefore, God knows A.

or

2*. P will do ~A.
3*. Therefore, God knows ~A

and you can't find anything self-contradictory or absurd about this and it is perfectly consistent with God's foreknowledge and human freedom. In fact, given the definition of validity, this is necessarily true.

matt

POWELL:
I concede that someone can sometimes guess right about the future. What I'm interested in is whether there are scenarios where God will likely be wrong in His prediction, which should not be the case if God really knew the future. I believe I have come up with one. It's the 3-stage one I presented in the debate with Jaltus.

What I want to demonstrate is that God cannot know the future because if He did then it could not be other than what he foreknew, but then free will to choose other than what God foreknew would not be possible, but we appear to have free will to choose without that kind of restriction, so we should conclude that God cannot know the future.

Ok, Matt, what if entity G commanded you to do A, but told you that you will do ~A? Could you then choose to do A?

If the answer is "no" please explain.

If the answer is "yes" then replace "entity G" with "God" and please answer the same question.

If the answer is "no" with God in place of entity G then please tell me whether you believe we have free will.

If the answer is "yes" with God in place of entity G then please tell me whether you think God knows the future.

If neither Yes nor No with God in place of entity G then please explain.

John Powell

mattbballman19

March 27th 2003, 11:13 PM

John,
You wrote,
Let A = "theists" and B = "those who believe in God or gods" Could it then be true that "All A are B" and "All B are A" and "A=B" and "B=A"? As another example, consider A = "human males" and B = "humans with XY genotype."

The problem here is that you are no longer saying "All A are B" but "All A are A."

You next asked me, "I'm suggesting that every case of "if p then q" in language in general does not necessarily follow the logical rules of the horseshoe logical operator. Do you claim that they do?"

No, if one deviates from logical discourse. But this is to admit that one is longer interested in the modus ponens, a feature I am happy to admit.

You present,
"If my assumptions as to what is meant by a valid-only M.P. are wrong then please supply how you would word this in long English:
if p then q
p
therefore q
What does this series of statements mean in long English if the proponent is only claiming the argument is valid, not sound?"

My contention is still the same as from my first post. The first premise is a hypothetical statement that need not have anything to do with the world, but premise 2 and the conclusion are existential statements and do depend on the world. I'm not sure if I can make it much clearer, but remember that example of U.S.C.

Regarding omnipotence vs. free will,
"Possibly. If you're right then I would argue the Christians prior to the earliest Christian philosophers, those who lived during the days of Paul for example, likely held to a view that ignored logical impossibility. They probably believed there was no logical restriction to God's omnipotence."

They may have been ignorant of "logical impossibility" but the critic is still hard-pressed to explain what sort of "thing" a "round triangle" is outside of a linguistic combination. The burden isn't to show that omnipotence doesn't entail "all things logically possible" for the NT writers but to show that "to do all things" includes the logically impossible vis-a-vis the NT writers. And if the NT writers were ignorant of this concept, then all the more reason to assert the definition I've provided for there are no such things as logically impossible concepts. Again, the point is it makes no difference what the NT writers thought for the one thing the logical positivists were correct about was that logically incompatible statements strung together do not make a "thing" even if the individual concepts have meaning.

On the question of divine foreknowledge, you have capitalized this error I keep bringing out -- the modal fallacy. Perhaps you are unfamiliar with modality. Let me explain. There are two types of modal expressions of necessity in a conditional. A necessary conditional can be (i) necessary de dicto or (ii) necessary de re. The former is sometimes called the necessity of consequence and the latter the necessity of consequent. Here's how each might look in an example:

(i) Necessarily [if the man is sitting then he is not standing].

(ii) If the man is sitting, then necessarily [he is not standing].

The difference between (i) and (ii) is simple. In case (i) it only expresses the truth that when the man sits, he cannot also be standing. Case (ii) is different because is suggests that when the man is sitting down then not-standing becomes logically necessary for him which is false. So, consider:

1. Necessarily, if God knows X then X will occur.

2. If God knows X, then, necessarily, X will occur.

Statement (1) is true but (2) is false. The argument for the incompatibility of foreknowledge and human freedom depends on statement (2). But because (2) is false and (1) is true, and (1) does not display an inconsistency between foreknowledge and human freedom, then the argument against such compatibility is vacated. It commits the modal fallacy of confusing the consequent with the consequence. You see, it is logically possible for God to be wrong about His foreknowledge, but God's knowledge of counterfactuals makes it true that God simply will not ever be wrong about what He foreknows (note the difference between "can't be wrong" and "won't be wrong").

matt

John Powell

March 31st 2003, 09:13 PM

mattbballman19:

John,
You wrote,

POWELL:
Let A = "theists" and B = "those who believe in God or gods" Could it then be true that "All A are B" and "All B are A" and "A=B" and "B=A"? As another example, consider A = "human males" and B = "humans with XY genotype."

MATTBALLMAN19:
The problem here is that you are no longer saying "All A are B" but "All A are A."

POWELL:
I don't think so. A and B are defined as different linguistic symbols with possibly different meanings. One could argue, for example, whether theists and human males are defined in those ways. If one accepts that A = B then one is agreeing that those definitions are appropriate.

When we say that A = B, we are not saying that A and B are identically the same, but are equivalent in some important way. For example, to write 3 = 2+1 does NOT mean that the symbol "3" is the same as the symbol "2+1." What it means is that if you do the operation on the right side then the result of that operation will be identical with what you have on the left side so either side can be replaced in other equations and one will obtain the same result.

Mattballman19:
You next asked me,

POWELL:
I'm suggesting that every case of "if p then q" in language in general does not necessarily follow the logical rules of the horseshoe logical operator. Do you claim that they do?

Mattballman19:
No, if one deviates from logical discourse. But this is to admit that one is longer interested in the modus ponens, a feature I am happy to admit.

POWELL:
So, Matt are you claiming that modus ponens is defined by the horseshoe logical operator:

A) A C B

and M.P. is NOT necessarily defined as:

B) if p then q
p
therefore, q

Is that your position?

Mattballman19:
You present,

POWELL:
If my assumptions as to what is meant by a valid-only M.P. are wrong then please supply how you would word this in long English:

if p then q
p
therefore q

What does this series of statements mean in long English if the proponent is only claiming the argument is valid, not sound?

Mattballman19:
My contention is still the same as from my first post. The first premise is a hypothetical statement that need not have anything to do with the world, but premise 2 and the conclusion are existential statements and do depend on the world.

POWELL:
I don't think you're helping enough, Matt. The mathematical statement "A = B" in long English means something like "the variable A is numerically equal to the variable B."

I understand that the horseshoe logical symbol is defined by a truth table in which the two logical variables can be true or false, such that the logical result is true for all possible cases except where the precedent variable is true and the consequent variable is false. Furthermore, I understand that the series of statements below is believed by logicians, at least sometimes, to be convertible to the horseshoe logical operator. I'm arguing that maybe this can't always be done.

What, however, is the long English meaning of the following series of linguistic statements when claimed to be a merely valid, not sound, argument?

if p then q
p
therefore q.

Mattballman19:
I'm not sure if I can make it much clearer, but remember that example of U.S.C.

POWELL:
I seem to have forgot that one.

Mattballman19:
Regarding omnipotence vs. free will,

POWELL:
Possibly. If you're right then I would argue the Christians prior to the earliest Christian philosophers, those who lived during the days of Paul for example, likely held to a view that ignored logical impossibility. They probably believed there was no logical restriction to God's omnipotence.

Mattballman19:
They may have been ignorant of "logical impossibility" but the critic is still hard-pressed to explain what sort of "thing" a "round triangle" is outside of a linguistic combination.

POWELL:
I suspect they didn't feel qualified to tell God what He could or could not do.

It's quite simple, Matt, if you would just free yourself from the rule of non-Contradiction which is, after all, a man-made concept that may not apply to God. If God can be 1 God and three Gods at the time and can know the future that doesn't exist yet, why should this seem so surprising?

A "round triangle" is a three-sided object that has straight line segments that are round like a circle. Although I have serious trouble trying to imagine such a thing and am confident that I couldn't draw such a thing on a piece of paper, that might just be because of the wide epistemic gulf between God and me. God, perhaps could do it, but I don't know how.

This is the kind of theist response I get to questions like: "Since giving up free will for assured eternal life seems a better option for us, so why didn't God do it that way?" or "You agree with me that what happened to the Midianite children in Num 31 and the Amalekite children in 1 Sam 15 seems evil, so why didn't God come up with a better solution?"

Mattballman19:
The burden isn't to show that omnipotence doesn't entail "all things logically possible" for the NT writers but to show that "to do all things" includes the logically impossible vis-a-vis the NT writers.

POWELL:
"All things" should be interpreted to mean "absolutely all things," not "all things except for certain excluded things" unless there are good reasons to think that's what they meant, right? Perhaps this bold statement about God's power was typical religious exaggeration.

Mattballman19:
And if the NT writers were ignorant of this concept, then all the more reason to assert the definition I've provided for there are no such things as logically impossible concepts.

POWELL:
You are overly constraining the meaning of "thing." There are more things than just what exists in the physical universe or what logicians might agree is a thing. Perhaps you are referring to "logical things."

Mattballman19:
Again, the point is it makes no difference what the NT writers thought for the one thing the logical positivists were correct about was that logically incompatible statements strung together do not make a "thing" even if the individual concepts have meaning.

POWELL:
Again your "thing" should be called a "logical thing," I think.

Mattballman19:
On the question of divine foreknowledge, you have capitalized this error I keep bringing out -- the modal fallacy. Perhaps you are unfamiliar with modality. Let me explain.

POWELL:
Thank you. I have a pretty good mind, so I don't feel like I'm asking too much of philosophers to explain their terminology.

Mattballman19:
There are two types of modal expressions of necessity in a conditional. A necessary conditional can be (i) necessary de dicto or (ii) necessary de re. The former is sometimes called the necessity of consequence and the latter the necessity of consequent. Here's how each might look in an example:

(i) Necessarily [if the man is sitting then he is not standing].

(ii) If the man is sitting, then necessarily [he is not standing].

The difference between (i) and (ii) is simple. In case (i) it only expresses the truth that when the man sits, he cannot also be standing. Case (ii) is different because is suggests that when the man is sitting down then not-standing becomes logically necessary for him which is false. So, consider:

1. Necessarily, if God knows X then X will occur.

2. If God knows X, then, necessarily, X will occur.

Statement (1) is true but (2) is false. The argument for the incompatibility of foreknowledge and human freedom depends on statement (2). But because (2) is false and (1) is true, and (1) does not display an inconsistency between foreknowledge and human freedom, then the argument against such compatibility is vacated. It commits the modal fallacy of confusing the consequent with the consequence. You see, it is logically possible for God to be wrong about His foreknowledge, but God's knowledge of counterfactuals makes it true that God simply will not ever be wrong about what He foreknows (note the difference between "can't be wrong" and "won't be wrong").

matt

POWELL:
I just did some reading on this issue since it's new to me and I thought maybe it would be helpful. Someone mentioned something about this earlier, but didn't explain enough of it to persuade me to investigate it right away. You may have an important point. I may need to revise my free will syllogism.

Let me explain things. Please tell me if it looks like I understand.

Modal logic has to do with considerations like "possibly" and "necessarily." "De dicto" means with respect to the statement and "de re" means with respect to the thing.

Case 1:
The number of planets in the Solar System MUST be an odd number.

The de dicto interpretation of case 1 says that it must be true in all possible worlds that "the number of planets in the Solar System is an odd number." In other worlds, it could not have been true that there ended up 8 or 10 planets in our solar system. This is false.

The de re interpretation says that it is must be true that "the number of planets in our Solar System" namely "9" is an odd number in all possible worlds. In other words, 9 must be an odd number. This is true.

Case 2:
Bachelors MUST be single men.

The de dicto interpretation says that, by definition in all possible worlds, to be a bachelor a person must be a single man. This is true.

The de re interpretation is that each man who currently happens to be a bachelor could not have done things differently in another possible world to be married. This is false.

A modal equivocation occurs when the de dicto and de re interpretations are confused.

Is that correct?

Let me say something about part of what you said:

Mattballman19:
. . . it is logically possible for God to be wrong about His foreknowledge, . . .

POWELL:
That depends on your definition of God. If part of the definition of God is an entity who "cannot" be wrong, not just "won't" be wrong, then God cannot be wrong about His foreknowledge.

I suspect that the majority of Christians would answer the following question with "No."

"Can God be wrong, yes or no?"

John Powell

mattbballman19

April 4th 2003, 01:39 PM

John,

(i) I understand that sentences can be token reflexive, but that’s not the point of my contention. The only way “A is B” can validly translate to “B is A” is if A and B are identical. But the form of the argument as it stands is in no wise valid for I can think of a great deal of counterexamples. Instead, one would have to assume a premise that would make the argument tautological – something not already true about the modus ponens.

(ii) Modus ponens is defined by a three-step argument pattern: the conditional statement, affirming the antecedent, and then the consequent as the conclusion. And this isn’t just my opinion, this is first-year logic.

(iii) You keep asking me about the “long English version” of modus ponens, something I have done for several posts already. I cannot keep belaboring that without a response, so check the previous messages on that one.

(iv) That God’s omnipotence would include logically impossible “things” is more of a problem for you than me. You see, if God can bring about logically impossible events and human freedom is and divine foreknowledge are together a logically impossible event, then God can bring about human freedom and divine foreknowledge. So much for the logical contradiction argument after all! Moreover, you have a misunderstanding of the doctrine of the Trinity. But nevermind if God can do the logically impossible.

(v) The de dicto and de re difference entail the conditional statement “If p then q” where the modal qualifier “necessary” will either modify the whole sentence or just the consequent. To alter your examples to be consistent with this, you would have to say “It is necessary that (if the solar system has 9 planets then it will not have ~9 planets)” which differs from “If the solar system has 9 planets then it is necessary that (the solar system will not have ~9 planets)”. The second instance, which is necessity de re, is false. It is not the case that the solar system must have not have ~9 planets as if it were now true of all possible worlds, and I think you see that but just worded your example differently.

matt

John Powell

April 4th 2003, 04:15 PM

mattbballman19:
John,

(i) I understand that sentences can be token reflexive, but that’s not the point of my contention. The only way “A is B” can validly translate to “B is A” is if A and B are identical. But the form of the argument as it stands is in no wise valid for I can think of a great deal of counterexamples. Instead, one would have to assume a premise that would make the argument tautological – something not already true about the modus ponens.

POWELL:
Yes, I think, for "A is B" and "B is A" to both be true they must be equivalent in some important way, such as one being the definition of the other.

For example, let's assume that by definition, a husband is a married man.

As reflexive conditionals:
If J is a husband then J is a married man.
If J is a married man then J is a husband.

I'm not sure how to handle the truth table for definitions like this because it's not possible for the precedent to have a truth value different from the consequent. It's like trying to write up the truth table for "If A then A." The only possibilities are both false or both true.

Here is the example as reflexive categoricals

All husbands are married men.
All married men are husbands.

MATTBALLMAN19:
(ii) Modus ponens is defined by a three-step argument pattern: the conditional statement, affirming the antecedent, and then the consequent as the conclusion. And this isn’t just my opinion, this is first-year logic.

POWELL:
Yes, Matt, IF you are treating the argument as sound. In that case you are claiming that the conditional IS true and that the precedent IS true and, therefore, the consequent IS true.

However, if you are merely asserting that the argument is valid then you are NOT affirming the antecedent, but merely arguing that IF the conditional were true and IF the antecedent were true THEN the consequent would be true, could not be false.

Isn't this right? I'm still reading a first year logic text, but I think I understand this part of it.

MATTBALLMAN19:
(iii) You keep asking me about the “long English version” of modus ponens, something I have done for several posts already. I cannot keep belaboring that without a response, so check the previous messages on that one.

POWELL:
That reminds me of the French politician who denied being ambiguous about which army he wanted to win the war, but wouldn't directly answer the question, insisting that the journalists reread what he had said in his address.

Please post below the English translation in full sentence form the meaning of the following terms when claimed to represent a valid, but not sound, argument.

If p then q
p
therefore, q

I think a very long answer is the following:

If the conditional "if p then q" happened to be true and (or then) if the statement "p" happened to be true, then (or therefore) the statement "q" would have to be true, could not be false.

I think an acceptable shorter version is the following:

If "if p then q" is true then if "p" is true then "q" is true.

I think a very short version of this is the following:

If "if p then q" then if "p" then "q."

Now please give your answers, Matt.

MATTBALLMAN19:
(iv) That God’s omnipotence would include logically impossible “things” is more of a problem for you than me. You see, if God can bring about logically impossible events and human freedom is and divine foreknowledge are together a logically impossible event, then God can bring about human freedom and divine foreknowledge. So much for the logical contradiction argument after all!

POWELL:
Touche'.

MATTBALLMAN19:
Moreover, you have a misunderstanding of the doctrine of the Trinity. But nevermind if God can do the logically impossible.

POWELL:
I don't think I misunderstand the Trinity significantly compared with those who believe it and think they understand it. My statements might not match what is the canonical view on the Trinity or your view, but I think it's a view that might be justified by a certain kind of extreme fundamentalist and I think it follows the "spirit" of those who allow too much of God to remain a mystery rather than revising their concept of God to something that is less mysterious, more like what the Mormons have tried to do. This 1 God = 3 Gods version of the Trinity is taking the "God is a mystery" apologetics to a certain extreme.

MATTBALLMAN19:
(v) The de dicto and de re difference entail the conditional statement “If p then q” where the modal qualifier “necessary” will either modify the whole sentence or just the consequent. To alter your examples to be consistent with this, you would have to say “It is necessary that (if the solar system has 9 planets then it will not have ~9 planets)” which differs from “If the solar system has 9 planets then it is necessary that (the solar system will not have ~9 planets)”. The second instance, which is necessity de re, is false. It is not the case that the solar system must have not have ~9 planets as if it were now true of all possible worlds, and I think you see that but just worded your example differently.
matt

POWELL:
Thanks. I'm still working on these modal issues.

Currently, I'm of the opinion that when logicians claim that "if p then q" is true they are really referring to something like "if p then necessarily q" or "necessarily (if p then q)," but they have omitted that important fact for some reason. Surely they don't mean "if p then possibly q" or would that work?

Perhaps M.P. would be more honestly written as

if p then necessarily q
p
therefore, necessarily q

On the otherhand, perhaps it should be:

Necessarily (if p then q)
p
necessarily therefore, q

The short English translation for the first one, if claimed to be merely valid, would be

If "if p then necessarily q" then if "p" then necessarily "q."

This one may not pose a problem for my M.P. circularity argument, but the second version might:

If "necessarily (if p then q)" then if "p" then necessarily "q."

Maybe the "necessarily" in the first premise when placed before the conditional should be associated with the precedent in premise 2 rather than the consequent in the conclusion, or maybe with both premise 2 and conclusion or neither.

I need to think about this some more. Perhaps I can find more answers in the logic text if you can't show me what important thing I'm missing.

John Powell.

mattbballman19

April 5th 2003, 12:04 PM

G'day John!

(i) Reflexive conditionals and reflexive categoricals can certainly occur but if and only if the variables are as you write them. But examples abound as to changing the variables to different data making the reflexive statements wrong (i.e., the argument "If J is married then J is a husband; Therefore, if J is a husband then J is married" might be invalid because J might be married and yet be a woman). And validity depends on every possibility leading necessarily to its conclusion. Only when you make the antecedents and consequents (and subjects and predicates) reflexive does your example work, but this only shows that some conclusions are accidentally true. Validity requires that conclusions be necessarily true.

(ii) I haven't treated modus ponens as a sound construction. I have been very specific to deal with it as a set of neutral truth-value statements. But understand that determining validity always asks the question, "If a variable is true . . . " and "If a variable is false . . ." It seeks all combinations of truth-values.

(iii) And If the conditional "'if p then q' happened to be true and (or then) if the statement 'p' happened to be true, then (or therefore) the statement 'q' would have to be true, could not be false" is, again, just a false explanation. You are making premise 1 identical to premise 2 + conclusion and this is false. Premise 2 is not hypothetical. It is actually happening. And, consequently, so is the conclusion. But premise 1 does not rely on anything actually happening.

(iv) The doctrine of the Trinity has never been understood as 1 God = 3 Gods. The only sources that exist toward this misunderstood definition are in the critics of mainstream Christianity. The doctrine has always been understood as 3 persons within the one God. As far as its "mysterious" nature, Christians have well-understood from a logical standpoint that the doctrine could be rationally conceived (beginning with Augustine in the 300's). And when the doctrine is properly understood, it is rationally acceptable.

(v) If you are going to defeat my counter-contention that divine foreknowledge is logically consistent with human free will, you will have to dispel the positive argument I gave. To date, that hasn't been done. And as it stands, no good reasons have been offered in favor of a contradiction so long as the possibilities of subjunctive counterfactuals exist.

matt

John Powell

April 8th 2003, 08:30 PM

POWELL:
This first part is a response to an earlier comment of yours.

MATTBALLMAN19:
(ii) Modus ponens is defined by a three-step argument pattern: the conditional statement, affirming the antecedent, and then the consequent as the conclusion. And this isn’t just my opinion, this is first-year logic.

POWELL:
You are obscuring the difference between M.P. merely as a valid argument and when considered to be a sound argument, Matt.

Copi & Cohen Glossary / Index pg. 637:
Modus Ponens (M.P.): One of the nine elementary valid argument forms; a rule of inference according to which, if the truth of the hypothetical premise is assumed, and the truth of the antecedent of that premiss is also assumed, we may conclude that the consequent of that premiss is true.

POWELL:
Let me rewrite the relevant part with emphasis:

*IF* the truth of the hypothetical, "if p then q," is assumed, and *IF* the truth of the antecedent "p" is also assumed, *THEN* we may conclude that the consequent "q" is true.

In other words, Matt: If "if p then q" and if "p" then "q."

Do you have a logic text definition that disagrees with me on this issue?

MATTBALLMAN19:
G'day John!

(i) Reflexive conditionals and reflexive categoricals can certainly occur but if and only if the variables are as you write them. But examples abound as to changing the variables to different data making the reflexive statements wrong (i.e., the argument "If J is married then J is a husband; Therefore, if J is a husband then J is married" might be invalid because J might be married and yet be a woman).

POWELL:
If J is a woman then how can "if J is married then J is a husband" be true?

MATTBALLMAN19:
And validity depends on every possibility leading necessarily to its conclusion. Only when you make the antecedents and consequents (and subjects and predicates) reflexive does your example work, but this only shows that some conclusions are accidentally true.

POWELL:
Fine. The argument form

If A is B then B is A

is not valid for all possible natural translations of the word "is". However, it could be valid for certain translations of that term. Furthermore, the argument form

If A = B then B = A

is valid under certain definitions for the equality sign.

MATTBALLMAN19:
Validity requires that conclusions be necessarily true.

POWELL:
De dicto or de re?

Are you saying that M.P. is actually something more like

1) If p then q
2) p
3) therefore, necessarily q

What about modal problems?

How would you rewrite Modus Ponens to include explicitly the word "necessarily" everywhere it belongs?

MATTBALLMAN19:
(ii) I haven't treated modus ponens as a sound construction.

POWELL:
I think you have, Matt, but don't realize it. As soon as you remove the implicit "if" in front of the second premise and, instead, assert that "p" is true then you are claiming the premise is true. That's part of claiming an argument is sound. A valid argument doesn't care whether p is true or even if the conditional is true. It only cares that if p were true and if the conditional were true then q would have to be true.

The following is a VALID DEDUCTIVE ARGUMENT of the M.P. form even though you know at least one premise is false and the conclusion is false. It is not a sound argument because at least one premise is false.

4. If dogs fly then snakes sing opera
5. dogs fly
6. therefore, snakes sing opera.

The following is a VALID DEDUCTIVE ARGUMENT of the M.P. form even though you know that at least one premise is false, yet the conclusion is true. It is not a sound argument because at least one of the premises is false.

7. If dogs fly then snakes hiss
8. dogs fly
9. therefore, snakes hiss.

Well, Matt, how can these be valid deductive arguments when no rational person will affirm the antecedents in these two arguments to be true? Didn't you essentially claim that "affirming the antecedent" is one of the three necessary or essential steps to being Modus Ponens?

MATTBALLMAN19:
I have been very specific to deal with it as a set of neutral truth-value statements. But understand that determining validity always asks the question, "If a variable is true . . . " and "If a variable is false . . ." It seeks all combinations of truth-values.

POWELL:
That seems fine about truth tables.

I feel like you have carefully obscured the distinction between arguments claimed to be merely valid and those claimed to be sound, namely valid with true premises.

MATTBALLMAN19:
(iii) And If the conditional "'if p then q' happened to be true and (or then) if the statement 'p' happened to be true, then (or therefore) the statement 'q' would have to be true, could not be false" is, again, just a false explanation.

POWELL:
It sure looks close enough to what Copi and Cohen say above in their definition of M.P. Do you have another logic text with a definition that supports your claims and contradicts my own?

MATTBALLMAN19:
You are making premise 1 identical to premise 2 + conclusion and this is false.

POWELL:
Perhaps.

MATTBALLMAN19:
Premise 2 is not hypothetical. It is actually happening. And, consequently, so is the conclusion. But premise 1 does not rely on anything actually happening.

POWELL:
Again, Matt, that could be true if you were claiming the argument was sound.

Please post the definitions for valid, sound, and Modus Ponens from the logic text of your choice.

MATTBALLMAN19:
(iv) The doctrine of the Trinity has never been understood as 1 God = 3 Gods.

POWELL:
Ask any child first taught this idea. Is the Father God? Yes. Is the Son God? Yes. Is the Holy Spirit God? Yes. Are these three the same person? No. Then it is natural to assume that you are speaking of 3 Gods, not just one. It is by mentally forcing yourself as a child to deny this intuitive conclusion that they can reply to the question "How many Gods are there?" with "One" rather the more likely "three." Later, as the child believers mature, they might find logical reasons to think differently, to not doubt, and more readily accept it, but I suspect that children as a rule just repeat it without understanding. It's just one of those things adults know, but children don't understand.

MATTBALLMAN19:
The only sources that exist toward this misunderstood definition are in the critics of mainstream Christianity. The doctrine has always been understood as 3 persons within the one God. As far as its "mysterious" nature, Christians have well-understood from a logical standpoint that the doctrine could be rationally conceived (beginning with Augustine in the 300's).

POWELL:
What did theologians before Augustine think?

MATTBALLMAN19:
And when the doctrine is properly understood, it is rationally acceptable.

POWELL:
Perhaps, but I think with great difficulty.

MATTBALLMAN19:
(v) If you are going to defeat my counter-contention that divine foreknowledge is logically consistent with human free will, you will have to dispel the positive argument I gave. To date, that hasn't been done.

POWELL:
Which argument was that? Was it having to do with God being able to do the impossible, so God could have foreknowledge and man could have free will even if they were logically incompatible? That was an argument that my ficticious extreme fundamentalist might believe. I don't believe it.

If it wasn't that, please repost your argument.

MATTBALLMAN19:
And as it stands, no good reasons have been offered in favor of a contradiction so long as the possibilities of subjunctive counterfactuals exist.
matt

POWELL:
What are the subjunctive counterfactuals you are referring to, Matt?

Just because G could foretell A and J chooses to do A doesn't demonstrate that foreknowledge and free will are incompatible. Maybe G was just guessing and J decided to do what G said. What could demonstrate their incompatibility is if G foretells A because supposedly he knows the future, but J chooses to do B.

Here's my revised foreknowledge-free-will argument that tries to deal properly with the modal problem of possible worlds when using "necessary."

1. If, in possible world w, J has free will to choose A or B then in w it is NOT necessary that J chooses A {by definition of free will}
2. If, in possible world w, G knows that J will choose A then in w it IS necessary that J chooses A {by definition of knowing the future}
3. It is not the case that both (in w it is NOT necessary that J chooses A) AND (in w it IS necessary that J chooses A.) {by law of excluded middle}
4. Therefore, it is not the case that both (in possible world w, J has free will to choose A or B) AND (in possible world w, G knows that J will choose A) {by modus tollens-type conclusion}.

Is this argument persuasive that in the situation / world defined by w, foreknowledge and free will are incompatible?

John Powell

nomad

April 16th 2003, 11:29 AM

i've only skimmed, but maybe we are looking at this the wrong way.

or maybe i am seeing your point, and not seeing the proper consequences.

i think you are right... but i think this is sort of the point of modus ponens.

we have the premises:
P1: if p then q
P2: p
P3: therefore, q

which is a tautology. but that's what makes a valid argument!
take:

P1: if p then q
P2: r
P3: therefore, q

this is not a tautology, but neither is it a valid argument.
extending it works the same way.

it can make no statement about the conclusions, one way or another, because there are no values 'substituted in'.

you have pointed to the use of identities in math and science, i really don't think this is all that different.

i admit i am having trouble supporting this, so i'm throwing it out there for the time being.

as an example, this might not be that different from something like 'solving the quadratic' - we create an equality, and then plug the values in and see if they work. and we have ways of manipulating it such that we can discover easily which values work in the argument.

this seems on the surface, possibly a similar concept.

i will have to think about this some more so i can give a better defense.

John Powell

April 17th 2003, 01:58 PM

POWELL:
To NOMAD.

NOMAD:
i've only skimmed, but maybe we are looking at this the wrong way.

or maybe i am seeing your point, and not seeing the proper consequences.

i think you are right... but i think this is sort of the point of modus ponens.

we have the premises:
P1: if p then q
P2: p
P3: therefore, q

which is a tautology. but that's what makes a valid argument!

POWELL:
It sounds to me like you understand my point, but I haven't been calling them tautologies. Maybe I should.

NOMAD:
take:

P1: if p then q
P2: r
P3: therefore, q

this is not a tautology, but neither is it a valid argument. extending it works the same way.

it can make no statement about the conclusions, one way or another, because there are no values 'substituted in'.

you have pointed to the use of identities in math and science, i really don't think this is all that different.

POWELL:
Right.

NOMAD:
i admit i am having trouble supporting this, so i'm throwing it out there for the time being.

as an example, this might not be that different from something like 'solving the quadratic' - we create an equality, and then plug the values in and see if they work. and we have ways of manipulating it such that we can discover easily which values work in the argument.

this seems on the surface, possibly a similar concept.

POWELL:
Yes. Logicians make up a logical language distinct from a natural language (such as English) and then follow the rules of that language to decide if an inference in the logical language is justified. Whether that conclusion applies to the natural language is a separate question.

NOMAD:
i will have to think about this some more so i can give a better defense.

POWELL:
Defense of what? Of the utility of valid deductive arguments despite their circularity? I didn't mean to say they weren't useful just because they appear to be circular.

What is more persuasive than an argument in which you accept that the premise A is true and then you conclude that A must be true?

What I object to is obscuring the fact that M.P. when claimed to be merely valid, not sound, has this attribute.

John Powell

mattbballman19

April 17th 2003, 03:00 PM

John,

I appreciate your conversation with me and I always look forward to challenges to my own thoughts. Information is the name of the game for most of us, I'm sure you agree. I just believe I will end up looping my conversations which I don't want to do. My feeling is, much of what you are inquiring has already been addressed in previous posts notwithstanding some particular examples you bring to the forefront. So, I'm going to have to defer this conversation to our past exchanges on the matter. I do this, not out of spite or any idignation, but out of the interest of time. I just don't have too much leisure at this time to continue with such lengthy exchanges (but I wish I did).

I do not mean this as a closed door, only as a narrow hallway. Perhaps unique or specific issues can be exchanged in future correspondence.

With that, there is one unique matter you recently brought to light that I shall address here: the Trinity.

You write, "Ask any child first taught this idea. Is the Father God? Yes. Is the Son God? Yes. Is the Holy Spirit God? Yes. Are these three the same person? No. Then it is natural to assume that you are speaking of 3 Gods, not just one. It is by mentally forcing yourself as a child to deny this intuitive conclusion that they can reply to the question "How many Gods are there?" with "One" rather the more likely "three." Later, as the child believers mature, they might find logical reasons to think differently, to not doubt, and more readily accept it, but I suspect that children as a rule just repeat it without understanding. It's just one of those things adults know, but children don't understand."

--The grain of truth in this is that a child's mind will comprehend matters on a more superficial level than adults (to this I don't deny). But children will also picture Satan to look like men with gotees in red union suits running around with pitchforks in their hands. That's just the progressive nature of a child's learning curve. And remember when we thought what "being in love" was about when we were teenagers? Concepts may be skewed by superficial outlooks due to maturity levels, but that in no way indicts the concepts themselves. Still, and you should appreciate this as a logic student, many adults think that love is the logical opposite of hate. However, logically, love is the opposite of not-love, and not-love could be a state of lukewarmth or indifference. When the Trinity is understood properly, it is rationally unobjectionable. I don't see anything about "forcing" one's self to apprehend such concepts as a truth about theology or even relevant (e.g., So what if it's difficult? College calculus is difficult, too.).

matt

nomad

April 17th 2003, 03:04 PM

well, actually, the idea i was thinking of was more like a mathematical proof...i seem to remember that some concepts were proven by putting down a mathematical expression of equality, and then the 'proof' was basically substituting values and seeing if the equality holds up. this model would match what you've pointed out is modus ponens.

sometimes you substitute values and you get the tautology or the opposite of one; then you get a proof yes or no.
sometimes you substitute values and can't reduce it to anything, then you can't say anything meaningful the equation. but it's still written as an equality.

i don't have much formal philosophical background though, i hope it doesn't show too much :)

problem was, college was a long time ago, and i can't remember any concepts from math or engineering that were proven that way :) therefore the defer.

most things still require a modus ponens at some point.

however, i think i see more of what you are saying. let me try positing the difference between a 'sound' and 'valid' argument:

sound:
P1: i know that the statement 'if p then q' is true
P2: i know that the statement 'p' is true
C: i know that the statement 'q' is true

valid but unsound:

P1: i know that the statement 'if p then q' is true
P2: i don't know if the statement 'p' is true
C: i don't know anything about statement 'q'

what you are saying is that a valid but unsound argument doesn't say anything.

in the sound argument, clearly the conclusion differs from the postulates.

in the valid argument, you are right, it doesn't add any new information. but since it doesn't claim to say anything, does this invalidate modus ponens? does it really *mean* anything to discredit a merely valid modus ponens, which doesn't claim to offer any new truth anyways?

i propose it's more like an incompletely reduced equation.

John Powell

April 17th 2003, 05:34 PM

POWELL:
To MATTBALLMAN19

I've enjoyed the discussion too.

Your idea that the opposite of love is non-love is a useful way to think of opposites (everything that isn't in the class is out of the class), but it's not the only useful way of defining opposites nor the most common way opposites are used in the natural language. By that definition "liking" someone could be considered the opposite of "loving" them.

It's true that children often have mistaken ideas about the universe (e.g., evil men always wear black clothing and are afraid of the light, good men never wear black and welcome the light.) What you fail to appreciate sufficiently well, I think, is that even educated adults too often suffer the same problems.

To me the Christian God can be thought of as an adult version of Santa Claus. It's a more mature version of a child's make-believe friend. The attributes of God, like those of Santa Claus, have been adjusted to deal with the doubts.

If Santa Claus is real why can't we visit him right now? Because he lives at the north pole. How does Santa Claus read the letters and make gifts for all those kids? He is magical. He has an army of magical elves. How does he visit all those homes? He has magical flying reindeer.

If God is real why can't we visit Him right now? Because God dwells in the high mountains, err clouds, err beyond the stars, err in an alternative dimension. How does God listen to and answer all those prayers? He is magical. He is timeless. He has angels to help. How does God interact with distant parts of the universe simultaneously? God is omnipresent and timeless.

It looks to me like the attributes of God have changed as the criticisms have become more sophisticated. The modern concept of God has BECOME the answer to the criticisms.

Yahweh is no longer the bloodthirsty human-like war God of the ancient Jewish tribe, but is now the incomprehensible omniBeing of Greek Philosophy and modern physics.

John Powell

John Powell

April 17th 2003, 06:25 PM

POWELL:
To NOMAD

NOMAD:
well, actually, the idea i was thinking of was more like a mathematical proof...i seem to remember that some concepts were proven by putting down a mathematical expression of equality, and then the 'proof' was basically substituting values and seeing if the equality holds up. this model would match what you've pointed out is modus ponens.

POWELL:
Perhaps.

NOMAD:
sometimes you substitute values and you get the tautology or the opposite of one; then you get a proof yes or no. sometimes you substitute values and can't reduce it to anything, then you can't say anything meaningful the equation. but it's still written as an equality.

i don't have much formal philosophical background though, i hope it doesn't show too much :)

problem was, college was a long time ago, and i can't remember any concepts from math or engineering that were proven that way :) therefore the defer.

most things still require a modus ponens at some point.

however, i think i see more of what you are saying. let me try positing the difference between a 'sound' and 'valid' argument:

sound:
P1: i know that the statement 'if p then q' is true
P2: i know that the statement 'p' is true
C: i know that the statement 'q' is true

valid but unsound:

P1: i know that the statement 'if p then q' is true
P2: i don't know if the statement 'p' is true
C: i don't know anything about statement 'q'

POWELL:
I think it's more like the following:

Claimed to be Sound:

I claim that
P1: "if p then q" is true.
P2: and "p" is true
C3: and "q" is true.

Claimed to be Valid:

I claim that
P1': IF "if p then q" were true and
P2': IF "p" happened to be true
C3': THEN "q" would have to be true, could not be false.

For example, the following would be considered a valid deductive argument because it has the Modus Ponens form, but it is not sound because at least one of the premises is false.

1) If dogs bark then snakes sing opera.
2) dogs bark
3) therefore, snakes sing opera.

However, the features contradict what you said about valid deductive arguments. To be specific, the first premise is known to be false (contradicting your explanation) since the antecedent "dogs bark" is true, but the consequent "snakes sing opera" is false. Also, the second premise is known to be true (also contradicting what you said). Furthermore, the conclusion is known to be false (again contradicting you).

A conditional ("if p then q") is true according to symbolic logic for all combinations of truth values of the antecedent (p) and the consequent (q) except for the one in which p = true and q = false.

NOMAD:
what you are saying is that a valid but unsound argument doesn't say anything.

POWELL:
Absolutely not. I'm saying that M.P., when claimed to be merely valid, is saying the following:

If "if p then q" then if "p" then "q".

or in longer English,

If the conditional "if p then q" were true and (or then ) if "p" were true then "q" would have to be true, could not be false.

NOMAD:
in the sound argument, clearly the conclusion differs from the postulates.

in the valid argument, you are right, it doesn't add any new information. but since it doesn't claim to say anything, does this invalidate modus ponens? does it really *mean* anything to discredit a merely valid modus ponens, which doesn't claim to offer any new truth anyways?

POWELL:
I'm inclined to agree with the "spirit" of what I think you're saying, but not the wording. If the argument is not valid then it cannot be sound, so testing validity is an important element of testing whether a conclusion should be believed.

The merely valid argument is not claiming the premises are true. Nor is it claiming the conclusion is true. It's claiming that IF the premises were true then the conclusion would have to be true. The sound argument, on the other hand, claims that the argument is valid AND the premises are true, so the conclusion is true, cannot be false.

NOMAD:
i propose it's more like an incompletely reduced equation.

POWELL:
Perhaps. Those mathematical manipulations are analogous to tests of validity, not soundness.

I think claiming an argument is valid is more like claiming the Pythagorean relationship of the sides of a right triangle is a correct relationship between the lengths of those sides.

If you have a right triangle and if the longest side has length C and if one of the other sides has length A then the third side would have to have the length SQR ROOT ( C^2 - A^2).

A sound argument would be more like

This face of the block of wood is in the shape of a right triangle and the long side has the length 5 inches and one of the other sides has length 4 inches. Therefore, the length of the third side is SQR ROOT (5^2 - 4^2).

For an argument to go from valid to sound it would have to have real linguistic terms (not variable names) and you would go from saying "if true" to "is true."

John Powell

nomad

April 21st 2003, 10:12 AM

first, sorry for the long delay, got caught up in other stuff, and a couple times as i started posting, other questions leapt out and i didn't want to post until i had dealt with them (or forgotten them :), which unfortunately is about as likely.

POWELL:

(sound argument explanation snipped)

I claim that
P1': IF "if p then q" were true and
P2': IF "p" happened to be true
C3': THEN "q" would have to be true, could not be false.

i think we mostly agree. i wasn't being exhaustive with the 'valid not sound'' form; of course, either premise could be false, or both premises false, or even unknown (it could still be a valid argument if we do not know if a premise is true or false).

it is only sound when all premises are true, leading to my point that a 'valid' argument looks identical to a 'sound' argument, except for the absence of all-true truth values. i think you agreed with this somewhere, so i won't belabor the point.

1) If dogs bark then snakes sing opera.
2) dogs bark
3) therefore, snakes sing opera.

btw, i wasn't thinking of the method where MP is used 'backwards' - i.e. take a known conclusion, and test a premise to see if it gets you where you want to go. i was only thinking that if the premises aren't true, you can't know anything about the conclusions.

but.... this is the in the form

if 'if dogs bark, then snakes sing opera', then 'if dogs bark, then snakes sing opera', as you postulated. if i am using this form, it is again a valid but unsound argument, but it is also an equivalence, or tautology, whatever we are calling it.

if it weren't an equivalence, if there is ANY difference between the 'if' clause and the 'then' clause, then we no longer have a valid argument.

to change it into an assertive statement requires all premises to be true, and then the conclusion.

NOMAD:
what you are saying is that a valid but unsound argument doesn't say anything.
”

POWELL:
Absolutely not. I'm saying that M.P., when claimed to be merely valid, is saying the following:

If "if p then q" then if "p" then "q".

or in longer English,

If the conditional "if p then q" were true and (or then ) if "p" were true then "q" would have to be true, could not be false.

the original assertion was that MP reduces to if 'if p then q' then 'if p then q', or the eventual form a -> a. in my mind, this says 'nothing'.

if we can write it linguistically so that it DOES say 'something', then we will need to look at those linguistic transformations and hold them suspect...

perhaps there IS a difference between

if 'if p then q' AND if p THEN q
and
if 'if p then q' THEN 'if p then q'

POWELL:

I'm inclined to agree with the "spirit" of what I think you're saying, but not the wording. If the argument is not valid then it cannot be sound, so testing validity is an important element of testing whether a conclusion should be believed.

ok, maybe the wording needs to change.

i'm starting to get lost in this argument now :) so let's go back:

'valid-only modus ponens is [an] essentially circular [argument]'

the unsaid part of this was 'and therefore, MP is not what it's cracked up to be'.

my assertion is that the above is a DESCRIPTIVE statement... for which the contrapositive is 'if an argument is not essentially circular, it is not a valid modus ponens'.

and that therefore, the conclusion reached is unjustified.

POWELL:

Perhaps. Those mathematical manipulations are analogous to tests of validity, not soundness.

yes! THAT is what i am thinking.

I think claiming an argument is valid is more like claiming the Pythagorean relationship of the sides of a right triangle is a correct relationship between the lengths of those sides.

If you have a right triangle and if the longest side has length C and if one of the other sides has length A then the third side would have to have the length SQR ROOT ( C^2 - A^2).

A sound argument would be more like

This face of the block of wood is in the shape of a right triangle and the long side has the length 5 inches and one of the other sides has length 4 inches. Therefore, the length of the third side is SQR ROOT (5^2 - 4^2).

For an argument to go from valid to sound it would have to have real linguistic terms (not variable names) and you would go from saying "if true" to "is true."

right, that is more or less what i am thinking.

the example i was thinking of was slightly different, so i'll go ahead and post it now though (finally came up with one):

if we define a circle as 'a figure in 2D space where every point is equidistant from a central point', then we can use the difference formula to reduce this to

((x-x0)^2)/r^2 + ((y-y0)^2)/r^2 = 1

this is an equation. let's simplify it (and to avoid having to keep writing ^2, assume for this purpose the form 'x2' = 'x^2') to x2/r2 + y2/r2 = 1. and add the ellipse as x2/a2 + y2/b2 = 1, for purposes of the argument.

now, is x2/r2 + y2/r2 = 1 a circle?

no, it is NOT a circle... it is merely an equation that DESCRIBES one. you cannot draw a circle on a piece of paper, or virtually in a computer, that is exactly 'x2/r2 + y2/r2 = 1''. because a is still a THEORETICAL value; without a binding to a real physical value, this cannot be a physical circle.

is x2/9 + y2/9 = 1 a circle? yes. we would put this in MP as

P1: x2/r2 + y2/r2 = 1
P2: r = 3
C: x2/9 + y2/9 = 1

we can do the substitution and show an identity. therefore, it's a circle, and it is a REAL circle... ok, we have to add units :) but i can now draw this 3cm circle on a piece of paper. and it is a 1:1 relationship, this formula corresponds to exactly one circle.

what about x2/9 + y2/16 = 1?

P1: x2/r2 + y2/r2 = 1
P2: a = 3, b = 4, {r = 3 or r = 4}
C: x2/9 + y2/16 = 1

there are no valid mathematical substitutions, or transformations, which will get you from one to the other. in fact, in this case, because we end up via substitution with the statement x2/9 + y2/16 = x2/9 + y2/9 or x2/9 + y2/16 = x2/16 + y2/16. therefore, this is not a circle, it is in fact an ellipse. not only is it not a circle, but because this is not an equality, it can *never* be true that this is a circle, it is *definitively* not a circle.

what about x2/p2 + y2/q2 = 1?
P1: x2/r2 + y2/r2 = 1
P2: r = p or r = q
C: x2/p2 + y2/q2 = 1

now, whether we can prove this or not, it will not be a circle - there are no real values p and q, they are placeholders, for which we don't have real values. but we CAN determine if, when the values p and q are substituted, if we can say anything about whether it is a circle or not.

in this case, there are no valid substitutions or mathematical transformations which will get us to the conclusion. we cannot say whether this is a circle or not. however, we don't know ANYTHING about p or q, so we can't definitively make the case that it isn't a circle - after all, p could equal q. what we CAN say is we can create an equality that if we just plugged values into, we could tell you.

P1: x2/r2 + y2/r2 = 1
P2: p = q
P3: r = p or r = q
C: x2/p2 + y2/q2 = 1

now, we DO have valid mathematical transformations we can use to get from the premises to the conclusion.

the only information added was 'p = q', this is like going from a valid argument and saying 'p IS true' to a sound argument.

i think.

now, this is still all theoretical, and i haven't PROVEN this, but it seems reasonable.

John Powell

April 23rd 2003, 03:58 PM

NOMAD:
formulae

first, sorry for the long delay, got caught up in other stuff, and a couple times as i started posting, other questions leapt out and i didn't want to post until i had dealt with them (or forgotten them :), which unfortunately is about as likely.

POWELL:
He who is without sin cast the first stone. I'm guilty of this too.

POWELL:
(sound argument explanation snipped)

I claim that
P1': IF "if p then q" were true and
P2': IF "p" happened to be true
C3': THEN "q" would have to be true, could not be false.

NOMAD:
i think we mostly agree.

POWELL:
Excellent!:yipee:

NOMAD:
i wasn't being exhaustive with the 'valid not sound'' form; of course, either premise could be false, or both premises false, or even unknown (it could still be a valid argument if we do not know if a premise is true or false).

POWELL:
Right.

NOMAD:
it is only sound when all premises are true, leading to my point that a 'valid' argument looks identical to a 'sound' argument, except for the absence of all-true truth values. i think you agreed with this somewhere, so i won't belabor the point.

POWELL:
Right.

POWELL:
1) If dogs bark then snakes sing opera.
2) dogs bark
3) therefore, snakes sing opera.

NOMAD:
btw, i wasn't thinking of the method where MP is used 'backwards' - i.e. take a known conclusion, and test a premise to see if it gets you where you want to go. i was only thinking that if the premises aren't true, you can't know anything about the conclusions.

POWELL:
Right. YOu can't know if the conclusion is true or false if the premises are false.

NOMAD:
but.... this is the in the form

if 'if dogs bark, then snakes sing opera', then 'if dogs bark, then snakes sing opera', as you postulated. if i am using this form, it is again a valid but unsound argument, but it is also an equivalence, or tautology, whatever we are calling it.

POWELL:
Perhaps. I've avoided the term "tautology" but maybe it applies.

NOMAD:
if it weren't an equivalence, if there is ANY difference between the 'if' clause and the 'then' clause, then we no longer have a valid argument.

POWELL:
Good point.

NOMAD:
to change it into an assertive statement requires all premises to be true, and then the conclusion.

POWELL:
Perhaps you meant something more like "to change it into a statement that asserts that all the premises are true then you should believe that all the premises are true." Clearly, to assert that an argument is valid is an assertive statement.

NOMAD:
what you are saying is that a valid but unsound argument doesn't say anything.

POWELL:
Absolutely not. I'm saying that M.P., when claimed to be merely valid, is saying the following:

If "if p then q" then if "p" then "q".

or in longer English,

If the conditional "if p then q" were true and (or then ) if "p" were true then "q" would have to be true, could not be false.

NOMAD:
the original assertion was that MP reduces to if 'if p then q' then 'if p then q', or the eventual form a -> a. in my mind, this says 'nothing'.

POWELL:
I think I better understand what you meant, but I don't agree. A circular argument does say something. Like all valid arguments, it claims that if the premises are true then the conclusion must be true.

NOMAD:
if we can write it linguistically so that it DOES say 'something', then we will need to look at those linguistic transformations and hold them suspect...

perhaps there IS a difference between

if 'if p then q' AND if p THEN q
and
if 'if p then q' THEN 'if p then q'

POWELL:
Maybe

POWELL:
I'm inclined to agree with the "spirit" of what I think you're saying, but not the wording. If the argument is not valid then it cannot be sound, so testing validity is an important element of testing whether a conclusion should be believed.

NOMAD:
ok, maybe the wording needs to change.

i'm starting to get lost in this argument now :) so let's go back:

'valid-only modus ponens is [an] essentially circular [argument]'

the unsaid part of this was 'and therefore, MP is not what it's cracked up to be'.

my assertion is that the above is a DESCRIPTIVE statement... for which the contrapositive is 'if an argument is not essentially circular, it is not a valid modus ponens'.

and that therefore, the conclusion reached is unjustified.

POWELL:
Not quite true. A circular argument is probably the most persuasive argument if one accepts the premises to be true. If the premise "A" is true then how could you be unjustified in accepting that the conclusion "A" is true?

POWELL:
Perhaps. Those mathematical manipulations are analogous to tests of validity, not soundness.

NOMAD:
yes! THAT is what i am thinking.

POWELL:
I think claiming an argument is valid is more like claiming the Pythagorean relationship of the sides of a right triangle is a correct relationship between the lengths of those sides.

If you have a right triangle and if the longest side has length C and if one of the other sides has length A then the third side would have to have the length SQR ROOT ( C^2 - A^2).

A sound argument would be more like

This face of the block of wood is in the shape of a right triangle and the long side has the length 5 inches and one of the other sides has length 4 inches. Therefore, the length of the third side is SQR ROOT (5^2 - 4^2).

For an argument to go from valid to sound it would have to have real linguistic terms (not variable names) and you would go from saying "if true" to "is true."

NOMAD:
right, that is more or less what i am thinking.

the example i was thinking of was slightly different, so i'll go ahead and post it now though (finally came up with one):

if we define a circle as 'a figure in 2D space where every point is equidistant from a central point', then we can use the difference formula to reduce this to

((x-x0)^2)/r^2 + ((y-y0)^2)/r^2 = 1

this is an equation. let's simplify it (and to avoid having to keep writing ^2, assume for this purpose the form 'x2' = 'x^2') to x2/r2 + y2/r2 = 1. and add the ellipse as x2/a2 + y2/b2 = 1, for purposes of the argument.

now, is x2/r2 + y2/r2 = 1 a circle?

no, it is NOT a circle... it is merely an equation that DESCRIBES one. you cannot draw a circle on a piece of paper, or virtually in a computer, that is exactly 'x2/r2 + y2/r2 = 1''. because a is still a THEORETICAL value; without a binding to a real physical value, this cannot be a physical circle.

is x2/9 + y2/9 = 1 a circle? yes. we would put this in MP as

P1: x2/r2 + y2/r2 = 1
P2: r = 3
C: x2/9 + y2/9 = 1

POWELL:
The following would be what is claimed to be a valid argument:

If "x2/r2 + y2/r2 = 1" is true and if "r = 3" is true then "x2/9 + y2/9 = 1" would be true.

The following would be what is claimed to be a sound argument:

"x2/r2 + y2/r2 = 1" is true and "r = 3" is true, and so "x2/9 + y2/9 = 1" is true.

NOMAD:
we can do the substitution and show an identity. therefore, it's a circle, and it is a REAL circle... ok, we have to add units :) but i can now draw this 3cm circle on a piece of paper. and it is a 1:1 relationship, this formula corresponds to exactly one circle.

what about x2/9 + y2/16 = 1?

P1: x2/r2 + y2/r2 = 1
P2: a = 3, b = 4, {r = 3 or r = 4}
C: x2/9 + y2/16 = 1

there are no valid mathematical substitutions, or transformations, which will get you from one to the other. in fact, in this case, because we end up via substitution with the statement x2/9 + y2/16 = x2/9 + y2/9 or x2/9 + y2/16 = x2/16 + y2/16. therefore, this is not a circle, it is in fact an ellipse. not only is it not a circle, but because this is not an equality, it can *never* be true that this is a circle, it is *definitively* not a circle.

what about x2/p2 + y2/q2 = 1?
P1: x2/r2 + y2/r2 = 1
P2: r = p or r = q
C: x2/p2 + y2/q2 = 1

now, whether we can prove this or not, it will not be a circle - there are no real values p and q, they are placeholders, for which we don't have real values. but we CAN determine if, when the values p and q are substituted, if we can say anything about whether it is a circle or not.

POWELL:
Given the distinctions I'm trying to illuminate, I would revise this to say ". . . if, when the values of p and q are substituted, if we can say anything about whether it would be a circle or not."

NOMAD:
in this case, there are no valid substitutions or mathematical transformations which will get us to the conclusion. we cannot say whether this is a circle or not. however, we don't know ANYTHING about p or q, so we can't definitively make the case that it isn't a circle - after all, p could equal q. what we CAN say is we can create an equality that if we just plugged values into, we could tell you.

P1: x2/r2 + y2/r2 = 1
P2: p = q
P3: r = p or r = q
C: x2/p2 + y2/q2 = 1

now, we DO have valid mathematical transformations we can use to get from the premises to the conclusion.

the only information added was 'p = q', this is like going from a valid argument and saying 'p IS true' to a sound argument.

i think.

now, this is still all theoretical, and i haven't PROVEN this, but it seems reasonable.

POWELL:
Reasonable, yes. However it appears to be missing the crucial difference between validity and soundness. These mathematical manipulations are analogous to tests of validity, not soundness.

For example, do you claim that "p IS true" is a true statement? If you don't then you should not use it as a premise in a sound argument, only a valid one. "P" should be replaced with a linguistic term before it is considered to be true. It's ok to say "if p is true then. . ." But you shouldn't claim "p is true" unless you know what p is referring to.

John Powell

nomad

April 23rd 2003, 05:59 PM

i think i am just doing a bad job of presenting the idea :)

POWELL:

Given the distinctions I'm trying to illuminate, I would revise this to say ". . . if, when the values of p and q are substituted, if we can say anything about whether it would be a circle or not."

what i am really trying to illustrate is this: mathematics also has rules about form (which are related to validity) and then tests for equality etc. (which are related to soundness). i am trying to describe an idea that might be similar to an argument in mathematical terms. the problem is that i have imported some logical terminology into this, so instead of mathematics, i have remained in logic. it is difficult to not do so.

validity would cover this:

x^2 - 6x + 9
solve for x.

you say 'what?' and you should - this is not a valid equation. this is sort of equivalent to validity of an argument.

x^2 - 6x + 9 = 0
solve for x.

now, we don't know what x is, we don't even know yet if there is a valid value of x that will solve this equation. but, we can now approach the problem of determining if there is a value of x that will fulfill this equation. this is a valid but perhaps unsound argument.

math doesn't have true or false, it has numbers that plug into its variables:

x^2 - 6x + 9 = 0
x = 3

this is a valid and sound argument.

not that i am saying they ARE arguments at all. but, since both math and logic are 'artificial' languages with artificial rules that say something, so these are roughly (and perhaps only roughly) analogous.

and i am thinking of p and q as 'truth variables'.

POWELL:

Reasonable, yes. However it appears to be missing the crucial difference between validity and soundness. These mathematical manipulations are analogous to tests of validity, not soundness.

perhaps. maybe i'll finally express it correctly this time, and you can tell me :)

For example, do you claim that "p IS true" is a true statement? If you don't then you should not use it as a premise in a sound argument, only a valid one.

doesn't this lead to infinite regress?
the statement ''p is true' is true' is true etc.... at some point we have to call foul...

"P" should be replaced with a linguistic term before it is considered to be true. It's ok to say "if p is true then. . ." But you shouldn't claim "p is true" unless you know what p is referring to.

you can claim it is true :) but it may not have any application in the real world. it may have some application in theoretical study of logic itself though. calculus had to be shown to be mathematically consistent before it could be used for magnetic fields or plotting paths of heavenly bodies...

but you're right, for any useful application it has to map back into real linguistic statements... always problematic..

CriscoDisco

April 24th 2003, 01:53 PM

Does this joke represent your argument?

Comedy is a dead art form, but tragedy-- now that's funny.

Hiramjr

April 27th 2003, 11:32 AM

New subscriber here.

In briefly looking over your proposal about M.P., I think you may be confusing different subjects.

When someone asks, "What is M.P.?" the answer is that it is a valid argument form. That form can be symbolized like this:

p -> q
p
.: q

M.P. is not an argument. It is an argument form. It is a template for constructing arguments. If an argument is proposed such that it follows the pattern of M.P., then it is a valid argument. (Note that it is the argument that is valid. It isn't that M.P. is valid)

Suppose an argument was proposed that could be symbolized like this:

p -> q
~p
.: ~q

We could say that the argument is invalid because it constitutes an invalid argument form.

The form isn't an argument. M.P. is merely a guideline. That guideline indicates that when a hypothetical is presented and its antecedent is affirmed, then its consequent would be the case.

That guideline is neither valid nor sound. That guideline is either true or false. So when you say:

----
Modus Ponens merely valid, non-sound, form:
If "If p then q" then if "p" then "q".
----

I think you are confusing the argument form with an argument.

1. If p then q
2. p
3. Therefore q

The 'explanation' for why this is a valid argument 'form' is that it is true that if (1) were true (not that it 'is' true) and if (2) were true, then (3) would have to be the case. (Note that this explanation is a proposition. It is either true or false, not valid or sound.)

So, we don't have the following:

P1: If "if p then q" then if "p" then "q"

Instead we have:

P2: If (("if p then q") and "p"), then "q"
or
P2': If (1) and (2), then (3)

This isn't circular. It is merely a statement of fact.

To expand it and to contrast validity with soundness, we could say:

P2'': If ("if p then q") were true and if ("p") were true, then "q" would be true

P3: ("if p then q") is true and ("p") is true, therefore "q" is true

Both P2'' and P3 are propositions, where P2' is a statement that indicates what validity means and P3 is a statement that indicates what soundness means. Neither is circular.

1) If dogs bark then snakes sing opera.
2) dogs bark
3) therefore, snakes sing opera.

Here, this argument is valid because it follows the proper argument form. The argument isn't circular because nothing in the conclusion is stated in (1). (1) entails a hypothetical but (2) and (3) don't.

You see, this isn't saying, in terms of validity:

P4: If (if dogs bark then snakes sing opera) is true, then if (if dogs bark then snakes sing opera) is true

P4 is a tautology.

Instead, the argument is saying:

P5: If (if dogs bark then snakes sing opera) is true and if (dogs bark) is true, then (snakes sing opera) would be true

P5 isn't circular.

Eric Smallwood <><
eric@hiramjr.com
http://hiramjr.com
------
"How lovely is your dwelling place, O Lord Almighty!
My soul yearns, even faints, for the courts of the Lord;
my heart and my flesh cry out for the living God."
psalm 84
------

John Powell

April 27th 2003, 11:58 PM

CriscoDisco:[/i]

Does this joke represent your argument?

Comedy is a dead art form, but tragedy-- now that's funny.

POWELL:
I assume this question is in reference to the title of this thread.

I don't think so, but I may be missing how the irony applies.

I would take your statement to mean something like "modern art forms that try to be funny usually aren't, but those that try to be tragic often turn out to be funny."

I laugh at many horror movies.

I thought it was very funny, the scene where the "water intolerant" aliens of the recent Mel Gibson movie "Signs" were stealing the cake or something like that from a birthday party, given that there's water in the cake.

John Powell

John Powell

April 28th 2003, 02:55 AM

HIRAMJR:
New subscriber here.

POWELL:
WELCOME, Eric / HIRAMJR! Have a banana. :yipee:

HIRAMJR:
In briefly looking over your proposal about M.P., I think you may be confusing different subjects.

POWELL:
That's possible.

I thought I was posting arguments. Are you claiming that my "proposal" is false?

HIRAMJR:
When someone asks, "What is M.P.?" the answer is that it is a valid argument form.

POWELL:
Don't you mean "it is ONE OF SEVERAL valid argument FORMS"?

HIRAMJR:
That form can be symbolized like this:

p -> q
p
.: q

M.P. is not an argument. It is an argument form. It is a template for constructing arguments. If an argument is proposed such that it follows the pattern of M.P., then it is a valid argument. (Note that it is the argument that is valid. It isn't that M.P. is valid)

POWELL:
I think I understand your point, Eric. What I mean to say is that arguments in a natural language (like English) of the M.P. form are essentially circular.

However, you seem to be contradicting yourself. Could you please clarify?

HIRAMJR (Requoted, emphasis by Powell):
When someone asks, "What is M.P.?" the answer is that it is a valid argument form.

. . .

(Note that it is the argument that is valid. It isn't that M.P. is valid)

POWELL:
Is M.P. valid, Eric?

HIRAMJR:
Suppose an argument was proposed that could be symbolized like this:

p -> q
~p
.: ~q

We could say that the argument is invalid because it constitutes an invalid argument form.

POWELL:
That would be a mistake in certain cases, Eric, since just because an argument in the natural language follows an invalid argument form doesn't mean the original argument is invalid. It just means that arguments in that invalid form won't be certain to be valid. On the other hand, supposedly arguments in the natural language that follow a valid form will be reliably valid themselves.

For example, the following argument follows the invalid "denying the antecedent" form you mentioned, yet the argument is valid, right?

1) If J is a husband then J is a married man.
2) J is not a husband
3) Therefore, J is not a married man.

This argument is special because p is equivalent to q.

Or, maybe this isn't an argument at all, but only an argument form. Which is it, Eric? If I replace J with some generic male name like John, would it then be an argument rather than argument form?

HIRAMJR:
The form isn't an argument. M.P. is merely a guideline.

POWELL:
I think I understand what you're trying to say. You're right about M.P. being a guideline or a template, since p and q are linguistic variables. My argument about circularity applies to arguments of the M.P. form. Just replace p and q with linguistically meaningful terms.

HIRAMJR:
That guideline indicates that when a hypothetical is presented and its antecedent is affirmed, then its consequent would be the case.

POWELL:
Right. IF the hypothetical is affirmed THEN (or "and") IF the antecedent is affirmed THEN the consequent would be the case.

HIRAMJR:
That guideline is neither valid nor sound. That guideline is either true or false.

POWELL:
Whoa, Eric. Please respond to the following proposition with "true," "false," or "other" (and explain):

Q. Modus Ponens is not a valid argument form, but rather it's a true proposition.

HIRAMJR:
So when you say:

----
Modus Ponens merely valid, non-sound, form:
If "If p then q" then if "p" then "q".
----

I think you are confusing the argument form with an argument.

1. If p then q
2. p
3. Therefore q

POWELL:
I explained why I do not initially use the syllogistic form, Eric. It's because the syllogistic form does not indicate whether the argument is claimed to be valid or sound. I use the M.P. argument form and the linguistic variables "p" and "q" in my arguments so that my conclusions apply generally.

HIRAMJR:
The 'explanation' for why this is a valid argument 'form' is that it is true that if (1) were true (not that it 'is' true) and if (2) were true, then (3) would have to be the case. (Note that this explanation is a proposition. It is either true or false, not valid or sound.)

POWELL:
I think arguments of the M.P. form are seen to be correct because of the circularity.

HIRAMJR:
So, we don't have the following:

P1: If "if p then q" then if "p" then "q"

Instead we have:

P2: If (("if p then q") and "p"), then "q"
or
P2': If (1) and (2), then (3)

POWELL:
Your P2 and P2' are possible ways of looking at M.P., but they hide the circularity I'm trying to expose. I believe you are mistaken in denying my P1 as one of the correct ways to translate M.P. into long English. You are grouping the terms in one possible way, I, in another. The location of the parentheses is not obvious linguistically.

For example, is the answer to the following mathematical equation 25 or 30?

x = 3 + 2 * 5?

The answer is ambiguous until you decide a rule for grouping terms (multiplication first, for example).

HIRAMJR:
This isn't circular. It is merely a statement of fact.

POWELL:
I think it still is. You could also translate M.P. as the following:

IF it were true that "if p then q", THEN IF "p" were also true THEN "q" would have to also be true.

The words "and" and "also" can be used to merely indicate that there are additional elements to the argument. This additive term might be dropped if the meaning is clear without it. I think "then" can be used instead of "and" before the second premise.

Is it your position, Eric, that arguments of the M.P. form are NOT essentially circular because "then" cannot justifiably be used instead of "and" immediately prior to the "p" premise?

HIRAMJR:
To expand it and to contrast validity with soundness, we could say:

P2'': If ("if p then q") were true and if ("p") were true, then "q" would be true

P3: ("if p then q") is true and ("p") is true, therefore "q" is true

Both P2'' and P3 are propositions, where P2' is a statement that indicates what validity means and P3 is a statement that indicates what soundness means. Neither is circular.

1) If dogs bark then snakes sing opera.
2) dogs bark
3) therefore, snakes sing opera.

Here, this argument is valid because it follows the proper argument form. The argument isn't circular because nothing in the conclusion is stated in (1). (1) entails a hypothetical but (2) and (3) don't.

You see, this isn't saying, in terms of validity:

P4: If (if dogs bark then snakes sing opera) is true, then if (if dogs bark then snakes sing opera) is true

POWELL:
I think it is in a way, Eric, but I'm not persuading you to see it.

POWELL:
P4 is a tautology.

Instead, the argument is saying:

P5: If (if dogs bark then snakes sing opera) is true and if (dogs bark) is true, then (snakes sing opera) would be true

P5 isn't circular.

POWELL:
I think the argument is also saying

P5': IF (if dogs bark then snakes sing opera) is true THEN IF (dogs bark) THEN (snakes sing opera) would be true.

Eric Smallwood <><
eric@hiramjr.com
http://hiramjr.com
------
"How lovely is your dwelling place, O Lord Almighty!
My soul yearns, even faints, for the courts of the Lord;
my heart and my flesh cry out for the living God."
psalm 84

POWELL:
Cheers.

John Powell

Woman

April 28th 2003, 04:43 AM

John,

I've been tied in a knot reading through this thread.:huh: Enjoying it very much though!

I have a question. If you think that MP (which affirms by affirming) is circular do you also think that Modus Tollens (which denies by denying) is also circular?

MP

1. If it is bright and sunny today, then I will wear my sunglasses.

2. It is bright and sunny today.

3. Therefore, I will wear my sunglasses.

MT

1. If it is bright and sunny today, then I will wear my sunglasses.

2. I will not wear my sunglasses.

3. Therefore, it is not bright and sunny today.

And would it look like this?

1. If MP is o, then MT is o

2. MP is o

3. Therefore MT is o

:rofl:

Socrates

April 28th 2003, 08:27 AM

:thumb: Very clever, Woman :yipee:

nomad

April 28th 2003, 09:17 AM

if MP is like 2=2, MT is like 2=3.

at least, that's what i've gotten out of these discussions.

P4: If (if dogs bark then snakes sing opera) is true, then if (if dogs bark then snakes sing opera) is true

P5: If (if dogs bark then snakes sing opera) is true and if (dogs bark) is true, then (snakes sing opera) would be true

well, in a way, the first statement actually has implicit truth qualifiers as well: IF (dogs bark) = TRUE, THEN (snakes sing opera) = TRUE would be an equivalent way to write the first statement in your MP. and if you write it that way, then it is more clear what John was trying to get at.

note that after some discussion, and looking at parallels in other theoretical disciplines, it makes perfect sense - no one would argue that equalities are useless in mathematics, merely because they are equalities. i really don't think the argument is that an argument IS an equality, but that it can REDUCE to an equality.

to solve x^2 - 2x + 1 = 0, you write it as an equality and then you solve. you will find that x = 1 is not a separate statement, but is a direct result of applying mathematical properties to the original equation:

x^2 - 2x + 1 = 0
through factoring we find this equal to
(x - 1)(x - 1) = 0

divide both sides by (x - 1) we get
x - 1 = 0

add 1 to each side

x = 1

now, let's talk about what this *really* means. what this really means is that 'some unknown value X is equal to 1'. to put this in parallel: 'if pigs oink, then cows moo'. this is equivalent to 'x = y' - it's an equality, but you can make no statements about whether it is true or not. and remember, equality, really, is not an *assignment* or anything, it is a *test*, and it is either true or false (the = in math is closer to the == in C++ than the =).

there is only one value of X that will make this a true statement; that value is 1. if we say 'x is 1', then we substitute and get the statement

1 = 1

this is a tautology. so, if x is 1, then x = 1 is true. this is the 'behind-the-scenes' logic for x = 1. that's sort of what we are talking about here, the 'behind-the-curtain' logic for MP.

in the same way, if we have the above statement, and say 'if pigs oink = TRUE, then cows moo = X', there is only one value of X that will make the equation 'work', and that value is true.

or, imagine trying to 'prove' factoring - how do you do it? you put the sides equal, and then do the math to show that they reduce to a tautology:

(x - 1)(x - 1) = x^2 - 2x + 1

x(x-1) - 1(x-1) = x^2 - 2x + 1

x^2 - x - x + 1 = x^2 - 2x + 1
x^2 - 2x + 1 = x^2 - 2x + 1

we usually stop here, but for absolute proof we don't have to:
subtract x^2 from both sides

-2x + 1 = -2x + 1

add 2x to both sides

1 = 1

we end up with tautology. the two sides are *absolutely* equal.

that just proves *this* factoring. but if you replace the numbers in the above with variables, you get the proof, and you end up with something like a = a, which is also always true.

this doesn't make it any less useful; as any college algebra student knows, this is a VERY useful substitution :)

Hiramjr

April 28th 2003, 01:58 PM

Powell:
I thought I was posting arguments. Are you claiming that my "proposal" is false?

ES
Your proposal was a proposition about M.P., while your arguments were presented to support your proposal. I believe your proposal is false.

H:
When someone asks, "What is M.P.?" the answer is that it is a valid argument form.

Powell:
Don't you mean "it is ONE OF SEVERAL valid argument FORMS"?

ES
It means the same thing. If we have a barrel full of apples and I point to one and say, "This is an apple," my statement is not, "This is the only apple." Similarly, my statement above is that M.P. is 'a' valid argument form, not the only valid argument form.

H:
That form can be symbolized like this:

p -> q
p
.: q

M.P. is not an argument. It is an argument form. It is a template for constructing arguments. If an argument is proposed such that it follows the pattern of M.P., then it is a valid argument. (Note that it is the argument that is valid. It isn't that M.P. is valid)

Powell:
I think I understand your point, Eric. What I mean to say is that arguments in a natural language (like English) of the M.P. form are essentially circular.

However, you seem to be contradicting yourself. Could you please clarify?

ES
I don't quite understand your question. How exactly is my comment contradictory?

An analogy. A month or so ago my daughter had to write a term paper for class. Her teacher instructed the class to follow a particular format for their papers. The format indicated where to put the title, where to put footnotes, where to put the bibliography and how to arrange the paragraphs. The format was a template. The format was not a term paper.

If my daughter follows the format and turns in her paper, then she has turned in a proper ("valid") term paper. This says nothing about the content of her paper, rather this indicates that she has followed the rules for a proper format.

M.P. can be viewed in a similar fashion. When a person constructs an argument according to the rules of formal logic, then the person has constructed a proper ("valid") argument. M.P. is a rule, it is a proper format for arguments, not an argument itself.

H (Requoted, emphasis by Powell):
When someone asks, "What is M.P.?" the answer is that it is a valid argument form...
(Note that it is the argument that is valid. It isn't that M.P. is valid)

Powell:
Is M.P. valid, Eric?

ES
It is neither valid nor invalid. It is a form for arguments.

H:
Suppose an argument was proposed that could be symbolized like this:

p -> q
~p
.: ~q

We could say that the argument is invalid because it constitutes an invalid argument form.

Powell:
That would be a mistake in certain cases, Eric, since just because an argument in the natural language follows an invalid argument form doesn't mean the original argument is invalid. It just means that arguments in that invalid form won't be certain to be valid. On the other hand, supposedly arguments in the natural language that follow a valid form will be reliably valid themselves.

For example, the following argument follows the invalid "denying the antecedent" form you mentioned, yet the argument is valid, right?

1) If J is a husband then J is a married man.
2) J is not a husband
3) Therefore, J is not a married man.

This argument is special because p is equivalent to q.

Or, maybe this isn't an argument at all, but only an argument form. Which is it, Eric? If I replace J with some generic male name like John, would it then be an argument rather than argument form?

ES
If an argument does not follow a valid argument form, then the argument is not valid.

In your example we have:

p: J is a husband
q: J is a married man

p -> q
~p
.: ~q

This is an argument and it is invalid. Determining validity has nothing to do with whether any premise or a conclusion is true. It doesn't matter that p 'means' the same thing as q. What matters is if the propositions are correctly ordered, if they follow the proper format for validity.

1) If J is a husband then J is a married man.
2') J is not a married man
3') Therefore, J is not a husband.

This is an argument and it is valid.

H:
The form isn't an argument. M.P. is merely a guideline.

Powell:
I think I understand what you're trying to say. You're right about M.P. being a guideline or a template, since p and q are linguistic variables. My argument about circularity applies to arguments of the M.P. form. Just replace p and q with linguistically meaningful terms.

ES
Yes, we can do this, however the arguments aren't circular.

The argument you posed above isn't circular.

The first premise is a hypothetical. It doesn't state whether J is or is not married. It doesn't make a positive statement about J's marital status. The second premise is a positive statement about J's marital status. The conclusion is a positive statement about J's marital status.

Those are three different subjects. We don't infer the conclusion from the second premise. We infer the conclusion from both the first and second premises. That is M.P. by definition.

In order for the argument to be circular the conclusion would have to say the same thing as is found in one of its premises. It doesn't. The conclusion isn't found in either the first or the second premise. It is inferred from both.

This is an important point. If you claim that an argument is circular, then you have to show where its conclusion is found in its premises. In basic M.P. formulation, the conclusion is not found in its premises. This means that your formulation of M.P. is mistaken. See below.

H:
That guideline indicates that when a hypothetical is presented and its antecedent is affirmed, then its consequent would be the case.

Powell:
Right. IF the hypothetical is affirmed THEN (or "and") IF the antecedent is affirmed THEN the consequent would be the case.

ES
I think you're confusing yourself with the language here. It's not "IF, THEN, THEN." It's IF, THEN.

This is vitally important because of your claim of circularity. Because you claim that an M.P. argument is circular 'according to your formulation above', then your formulation must have a conclusion that is found in its premise.

This means that what is found after the THEN must be found before it. You have two THEN's in your formulation. The THEN indicates an inference, it means 'therefore' some conclusion the case.

We have:

P1: The hypothetical is affirmed

Now, what are you inferring from this? Given P1, therefore what is the case? You can't infer from P1 that the antecedent 'is' true. You instead would be inferring:

C1: IF the antecedent is affirmed THEN the consequent would be the case.

You then claim circularity because C1 looks like what is found in P1. The problem however is that you are inferring a hypothetical from a hypothetical. That isn't what M.P. is about.

M.P. form is:

p -> q
p
.: q

Note that the THEN, i.e. the ‘therefore’ precedes q. Your formulation is something like:

(p -> q)
.: (p) -> (q)

(which would allow the inclusion of M.T.
(p -> q)
.: (p) -> (q) and (~q) -> (~p))

M.P. is inferring a proposition, while you are inferring a hypothetical. Again, it is because of your charge of circularity that it must be the case that you conclude with a hypothetical after the THEN. But that isn't what M.P. is about.

With M.P., there is nothing in the hypothetical, (p -> q), that entails THEN something would be the case. It is simply a proposition that is either true or false. When we 'add' an additional proposition, (p), it is THEN that something would be the case. This is why it is (p -> q) 'and' (p) that produces q.

Validity here addresses the subject of proper inference. When I say, "something would be the case," this means that we can properly infer that it is the case. We aren't somehow causing something to be the case. The conclusion (q) is properly inferred from both (p -> q) and (p). That is what a valid M.P. argument means.

The test for validity entails the situation where it would be impossible for the premises to be true and the conclusion false. This means that we take the premises as a unit.

I understand what you are thinking:

If (p -> q), then if (p) -> (q)

This makes it look like if a hypothetical is affirmed, then the same hypothetical is inferred.

The problem however is that this entails making an inference from the hypothetical, but M.P. is not about making an inference from the hypothetical. It is about making an inference from the hypothetical 'and' its antecedent, both premises as a unit. The THEN comes after the two are affirmed. Thus, what you are thinking actually doesn't properly reflect M.P.

1) If J is a husband then J is a married man.
2) J is a husband
3) Therefore, J is a married man.

Let's write this out:

P1: If it were true that if J is a husband then he is a married man and if it were the case that J was a husband, then it could properly be inferred that J is a married man.

P2: If it were true that if J is a husband then he is a married man, then it could be properly inferred that if it were the case that J was a husband, then it could properly be inferred that J is a married man.

Do you see the difference between P1 and P2? The conclusion of P1 is a proposition, while the conclusion of P2 is another hypothetical. P1 and P2 are two completely different arguments. P1’s conclusion is found nowhere in its premises.

H:
That guideline is neither valid nor sound. That guideline is either true or false.

Powell:
Whoa, Eric. Please respond to the following proposition with "true," "false," or "other" (and explain):

Q. Modus Ponens is not a valid argument form, but rather it's a true proposition.

ES
It is false. M.P. is a valid argument form. It is not however a valid argument (just as the format of a term paper is not a term paper). It instead entails a proposition that if (p -> q) and (p) are affirmed, then (q) would be the case, or it is impossible for (p -> q) and (p) to be the case and (q) false, which defines M.P. validity.

H:
So when you say:

----
Modus Ponens merely valid, non-sound, form:
If "If p then q" then if "p" then "q".
----

I think you are confusing the argument form with an argument.

1. If p then q
2. p
3. Therefore q

Powell:
I explained why I do not initially use the syllogistic form, Eric. It's because the syllogistic form does not indicate whether the argument is claimed to be valid or sound. I use the M.P. argument form and the linguistic variables "p" and "q" in my arguments so that my conclusions apply generally.

ES
I don't understand what you mean here. Whether an argument is "claimed" to be valid or sound is immaterial to the fact of whether it is valid or sound.

I don't see how you can both "use the M.P. argument form" and "not initially use the syllogistic form."

H:
The 'explanation' for why this is a valid argument 'form' is that it is true that if (1) were true (not that it 'is' true) and if (2) were true, then (3) would have to be the case. (Note that this explanation is a proposition. It is either true or false, not valid or sound.)

Powell:
I think arguments of the M.P. form are seen to be correct because of the circularity.

ES
I realize that this is your position. I simply disagree because I find nothing in M.P. form that indicates circularity.

H:
So, we don't have the following:

P1: If "if p then q" then if "p" then "q"

Instead we have:

P2: If (("if p then q") and "p"), then "q"
or
P2': If (1) and (2), then (3)

Powell:
Your P2 and P2' are possible ways of looking at M.P., but they hide the circularity I'm trying to expose. I believe you are mistaken in denying my P1 as one of the correct ways to translate M.P. into long English. You are grouping the terms in one possible way, I, in another. The location of the parentheses is not obvious linguistically.

ES
If how I have "grouped" things entails no circularity, then you've lost any objective ground for claiming that arguments the following the M.P. form are circular. All you can really say is that if anyone "groups" things your way then you can claim circularity. See above.

Powell:
For example, is the answer to the following mathematical equation 25 or 30?

x = 3 + 2 * 5?

The answer is ambiguous until you decide a rule for grouping terms (multiplication first, for example).

ES
M.P. itself is a "rule for grouping terms."

H:
This isn't circular. It is merely a statement of fact.

Powell:
I think it still is. You could also translate M.P. as the following:

IF it were true that "if p then q", THEN IF "p" were also true THEN "q" would have to also be true.

ES
Yes, you are inferring a hypothetical from a hypothetical. That isn't what M.P. does.

Powell:
The words "and" and "also" can be used to merely indicate that there are additional elements to the argument. This additive term might be dropped if the meaning is clear without it. I think "then" can be used instead of "and" before the second premise.

Is it your position, Eric, that arguments of the M.P. form are NOT essentially circular because "then" cannot justifiably be used instead of "and" immediately prior to the "p" premise?

ES
That is correct. In your translation above, where is your conclusion, that is, where are you making your concluding inference? Which THEN is the inference?

(p -> q)
.: p -> q
or
(p -> q) -> p
.: q

Neither one of these formulations properly reflects M.P.

H:
To expand it and to contrast validity with soundness, we could say:

P2'': If ("if p then q") were true and if ("p") were true, then "q" would be true

P3: ("if p then q") is true and ("p") is true, therefore "q" is true

Both P2'' and P3 are propositions, where P2' is a statement that indicates what validity means and P3 is a statement that indicates what soundness means. Neither is circular.

1) If dogs bark then snakes sing opera.
2) dogs bark
3) therefore, snakes sing opera.

Here, this argument is valid because it follows the proper argument form. The argument isn't circular because nothing in the conclusion is stated in (1). (1) entails a hypothetical but (2) and (3) don't.

You see, this isn't saying, in terms of validity:

P4: If (if dogs bark then snakes sing opera) is true, then if (if dogs bark then snakes sing opera) is true

Powell:
I think it is in a way, Eric, but I'm not persuading you to see it.

ES
Not by what you have offered thus far. You're asking me either to redefine what M.P. means or to redefine what circularity means.

John Powell

April 28th 2003, 06:40 PM

POWELL:
To NOMAD.

I hope I didn't offend you for skipping this, Nomad. I felt I should respond first to the new people.

NOMAD:
i think i am just doing a bad job of presenting the idea :)

POWELL:
I think you're doing fine. I've been thinking about what you've written, and have revised somewhat my view on this analogy between math and logic.

POWELL:
Given the distinctions I'm trying to illuminate, I would revise this to say ". . . if, when the values of p and q are substituted, if we can say anything about whether it would be a circle or not."

NOMAD:
what i am really trying to illustrate is this: mathematics also has rules about form (which are related to validity) and then tests for equality etc. (which are related to soundness). i am trying to describe an idea that might be similar to an argument in mathematical terms. the problem is that i have imported some logical terminology into this, so instead of mathematics, i have remained in logic. it is difficult to not do so.

validity would cover this:

x^2 - 6x + 9
solve for x.

you say 'what?' and you should - this is not a valid equation. this is sort of equivalent to validity of an argument.

x^2 - 6x + 9 = 0
solve for x.

now, we don't know what x is, we don't even know yet if there is a valid value of x that will solve this equation. but, we can now approach the problem of determining if there is a value of x that will fulfill this equation. this is a valid but perhaps unsound argument.

math doesn't have true or false, it has numbers that plug into its variables:

POWELL:
Math certainly does have true and false. Usually, true =1 and false = 0. For example,

True or False: a^2 + b^2 = c^2 where a and b are the two shorter sides of a right triangle and c is the hypotenuse?

Remember that math is merely a very powerful symbolic form of language. Every math equation can be expanded into linguistic terms.

NOMAD:
x^2 - 6x + 9 = 0
x = 3

this is a valid and sound argument.

POWELL:
The following would be a valid argument:

If "x^2 - 6x + 9" were to equal zero
and if x were a real number
then x would equal 3

This is what is done in math class when learning how to solve math problems. Likewise, logicians tend to study validity rather than soundness.

The following would be a sound argument:

"x^2 - 6x + 9" does equal zero
where x is a real number
Therefore, x = 3.

This is what happens when an engineer / scientist solves a real life problem.

NOMAD:
not that i am saying they ARE arguments at all. but, since both math and logic are 'artificial' languages with artificial rules that say something, so these are roughly (and perhaps only roughly) analogous.

and i am thinking of p and q as 'truth variables'.

POWELL:
Good points, but I think the analogy isn't working in the way that I previously thought it might, but validity is more like learning the rules of math and soundness is more like applying them to real life problems.

POWELL:
Reasonable, yes. However it appears to be missing the crucial difference between validity and soundness. These mathematical manipulations are analogous to tests of validity, not soundness.

NOMAD:
perhaps. maybe i'll finally express it correctly this time, and you can tell me :)

POWELL:
I hope my distinction given above for the x=3 problem helps to clarify how I'm thinking about this.

POWELL
For example, do you claim that "p IS true" is a true statement? If you don't then you should not use it as a premise in a sound argument, only a valid one.

NOMAD:
doesn't this lead to infinite regress?

the statement ''p is true' is true' is true etc.... at some point we have to call foul...

POWELL:
Good point. Is the following proposition true or false?

P

If you won't say "true" then you should not use it in sound argument.

POWELL:
"P" should be replaced with a linguistic term before it is considered to be true. It's ok to say "if p is true then. . ." But you shouldn't claim "p is true" unless you know what p is referring to.

NOMAD:
you can claim it is true :) but it may not have any application in the real world. it may have some application in theoretical study of logic itself though.

POWELL:
Wait a minute, Nomad. In that case you would be saying "If P" or "Assuming P." That's in the regime of validity again. Until you will affirm "P" it should not be part of a sound argument. You cannot justifiably affirm P until you know what P corresponds to.

NOMAD:
calculus had to be shown to be mathematically consistent before it could be used for magnetic fields or plotting paths of heavenly bodies...

but you're right, for any useful application it has to map back into real linguistic statements... always problematic..

POWELL:
Interesting ideas, Nomad. Thanks.

John Powell

John Powell

April 28th 2003, 06:58 PM

POWELL:
To Woman.

WOMAN:
John,

I've been tied in a knot reading through this thread. Enjoying it very much though!

POWELL:
It's been enjoyable for me too.

WOMAN:
I have a question. If you think that MP (which affirms by affirming) is circular do you also think that Modus Tollens (which denies by denying) is also circular?

POWELL:
Gavin asked this early on. He seemed to think that if I were right about M.P. being circular then M.T. should also. I still don't know. I've thought about it some.

When I first looked at M.P. and M.T. long ago, I accepted M.P. without difficulty, but I couldn't see the logical necessity of M.T. How could logicians conclude that not p just because not q?

Since I looked at them again after beginning to read a logic text, I now think the reason that I couldn't see the logic is that M.P. does not explicitly use modal terms, so whatever modal term you use in the conditional should be carried into the conclusion regardless of whether you use the strong or weak modal terms and whether you assume the modal term is part of the inference or attached to the consequent of the conditional, but the same doesn't clearly apply to M.T.

For example,

If p then (necessarily q)
p
therefore, (necessarily q)

or

if p (then necessarily) q
p
therefore, (necessarily) q

Likewise, if you use the weak modal term, probably.

However, things are more complicated with M.T. I think logicians think of "necessarily" as being part of the conditional.

If p then necessarily q
not q
therefore, necessarily not p.

I've been hoping to persuade acceptance of my claim about M.P. before going on to M.T., but maybe I shouldn't delay that anymore.

I hope this answers your questions.

John Powell

John Powell

April 28th 2003, 07:22 PM

POWELL:
To NOMAD

NOMAD:

if MP is like 2=2, MT is like 2=3.

at least, that's what i've gotten out of these discussions.

POWELL:
This might be a useful analogy, however then wouldn't MT be "2 not = 3"?

POWELL:
P4: If (if dogs bark then snakes sing opera) is true, then if (if dogs bark then snakes sing opera) is true

P5: If (if dogs bark then snakes sing opera) is true and if (dogs bark) is true, then (snakes sing opera) would be true

NOMAD:
well, in a way, the first statement actually has implicit truth qualifiers as well: IF (dogs bark) = TRUE, THEN (snakes sing opera) = TRUE would be an equivalent way to write the first statement in your MP. and if you write it that way, then it is more clear what John was trying to get at.

note that after some discussion, and looking at parallels in other theoretical disciplines, it makes perfect sense - . . .

POWELL:
I wish I could take credit for persuading you properly, Nomad, but you seem to misunderstand. If the conditional "if p then q" is true that does NOT mean that "p is true" and "q is true." The conditional is true for 3 of the 4 combinations, all except for p = true and q = false. The conditional is true if p=1,q=1; p=0,q=0; or p=0,q=1.

NOMAD:
. . . no one would argue that equalities are useless in mathematics, merely because they are equalities. i really don't think the argument is that an argument IS an equality, but that it can REDUCE to an equality.

to solve x^2 - 2x + 1 = 0, you write it as an equality and then you solve. you will find that x = 1 is not a separate statement, but is a direct result of applying mathematical properties to the original equation:

POWELL:
Even in math, the statement "x=1" is considered separate from "x^2 - 2x + 1 = 0." They are equivalent.

NOMAD:
x^2 - 2x + 1 = 0
through factoring we find this equal to
(x - 1)(x - 1) = 0

divide both sides by (x - 1) we get
x - 1 = 0

add 1 to each side

x = 1

now, let's talk about what this *really* means. what this really means is that 'some unknown value X is equal to 1'. to put this in parallel: 'if pigs oink, then cows moo'. this is equivalent to 'x = y' - it's an equality, . . .

POWELL:
I don't think your pigs / cows conditional is an equality of the pigs and cows separately. Perhaps, you can justifiably consider it an equality if you claim the conditional is true. "If pigs oink then cows moo" = true.

NOMAD:
. . . but you can make no statements about whether it is true or not. and remember, equality, really, is not an *assignment* or anything, it is a *test*, and it is either true or false (the = in math is closer to the == in C++ than the =).

there is only one value of X that will make this a true statement; that value is 1. if we say 'x is 1', then we substitute and get the statement

1 = 1

this is a tautology. so, if x is 1, then x = 1 is true. this is the 'behind-the-scenes' logic for x = 1. that's sort of what we are talking about here, the 'behind-the-curtain' logic for MP.

POWELL:
This is sounding better to me. I'm saying that if the conditional proposition is true then the conditional is true, P = P.

NOMAD:
in the same way, if we have the above statement, and say 'if pigs oink = TRUE, then cows moo = X', there is only one value of X that will make the equation 'work', and that value is true.

POWELL:
Again, you don't understand the truth table for a conditional. If the conditional "if p then q" is true that means that p=1,q=1; or p=0,q=0; or p=0,q=1; but NOT p=1, q=0. A false conditional is one in which p=1, q=0.

NOMAD:
or, imagine trying to 'prove' factoring - how do you do it? you put the sides equal, and then do the math to show that they reduce to a tautology:

(x - 1)(x - 1) = x^2 - 2x + 1

x(x-1) - 1(x-1) = x^2 - 2x + 1

x^2 - x - x + 1 = x^2 - 2x + 1

x^2 - 2x + 1 = x^2 - 2x + 1

we usually stop here, but for absolute proof we don't have to:
subtract x^2 from both sides

-2x + 1 = -2x + 1

add 2x to both sides

1 = 1

we end up with tautology. the two sides are *absolutely* equal.

that just proves *this* factoring. but if you replace the numbers in the above with variables, you get the proof, and you end up with something like a = a, which is also always true.

this doesn't make it any less useful; as any college algebra student knows, this is a VERY useful substitution :)

POWELL:
I think we are progressing at understanding each other.

John Powell

John Powell

April 28th 2003, 09:40 PM

POWELL:
To ES / HIRAMJR. This is a long one.

Powell:
I thought I was posting arguments. Are you claiming that my "proposal" is false?

ES:
Your proposal was a proposition about M.P., while your arguments were presented to support your proposal. I believe your proposal is false.

POWELL:
Yes, it's a proposal with supporting arguments. I look forward to more opportunity to persuade you to change your opinion.

ES:
When someone asks, "What is M.P.?" the answer is that it is a valid argument form. ”

Powell:
Don't you mean "it is ONE OF SEVERAL valid argument FORMS"?

ES:
It means the same thing. If we have a barrel full of apples and I point to one and say, "This is an apple," my statement is not, "This is the only apple." Similarly, my statement above is that M.P. is 'a' valid argument form, not the only valid argument form.

POWELL:
Yes, what you say does not necessarily mean that every valid argument form is M.P., but linguistically your words could mean that. We are not having a normal conversation, so extra care needs to be made to be clear.

Powell:
I think I understand your point, Eric. What I mean to say is that arguments in a natural language (like English) of the M.P. form are essentially circular.

However, you seem to be contradicting yourself. Could you please clarify?

ES:
I don't quite understand your question. How exactly is my comment contradictory?

POWELL:
Because you said in one place that M.P. is valid and elsewhere that it isn't. What you meant to say is that it IS a valid argument form, but it is NOT a valid argument.

ES:
<school paper analogy>

POWELL:
Excellent analogy! I think I understand you, but some things below suggest you're being inconsistent, so let me ask this. What if the teacher gave an example paper and asked the students to follow the same form as that paper? Was the example paper a real paper or only a form?

ES (requoted):
When someone asks, "What is M.P.?" the answer is that it is a valid argument form...

. . .

(Note that it is the argument that is valid. It isn't that M.P. is valid)

Powell:
Is M.P. valid, Eric?

ES:
It is neither valid nor invalid. It is a form for arguments.

POWELL:
Don't you mean M.P. IS a valid argument form, but it is NOT a valid argument?

ES:
Suppose an argument was proposed that could be symbolized like this:

p -> q
~p
.: ~q

We could say that the argument is invalid because it constitutes an invalid argument form.

Powell:
That would be a mistake in certain cases, Eric, since just because an argument in the natural language follows an invalid argument form doesn't mean the original argument is invalid. It just means that arguments in that invalid form won't be certain to be valid. On the other hand, supposedly arguments in the natural language that follow a valid form will be reliably valid themselves.

For example, the following argument follows the invalid "denying the antecedent" form you mentioned, yet the argument is valid, right?

1) If J is a husband then J is a married man.
2) J is not a husband
3) Therefore, J is not a married man.

This argument is special because p is equivalent to q.

Or, maybe this isn't an argument at all, but only an argument form. Which is it, Eric? If I replace J with some generic male name like John, would it then be an argument rather than argument form?

ES:
If an argument does not follow a valid argument form, then the argument is not valid.

In your example we have:

p: J is a husband
q: J is a married man

p -> q
~p
.: ~q

This is an argument and it is invalid.

POWELL:
I believe you are inconsistent about calling this an "argument" rather than an "argument form" and you are mistaken about its validity.

First, on the possible inconsistency. I have not specified what J represents. It's a linguistic variable that could have names like John, Jack, Joe, even female names starting with J, even names not starting with J. Isn't that the reason you call M.P. an "argument form" rather than an "argument," because p and q are linguistic variables? Wouldn't J have to be identified as a specific person to be what you consider an argument, rather than merely an argument form? If no, please explain why

JP1. if p then q
JP2. p
JP3. therefore, q

is NOT an argument, but only an argument form, whereas

JP4. if J is a husband then J is a married man.
JP5. J is not a married man
JP6. therefore, J is not a husband.

is an argument, not just an argument form.

Now, on the issue of validity. Are you saying, Eric, that if it is true that J is not a married man that you cannot be assured that J is not a husband, in other words J could be a husband even if J is not a married man? If yes, then what are your definitions for husband and married man?

ES:
Determining validity has nothing to do with whether any premise or a conclusion is true.

POWELL:
Are you saying, Eric, that an argument can be valid even if the premises were true, but the conclusion false? What is your definition of a valid argument?

ES:
It doesn't matter that p 'means' the same thing as q. What matters is if the propositions are correctly ordered, if they follow the proper format for validity.

POWELL:
You're right that "denying the antecedent" is an invalid argument form, but I still think you're mistaken that that means that all substitutions of p and q in a denying the antecedent form argument results in invalid arguments. My counter-example remains secure, I think.

ES:
1) If J is a husband then J is a married man.
2') J is not a married man
3') Therefore, J is not a husband.

This is an argument and it is valid.

POWELL:
Now, I'm confused. Are you saying my husband / married man example is a valid argument or an invalid argument? Above you call it invalid, but here you call it valid. Once you make my substitutions for p and q then you obtain a valid argument, right?

ES:
The form isn't an argument. M.P. is merely a guideline. ”

Powell:
I think I understand what you're trying to say. You're right about M.P. being a guideline or a template, since p and q are linguistic variables. My argument about circularity applies to arguments of the M.P. form. Just replace p and q with linguistically meaningful terms.

ES:
Yes, we can do this, however the arguments aren't circular.

The argument you posed above isn't circular.

The first premise is a hypothetical. It doesn't state whether J is or is not married. It doesn't make a positive statement about J's marital status. The second premise is a positive statement about J's marital status. The conclusion is a positive statement about J's marital status.

POWELL:
You're now speaking about soundness, Eric. Valid arguments do NOT make positive statements about the premises. They make conditional / hypothetical statements. A valid argument says "if the premises were true then the conclusion would have to be true." A sound argument, on the other hand, makes positive statements about the premises. A sound argument says "The premises are true and, because the argument is valid, the conclusion is true." I am NOT claiming that arguments of the M.P. form when claimed to be sound are essentially circular. I'm claiming that arguments of the M.P. form when claimed to be merely valid are essentially circular.

This ambiguity of the syllogistic form is one of the reasons I avoided it initially in my arguments.

ES:
Those are three different subjects. We don't infer the conclusion from the second premise. We infer the conclusion from both the first and second premises. That is M.P. by definition.

POWELL:
I disagree, for arguments that are claimed to be merely valid, not sound, you are inferring the conclusion from the initial conditional.

Let me expand what the conditional linguistically means to try to show this.

JP7. "If p then q" = "If you happen to have p isolated as a true premise then you must have q isolated as a true conclusion."

What this conditional means is that if "you happen to have p isolated as a true premise" then "you must have q isolated as a true conclusion."

In other words,

JP8. If "If you happen to have p isolated as a true premise then you must have q isolated as a true conclusion" then if "you happen to have p isolated as a true premise" then "you must have q isolated as a true conclusion."

or

JP9. If "if p then q" then if "p" then "q."

or

JP10. If "if p then q" then "if p then q."

This circularity claim doesn't seem to work for arguments claimed to be sound, however.

ES:
In order for the argument to be circular . . .

POWELL:
Perhaps my expanded conditional above helps to answer this.

ES:
That guideline indicates that when a hypothetical is presented and its antecedent is affirmed, then its consequent would be the case.

Powell:
Right. IF the hypothetical is affirmed THEN (or "and") IF the antecedent is affirmed THEN the consequent would be the case.

ES:
I think you're confusing yourself with the language here. It's not "IF, THEN, THEN." It's IF, THEN.

This is vitally important because of your claim of circularity. Because you claim that an M.P. argument is circular 'according to your formulation above', then your formulation must have a conclusion that is found in its premise.

This means that what is found after the THEN must be found before it. You have two THEN's in your formulation. The THEN indicates an inference, it means 'therefore' some conclusion the case.

POWELL:
There are several "thens"

JP11. If "if p THEN q" THEN "if p THEN q." Clearly circular.

JP12. If "if p THEN q" THEN if "p" THEN "q." M.P. Not so clearly circular.

All I've done is change where the quotes go in the second half of the sentence. It's true you could replace the THEN after the first q with "and," but that's not required.

ES:
We have:

P1: The hypothetical is affirmed

POWELL:
Again you're confusing soundness with validity, Eric. The hypothetical is affirmed if you're talking about soundness, not merely validity. For mere validity you're claiming "If the hypothetical were to be affirmed..." not "The hypothetical is affirmed."

ES:
Now, what are you inferring from this? Given P1, therefore what is the case? You can't infer from P1 that the antecedent 'is' true. You instead would be inferring:

C1: IF the antecedent is affirmed THEN the consequent would be the case.

POWELL:
You seem to have made a hybrid argument between valid and sound. You're claiming the conditional is true, but then asking what would be true if the antecedent were true. What kind of an argument do you call that, valid, sound or what?

ES:
You then claim circularity because C1 looks like what is found in P1. The problem however is that you are inferring a hypothetical from a hypothetical. That isn't what M.P. is about.

M.P. form is:

p -> q
p
.: q

Note that the THEN, i.e. the ‘therefore’ precedes q. Your formulation is something like:

(p -> q)
.: (p) -> (q)

(which would allow the inclusion of M.T.
(p -> q)
.: (p) -> (q) and (~q) -> (~p))

POWELL:
Please write out in complete sentences in long English the translation of your symbolic representations above. When you use this syllogistic form I can't tell if you're claiming the argument is sound or merely valid. I need to see your "ifs" and "thens" to help show you when you jump from valid arguments to sound ones. Again, I am not claiming that M.P., when claimed to be sound, is circular, only when it is claimed to be merely valid.

ES:
M.P. is inferring a proposition, while you are inferring a hypothetical. Again, it is because of your charge of circularity that it must be the case that you conclude with a hypothetical after the THEN. But that isn't what M.P. is about.

With M.P., there is nothing in the hypothetical, (p -> q), that entails THEN something would be the case. It is simply a proposition that is either true or false. When we 'add' an additional proposition, (p), it is THEN that something would be the case. This is why it is (p -> q) 'and' (p) that produces q.

Validity here addresses the subject of proper inference. When I say, "something would be the case," this means that we can properly infer that it is the case.

POWELL:
I disagree. Consider,

JP13. If dogs bark then snakes fly.
JP14. dogs bark.
JP15. therefore, snakes fly.

Since this is a valid argument, that means that if the conditional "if dogs bark then snakes fly" were true then (or and) if "dogs bark" were true that "snakes fly" would have to be true. Are you saying that because "snakes fly" would be the case here that this means that we can properly infer that it IS the case? Are you saying that snakes fly, Eric?

ES:
We aren't somehow causing something to be the case. . .

POWELL:
I believe you are better understanding me than I feared.

ES:
1) If J is a husband then J is a married man.
2) J is a husband
3) Therefore, J is a married man.

Let's write this out:

P1: If it were true that if J is a husband then he is a married man and if it were the case that J was a husband, then it could properly be inferred that J is a married man.

P2: If it were true that if J is a husband then he is a married man, then it could be properly inferred that if it were the case that J was a husband, then it could properly be inferred that J is a married man.

Do you see the difference between P1 and P2? The conclusion of P1 is a proposition, while the conclusion of P2 is another hypothetical. P1 and P2 are two completely different arguments. P1’s conclusion is found nowhere in its premises.

POWELL:
They look different, but one only hides the circularity that I think is there. You are adding commas to ARTIFICIALLY CHANGE the meaning.

Can you tell the difference between these two, Eric?

JP16. If if p then q then if p then q

and

JP17. If if p then q then if p then q

They look identical, don't they? Let me add quotes to ARTIFICIALLY SEPARATE what linguistically is not necessarily separated.

JP18. If "if p then q" then "if p then q." Clearly circular, right?

JP19. If "if p then q" then if "p" then "q." M.P., right?

Again, this doesn't work with arguments claimed to be sound because some of the "ifs" disappear.

ES:
That guideline is neither valid nor sound. That guideline is either true or false.

Powell:
Whoa, Eric. Please respond to the following proposition with "true," "false," or "other" (and explain):

Q. Modus Ponens is not a valid argument form, but rather it's a true proposition.

ES:
It is false. M.P. is a valid argument form. It is not however a valid argument (just as the format of a term paper is not a term paper). It instead entails a proposition that if (p -> q) and (p) are affirmed, then (q) would be the case, or it is impossible for (p -> q) and (p) to be the case and (q) false, which defines M.P. validity.

POWELL:
Thanks. I now understand what you meant when you seemed to say M.P. was valid, but wasn't valid.

ES:
So when you say:

----
Modus Ponens merely valid, non-sound, form:
If "If p then q" then if "p" then "q".
----

I think you are confusing the argument form with an argument.

1. If p then q
2. p
3. Therefore q ”

Powell:
I explained why I do not initially use the syllogistic form, Eric. It's because the syllogistic form does not indicate whether the argument is claimed to be valid or sound. I use the M.P. argument form and the linguistic variables "p" and "q" in my arguments so that my conclusions apply generally.

ES:
I don't understand what you mean here. Whether an argument is "claimed" to be valid or sound is immaterial to the fact of whether it is valid or sound.

I don't see how you can both "use the M.P. argument form" and "not initially use the syllogistic form."

POWELL:
You don't seem to appreciate the fact that artificial languages like logic (and math) are symbolic representations of terms in the natural language. For example, the symbols "p -> q" have a linguistic meaning whether it is "if p then q" or "the truth table represented by 'not (p and not q)' "

To demonstrate my argument I need you to avoid more the symbolism and use more the long English which the symbolism represents. The symbolism HIDES the circularity I'm trying to show. You don't seem to realize the ambiguity of the syllogistic form. It doesn't clearly indicate if an argument is claimed to be sound or merely valid.

Let me illustrate this weakness. Can you confidently tell me if the following argument is sound? We agree that it's valid.

JP20. If it is raining then the streets are wet.
JP21. It is raining.
JP22. Therefore, the streets are wet.

If you can't tell whether this is merely valid or also sound by what I posted then I suggest that you should be careful using the syllogistic form in the present discussion because you might revert to claiming soundness when that's something I'm trying to avoid.

ES:
The 'explanation' for why this is a valid argument 'form' is that it is true that if (1) were true (not that it 'is' true) and if (2) were true, then (3) would have to be the case. (Note that this explanation is a proposition. It is either true or false, not valid or sound.) ”

Powell:
I think arguments of the M.P. form are seen to be correct because of the circularity.

ES:
I realize that this is your position. I simply disagree because I find nothing in M.P. form that indicates circularity.

POWELL:
Acknowledged.

ES:
So, we don't have the following:

P1: If "if p then q" then if "p" then "q"

Instead we have:

P2: If (("if p then q") and "p"), then "q"
or
P2': If (1) and (2), then (3) ”

Powell:
Your P2 and P2' are possible ways of looking at M.P., but they hide the circularity I'm trying to expose. I believe you are mistaken in denying my P1 as one of the correct ways to translate M.P. into long English. You are grouping the terms in one possible way, I, in another. The location of the parentheses is not obvious linguistically.

ES:
If how I have "grouped" things entails no circularity, then you've lost any objective ground for claiming that arguments the following the M.P. form are circular. All you can really say is that if anyone "groups" things your way then you can claim circularity. See above.

POWELL:
You think M.P. avoids circularity because linguistically you can use "and" instead of "then" after the first q and you are allowed to place quotation marks (or commas) where you like? In other words, you think that even though you are willing to concede that the following is a correct translation of M.P.

JP23. If "if p then q" then if "p" then "q"

however, because the following is also a correct translation

JP24. If "if p then q" and if "p" then "q"

M.P. avoids circularity. Is that your position?

If yes, then does the following avoid circularity because I use "also" instead of "then"?

JP25. If "if p then q" were true it would also be true that "if p then q."

What do you think?

Powell:
For example, is the answer to the following mathematical equation 25 or 30?

x = 3 + 2 * 5?

The answer is ambiguous until you decide a rule for grouping terms (multiplication first, for example).

ES:
M.P. itself is a "rule for grouping terms."

POWELL:
Interesting. Are you saying that M.P. is not circular by definition, by choice of how the terms are grouped?

ES:
This isn't circular. It is merely a statement of fact. ”

Powell:
I think it still is. You could also translate M.P. as the following:

IF it were true that "if p then q", THEN IF "p" were also true THEN "q" would have to also be true.

ES:
Yes, you are inferring a hypothetical from a hypothetical. That isn't what M.P. does.

POWELL:
Wait a minute. Are you saying that M.P. CANNOT BE JUSTIFIABLY TRANSLATED thusly:

JP26. If "if p then q" THEN if "p" then "q"

or, longer

JP27. If the conditional "if p then q" were true THEN if the antecedent "p" were true then the consequent "q" would be true?

Powell:
The words "and" and "also" can be used to merely indicate that there are additional elements to the argument. This additive term might be dropped if the meaning is clear without it. I think "then" can be used instead of "and" before the second premise.

Is it your position, Eric, that arguments of the M.P. form are NOT essentially circular because "then" cannot justifiably be used instead of "and" immediately prior to the "p" premise?

ES:
That is correct. In your translation above, where is your conclusion, that is, where are you making your concluding inference? Which THEN is the inference?

POWELL:
There are several ways to make the inference, Eric. One is to say "If the conditional were true then one could INFER that if the antecedent were true that (or then) the consequent would be true." Another is to say "If the conditional were true then if the antecedent were true one could INFER that the conclusion would be true." The words "then," "therefore," and even "infer" can be interchanged to some extent.

ES:
(p -> q)
.: p -> q
or
(p -> q) -> p
.: q

Neither one of these formulations properly reflects M.P.

POWELL:
Please convert these syllogisms into long English.

ES:
To expand it and to contrast validity with soundness, we could say:

P2'': If ("if p then q") were true and if ("p") were true, then "q" would be true

P3: ("if p then q") is true and ("p") is true, therefore "q" is true

Both P2'' and P3 are propositions, where P2' is a statement that indicates what validity means and P3 is a statement that indicates what soundness means. Neither is circular.

1) If dogs bark then snakes sing opera.
2) dogs bark
3) therefore, snakes sing opera.

Here, this argument is valid because it follows the proper argument form. The argument isn't circular because nothing in the conclusion is stated in (1). (1) entails a hypothetical but (2) and (3) don't.

You see, this isn't saying, in terms of validity:

P4: If (if dogs bark then snakes sing opera) is true, then if (if dogs bark then snakes sing opera) is true ”

Powell:
I think it is in a way, Eric, but I'm not persuading you to see it.

ES:
Not by what you have offered thus far. You're asking me either to redefine what M.P. means or to redefine what circularity means.

POWELL:
I'm asking you to see that M.P. is a correct rule of inference because of the linguistic meaning of the conditional "if p then q." The second premise and conclusion are merely restatements of what that conditional linguistically and logically means. Once you accept the conditional as true then M.P., when claimed to be merely valid, results by circularity.

If "if p then q" is true then it must be the case that "if you happen to have p then q will be true."

It is with sound arguments that this circularity might vanish because even if the conditional is true, that would not necessarily mean that the consequent is true. If the distinction between validity and soundness is confusing you then you probably aren't understanding well enough my argument.

John Powell

Hiramjr

April 29th 2003, 01:59 AM

To Powell:

P:
However, you seem to be contradicting yourself. Could you please clarify?

ES:
I don't quite understand your question. How exactly is my comment contradictory?

POWELL:
Because you said in one place that M.P. is valid and elsewhere that it isn't. What you meant to say is that it IS a valid argument form, but it is NOT a valid argument.

ES
The following is what I said:

When someone asks, "What is M.P.?" the answer is that it is a valid argument form. That form can be symbolized like this:

p -> q
p
.: q

M.P. is not an argument. It is an argument form. It is a template for constructing arguments. If an argument is proposed such that it follows the pattern of M.P., then it is a valid argument. (Note that it is the argument that is valid. It isn't that M.P. is valid)

Nothing here indicates that I am saying that M.P. is the only valid argument form. Nothing here indicates that I am saying that M.P. is a valid argument. Yes, we do have to be careful with our use of language, but we also have to be careful about the inferences we make.

ES:
<school paper analogy>

POWELL:
Excellent analogy! I think I understand you, but some things below suggest you're being inconsistent, so let me ask this. What if the teacher gave an example paper and asked the students to follow the same form as that paper? Was the example paper a real paper or only a form?

ES
It would be a term paper that followed the proper form.

Powell:
Is M.P. valid, Eric?

ES:
It is neither valid nor invalid. It is a form for arguments.

POWELL:
Don't you mean M.P. IS a valid argument form, but it is NOT a valid argument?

ES
No, it is neither valid or invalid. For example:

P1: The sun rose yesterday

Is P1 valid or invalid? It is neither. This means that the subject of validity is not applicable.

ES:
If an argument does not follow a valid argument form, then the argument is not valid.

In your example we have:

p: J is a husband
q: J is a married man

p -> q
~p
.: ~q

This is an argument and it is invalid.

POWELL:
I believe you are inconsistent about calling this an "argument" rather than an "argument form" and you are mistaken about its validity.

ES
What you proposed was an argument. That argument follows a certain form. That form is shown by the symbolization. The symbolization is utilized to easily show why the argument is invalid.

Because I defined p and q, the symbolization constitutes an argument.

POWELL:
First, on the possible inconsistency. I have not specified what J represents. It's a linguistic variable that could have names like John, Jack, Joe, even female names starting with J, even names not starting with J.

ES
It doesn't matter what J is. What matters is that your argument had a first premise, which was a hypothetical consisting of an antecedent and a consequent. Your argument had a second premise that denied the antecedent. This entails a fallacy of logic even if we never know what J means. Validity isn't determined by knowing J.

POWELL:
Isn't that the reason you call M.P. an "argument form" rather than an "argument," because p and q are linguistic variables?

ES
No. M.P. is an argument form by definition. That has nothing to do with how it is symbolized. In other words, it isn't an argument form because p and q are variables sometimes used to symbolized it. M.P. does not define p and q.

POWELL:
JP1. if p then q
JP2. p
JP3. therefore, q

is NOT an argument, but only an argument form, whereas

JP4. if J is a husband then J is a married man.
JP5. J is not a married man
JP6. therefore, J is not a husband.

is an argument, not just an argument form.

ES
This is correct, unless we have:

p: J is a husband
q: J is a married man

This renders JP1-JP3 as an argument. You are confusing that which is a shorthand method of demonstrating an argument form, in contrast to a shorthand method of representing an argument.

POWELL:
Now, on the issue of validity. Are you saying, Eric, that if it is true that J is not a married man that you cannot be assured that J is not a husband, in other words J could be a husband even if J is not a married man? If yes, then what are your definitions for husband and married man?

ES
The fact that an argument is invalid does not mean that its conclusion is false. It only means that the argument does not, for whatever reason, follow the rules of formal logic.

If a term paper is handed in and it doesn't follow the proper form, it is still a term paper. It simply needs to be put in the proper format.

ES:
Determining validity has nothing to do with whether any premise or a conclusion is true.

POWELL:
Are you saying, Eric, that an argument can be valid even if the premises were true, but the conclusion false? What is your definition of a valid argument?

ES
An argument that follows the pattern of M.P. is a valid argument. It doesn't matter what the premises are.

1. If square circles exist, then oceans fly
2. Square circles exist
3. Therefore oceans fly

This is a valid argument via M.P. IF (1) and (2) 'were' true, then (3) would be the case. This does not say that (1) and (2) 'are' true.

ES:
It doesn't matter that p 'means' the same thing as q. What matters is if the propositions are correctly ordered, if they follow the proper format for validity.

POWELL:
You're right that "denying the antecedent" is an invalid argument form, but I still think you're mistaken that that means that all substitutions of p and q in a denying the antecedent form argument results in invalid arguments. My counter-example remains secure, I think.

ES
You can't rationally affirm that denying the antecedent is an invalid argument form, and at the same time maintain that an argument that follows this form is valid.

ES:
1) If J is a husband then J is a married man.
2') J is not a married man
3') Therefore, J is not a husband.

This is an argument and it is valid.

POWELL:
Now, I'm confused. Are you saying my husband / married man example is a valid argument or an invalid argument? Above you call it invalid, but here you call it valid.

ES
What I offer immediately above is a reworking of your original argument. The above argument follows the pattern of M.T. It is valid. What this means is that there is a proper manner in which to formulate your argument.

ES:
The argument you posed above isn't circular.

The first premise is a hypothetical. It doesn't state whether J is or is not married. It doesn't make a positive statement about J's marital status. The second premise is a positive statement about J's marital status. The conclusion is a positive statement about J's marital status.

POWELL:
You're now speaking about soundness, Eric. Valid arguments do NOT make positive statements about the premises.

ES
No, my comments aren't about soundness. I indicated that your argument contains two premises and a conclusion, which means that we have three distinct propositions. This doesn't speak of the truth status of any these propositions.

Q: J's marital status
Q1: J is married
Q2: J is not married

Both Q1 and Q2 can be considered positive statements about J's marital status (that is a subject, not a premise), in the sense of saying, "It is the case that J is married," or "It is the case that J is not married." This is not however the same as saying that Q1 or Q2 is a 'true' statement about J's marital status.

ES:
Those are three different subjects. We don't infer the conclusion from the second premise. We infer the conclusion from both the first and second premises. That is M.P. by definition.

POWELL:
I disagree, for arguments that are claimed to be merely valid, not sound, you are inferring the conclusion from the initial conditional.

ES
No, this is simply not the case. An M.P. argument does not infer its conclusion from its hypothetical. It infers its conclusion from its hypothetical 'and' the affirmation of the antecedent.

The hypothetical is one proposition and the affirmation of the antecedent is a different proposition. The conclusion (yet another proposition) is inferred from both of these propositions. That is the point I was making in my comments.

As I said, in order to prove circularity, you must demonstrate that the proposition of the conclusion is found in the premises that are proposed to lead to it.

POWELL:
Let me expand what the conditional linguistically means to try to show this.

JP7. "If p then q" = "If you happen to have p isolated as a true premise then you must have q isolated as a true conclusion."

What this conditional means is that if "you happen to have p isolated as a true premise" then "you must have q isolated as a true conclusion."

In other words,

JP8. If "If you happen to have p isolated as a true premise then you must have q isolated as a true conclusion" then if "you happen to have p isolated as a true premise" then "you must have q isolated as a true conclusion."

or

JP9. If "if p then q" then if "p" then "q."

or

JP10. If "if p then q" then "if p then q."

This circularity claim doesn't seem to work for arguments claimed to be sound, however.

ES
It doesn't work here either. All you are doing is drawing an inference from the hypothetical. What you infer from a hypothetical is another hypothetical. M.P. does not do this. See below.

As I said:

ES:
The problem however is that you are inferring a hypothetical from a hypothetical. That isn't what M.P. is about.

M.P. form is:

p -> q
p
.: q

Note that the THEN, i.e. the ‘therefore’ precedes q. Your formulation is something like:

(p -> q)
.: (p) -> (q)

(which would allow the inclusion of M.T.
(p -> q)
.: (p) -> (q) and (~q) -> (~p))

POWELL:
Please write out in complete sentences in long English the translation of your symbolic representations above. When you use this syllogistic form I can't tell if you're claiming the argument is sound or merely valid. I need to see your "ifs" and "thens" to help show you when you jump from valid arguments to sound ones. Again, I am not claiming that M.P., when claimed to be sound, is circular, only when it is claimed to be merely valid.

ES
There is nothing about the subject of soundness in my comments. The problem here is that you're not understanding the inference that M.P. makes.

In your English translation above, you are dealing only with the hypothetical and what you infer from that. M.P., on the other hand, deals with 'two' propositions, not just the one. This means that your translation doesn't reflect M.P.

To make it clear:

"Given the propositions (p -> q) and p, if (p -> q) and p were true, then q would be true."

There is nothing circular here. See below.

POWELL:
You think M.P. avoids circularity because linguistically you can use "and" instead of "then" after the first q and you are allowed to place quotation marks (or commas) where you like? In other words, you think that even though you are willing to concede that the following is a correct translation of M.P.

JP23. If "if p then q" then if "p" then "q"

ES
You're missing the point here. I don't agree that this is a correct translation of M.P.

It reflects inferring a hypothetical from a hypothetical. M.P. nowhere infers a hypothetical. Of course the following is true:

JP25. If "if p then q" were true it would also be true that "if p then q."

But this is 'not' what M.P. is reduced to. See below.

POWELL:
Interesting. Are you saying that M.P. is not circular by definition, by choice of how the terms are grouped?

ES
It is not circular both by what the terms mean and how they are grouped. As I said, we are dealing with three different propositions. If you can show that the last proposition, the conclusion, is found in the former two, then you have circularity.

ES:
Yes, you are inferring a hypothetical from a hypothetical. That isn't what M.P. does.

POWELL:
Wait a minute. Are you saying that M.P. CANNOT BE JUSTIFIABLY TRANSLATED thusly:

JP26. If "if p then q" THEN if "p" then "q"

or, longer

JP27. If the conditional "if p then q" were true THEN if the antecedent "p" were true then the consequent "q" would be true?

ES
That is what I have been saying, yes. You're still not understanding that your THEN is the point of inference in 'your' formulation. This means that your conclusion is a hypothetical. M.P.'s conclusion is not a hypothetical.

That is why the symbology actually makes things clearer.

p -> q
p
.: q

Here, it is obvious where the inference is being made. It is 'not' made after the hypothetical. It is made from 'both' the hypothetical and the second premise. The conclusion is not a hypothetical.

The only way this could be circular is if q was found in the preceding premises. It isn't.

(p -> q)
.: (p) -> (q)

Here, in your formulation, the inference is made from the hypothetical. Your conclusion ends up being a hypothetical. This doesn't properly reflect M.P.

Note your comment:

POWELL:
I'm asking you to see that M.P. is a correct rule of inference because of the linguistic meaning of the conditional "if p then q."

ES
That is the problem in a nutshell. You are reducing M.P. to only be addressing the hypothetical. This isn't the case.

This is what M.P. is about:

p -> q (if this proposition were true, then if p was the case, q would be the case)
p (if this proposition were true, then p would be the case)
.: q

You see, you're stopping at the hypothetical, but that doesn't produce the conclusion. If (p -> q) and (p) were true, then q would be the case. There is nothing circular here.

nomad

April 29th 2003, 10:15 AM

I hope I didn't offend you for skipping this, Nomad. I felt I should respond first to the new people.

not at all! i think we mostly understand each other anyways, so totally agreed.

POWELL:

Math certainly does have true and false. Usually, true =1 and false = 0.

was that actually ever used as a convention? i thought assigning numerical values to true and false wasn't until the time of computers. before that, it was just true and false (and really was in the realm of logic at that point, just like logic works with science as well).

some computers use -1 for true as well.

For example,

True or False: a^2 + b^2 = c^2 where a and b are the two shorter sides of a right triangle and c is the hypotenuse?

well, the problem is that i'm trying to isolate math (as a theoretical language) without using logic, but it's turning out to be very difficult.

a^2 + b^2 = c^2 in a right triangle may be true or false, but what about the mere statement a^2 + b^2 = c^2? is it true or false? it is a valid equation, but neither true or false. and this, truly, is a purely theoretical statement.

POWELL:

Good points, but I think the analogy isn't working in the way that I previously thought it might, but validity is more like learning the rules of math and soundness is more like applying them to real life problems.

i think that is along the same lines.

POWELL:

I hope my distinction given above for the x=3 problem helps to clarify how I'm thinking about this.

it does. but i was trying to avoid commingling logic, at least for the purposes of example. i guess it is impossible to do that :)

POWELL:

Good point. Is the following proposition true or false?
P
If you won't say "true" then you should not use it in sound argument.

is the following a sound argument?

P1: 'p->q' IS TRUE
P2: p IS TRUE
C: therefore, q IS TRUE

that is a sound argument. yet, p and q aren't anything 'real' - i can't go run a scientific experiment and see if p really is, in fact, true, because these are just theoretical statements.

as a scientist, this may seem really strange for me to claim that p is true when i don't even know what p represents, but it is perfectly valid inside theoretical logic examples to do so. you see this done a lot in math in proofs and such.

as an example, suppose i wanted to know what the angular velocity of the earth would be if it were a different mass, or in a different (say, more distant) orbit around the sun. i can plug those _theoretical_ values into the equations and get values that i can put some faith in. yet, since the assumptions i plugged into the equations do not correspond to the real world, the results don't match the real world either. yet, they may be useful in some sense, and perhaps not even just for proving concepts, but in testing theories.

POWELL:

Wait a minute, Nomad. In that case you would be saying "If P" or "Assuming P." That's in the regime of validity again. Until you will affirm "P" it should not be part of a sound argument. You cannot justifiably affirm P until you know what P corresponds to.

ok, so this is exactly what i thought you were complaining about :) justifiably? maybe not, if 'justifiably' means 'i can back up my assertion of P with a scientific experiment in the real world'. but i can certainly say 'P is true' for the purposes of a theoretical investigation.

i see what you are getting at about soundness and validity though.

POWELL:

This might be a useful analogy, however then wouldn't MT be "2 not = 3"?

no. for a math equation, if you can reduce the equation to a 'tautology' (say, 1 = 1), that shows that for all substitutions of all variables, the equation remains true: the equals sign will return 'true' for all substitutions. this is equivalent to saying 'anytime you have what was originally on the left side of the equals side, you can replace it with what is on the right side of the equals side without reservation'. the parallel to MP is obvious.

if you reduce the equation and you end up with an impossibility (say, 1 = 2), that means that there is no value of any variable that will make the equation valid. the equals will always return false. this is equivalent to saying 'if you have what was originally on the left side of the equation, you can never replace it with what is on the right side, without reservation'. this parallels to MT in that if you have ~q, you can never have p. not directly perhaps, but that was my line of thought, as a parallel.

POWELL:

Even in math, the statement "x=1" is considered separate from "x^2 - 2x + 1 = 0." They are equivalent.

ok, that works for me.

POWELL:

I don't think your pigs / cows conditional is an equality of the pigs and cows separately. Perhaps, you can justifiably consider it an equality if you claim the conditional is true. "If pigs oink then cows moo" = true.

i think i am still not doing any good at expressing 'conceptual' equivalents. so i think i will stop trying, i don't know any different way to do it.

i don't mean it's an equality at all, i just mean by itself, it doesn't assert anything. 'x = y' is a valid equation: if you tell me the value of X, i can then tell you the value of Y. but right now, since i don't know the value for either X OR Y, i can't tell you what either of them are.
if you give me a specific X and Y though, i can tell you whether they fit the pattern.

POWELL:

Again, you don't understand the truth table for a conditional. If the conditional "if p then q" is true that means that p=1,q=1; or p=0,q=0; or p=0,q=1; but NOT p=1, q=0. A false conditional is one in which p=1, q=0.

let me try again: if we assert that 'p->q' is a true proposition, there are three valid solutions for (p,q) = (0, 0), (0, 1), (1, 1) and one invalid solution for (p, q) = (1, 0). IF (p->q) is true. so, if we say it's true, and then i tell you p is one, there is only coordinate (1,1) that fulfills the truth of the original proposition.

POWELL:

I think we are progressing at understanding each other.

i think we are getting closer. though, i am getting more confused :)

John Powell

April 29th 2003, 10:45 PM

POWELL:
I think I'm understanding you better, Eric. I hope you're interested in continuing this interesting and challenging discussion.

POWELL:
However, you seem to be contradicting yourself. Could you please clarify?

ES:
I don't quite understand your question. How exactly is my comment contradictory?

POWELL:
Because you said in one place that M.P. is valid and elsewhere that it isn't. What you meant to say is that it IS a valid argument form, but it is NOT a valid argument.

ES:
The following is what I said:

ES:
When someone asks, "What is M.P.?" the answer is that it is a valid argument form. That form can be symbolized like this:

p -> q
p
.: q

M.P. is not an argument. It is an argument form. It is a template for constructing arguments. If an argument is proposed such that it follows the pattern of M.P., then it is a valid argument. (Note that it is the argument that is valid. It isn't that M.P. is valid)

ES:
Nothing here indicates that I am saying that M.P. is the only valid argument form. Nothing here indicates that I am saying that M.P. is a valid argument. Yes, we do have to be careful with our use of language, but we also have to be careful about the inferences we make.

POWELL:
I think you could have rephrased things better to avoid a possible, but unwanted, interpretation.

ES:
<school paper analogy>

POWELL:
Excellent analogy! . . . Was the example paper a real paper or only a form?

ES:
It would be a term paper that followed the proper form.

POWELL:
Thanks.

POWELL:
Is M.P. valid, Eric?

ES:
It is neither valid nor invalid. It is a form for arguments.

POWELL:
Don't you mean M.P. IS a valid argument form, but it is NOT a valid argument?

ES:
No, it is neither valid or invalid. For example:

P1: The sun rose yesterday

Is P1 valid or invalid? It is neither. This means that the subject of validity is not applicable.

POWELL:
I realize you never said M.P. was a valid argument, Eric, but you did say it was a valid argument form. Do you deny that M.P. is a valid something?

ES:
If an argument does not follow a valid argument form, then the argument is not valid.

In your example we have:

p: J is a husband
q: J is a married man

p -> q
~p
.: ~q

This is an argument and it is invalid.

POWELL:
I believe you are inconsistent about calling this an "argument" rather than an "argument form" and you are mistaken about its validity.

ES:
What you proposed was an argument. That argument follows a certain form. That form is shown by the symbolization. The symbolization is utilized to easily show why the argument is invalid.

Because I defined p and q, the symbolization constitutes an argument.

POWELL:
First, on the possible inconsistency. I have not specified what J represents. It's a linguistic variable that could have names like John, Jack, Joe, even female names starting with J, even names not starting with J.

ES:
It doesn't matter what J is. What matters is that your argument had a first premise, which was a hypothetical consisting of an antecedent and a consequent. Your argument had a second premise that denied the antecedent. This entails a fallacy of logic even if we never know what J means. Validity isn't determined by knowing J.

POWELL:
More inconsistency, I think, Eric. Let me rephrase your words relevant to denying the antecedent to show how they support the notion that M.P. is an argument, not just an argument form.

It doesn't matter what p and q are. What matters is that your argument had a first premise (if p then q), which was a hypothetical consisting of an antecedent (p) and a consequent (q). Your argument had a second premise (p). This entails a correct inference even if we never know what p and q mean. Validity isn't determined by knowing p or q.

I believe to be consistent in your destinction between argument and argument form you should have called my J syllogism also an argument form. To be an argument, according to your definition, J must be identified.

POWELL:
Isn't that the reason you call M.P. an "argument form" rather than an "argument," because p and q are linguistic variables?

ES:
No. M.P. is an argument form by definition. That has nothing to do with how it is symbolized. In other words, it isn't an argument form because p and q are variables sometimes used to symbolized it. M.P. does not define p and q.

POWELL:
By definition? Absurd. Logicians didn't call it a "form" just because they liked the sound of the word, Eric. Surely, M.P. is called an argument form because p and q are stand-ins for a nearly infinite number of possible linguistic terms like "it is raining" and "the roads are wet" that would produce a natural language argument rather than something that merely had the shape or structure of a natural language argument.

POWELL:
JP1. if p then q
JP2. p
JP3. therefore, q

is NOT an argument, but only an argument form, whereas

JP4. if J is a husband then J is a married man.
JP5. J is not a married man
JP6. therefore, J is not a husband.

is an argument, not just an argument form.

ES
This is correct, unless we have:

p: J is a husband
q: J is a married man

This renders JP1-JP3 as an argument. You are confusing that which is a shorthand method of demonstrating an argument form, in contrast to a shorthand method of representing an argument.

POWELL:
Now I'm confused again. I thought an argument form was a shorthand method of representing an argument. I thought "if p then q" would be the form of a natural language conditional where p and q are linguistic variables. Could you present an argument form that isn't in shorthand, that's written out in complete English?

POWELL:
Now, on the issue of validity. Are you saying, Eric, that if it is true that J is not a married man that you cannot be assured that J is not a husband, in other words J could be a husband even if J is not a married man? If yes, then what are your definitions for husband and married man?

ES:
The fact that an argument is invalid does not mean that its conclusion is false. It only means that the argument does not, for whatever reason, follow the rules of formal logic.

If a term paper is handed in and it doesn't follow the proper form, it is still a term paper. It simply needs to be put in the proper format.

POWELL:
That's not a very good definition of "valid," Eric. Are you saying that valid arguments are arguments which follow the rules for making valid arguments, but you can't really explain better than that?

Let me give you a better definition then. Read my first post in "Invalidating Validity" in this same philosophy section.

COPI & COHEN (pg. 42-43):

1.7 Deduction and Validity

. . . Thus we define "validity" as follows: A deductive argument is valid when, if its premisses are true, its conclusion must be true. . .

POWELL:
According to this definition, my husband argument is valid, even though it follows the form of the invalid "denying the antecedent."

Do you have an authoritative definition for "valid" that supports your position in opposition to that of me and Copi & Cohen?

ES:
Determining validity has nothing to do with whether any premise or a conclusion is true.

POWELL:
Are you saying, Eric, that an argument can be valid even if the premises were true, but the conclusion false? What is your definition of a valid argument?

ES:
An argument that follows the pattern of M.P. is a valid argument.

POWELL:
Why, Eric? Is it that arguments that follow the M.P. form are defined to be valid regardless whether the conclusion must be true if the premises are true?

ES:
It doesn't matter what the premises are.

1. If square circles exist, then oceans fly
2. Square circles exist
3. Therefore oceans fly

This is a valid argument via M.P. IF (1) and (2) 'were' true, then (3) would be the case. This does not say that (1) and (2) 'are' true.

POWELL:
That's what I thought you probably meant, but you weren't clear. You said "Determining validity has nothing to do with whether any premise or a conclusion is true" but it does have something to do with the truth of such things. If the premises are true, but the conclusion is false then that argument is invalid. What you probably meant to say was something more like "Determining validity does not depend on whether the conclusion is true or whether a certain premise is true, but whether the conclusion must be true if the premises were true." Right?

ES:
It doesn't matter that p 'means' the same thing as q. What matters is if the propositions are correctly ordered, if they follow the proper format for validity.

POWELL:
You're right that "denying the antecedent" is an invalid argument form, but I still think you're mistaken that that means that all substitutions of p and q in a denying the antecedent form argument results in invalid arguments. My counter-example remains secure, I think.

ES:
You can't rationally affirm that denying the antecedent is an invalid argument form, and at the same time maintain that an argument that follows this form is valid.

POWELL:
That depends on your definition of "valid." You seem to have a misguided definition that "valid" is whatever follows a certain argument form. Please post your source for this flawed definition.

What happened, I think, is that logicians found that certain logical forms, such as M.P. and M.T. always produced for them valid arguments (those for which the conclusion was assured of being true if the premises were true) so they proclaimed them as valid argument forms. That doesn't mean, however, that the definition of valid argument is whatever follows those forms. Maybe logicians were wrong. Please see my "invalidating validity" for arguments in this regard.

ES:
1) If J is a husband then J is a married man.
2') J is not a married man
3') Therefore, J is not a husband.

This is an argument and it is valid.

POWELL:
Now, I'm confused. Are you saying my husband / married man example is a valid argument or an invalid argument? Above you call it invalid, but here you call it valid.

ES:
What I offer immediately above is a reworking of your original argument. The above argument follows the pattern of M.T. It is valid. What this means is that there is a proper manner in which to formulate your argument.

POWELL:
SORRY! I misread your revision. Yes, you converted my "denying the antecedent" argument into M.T. However, Eric, my question then remains, now rephrased:

Q. Is it true that if premise 1 were true "If J is a husband then J is a married man" and my original premise 2 were true "J is not a husband" then the conclusion would have be true, could not be false, 3 "J is not a married man."?

If the answer is yes, Eric, then the argument is valid according to Copi & Cohen.

ES:
The argument you posed above isn't circular.

The first premise is a hypothetical. It doesn't state whether J is or is not married. It doesn't make a positive statement about J's marital status. The second premise is a positive statement about J's marital status. The conclusion is a positive statement about J's marital status.

POWELL:
You're now speaking about soundness, Eric. Valid arguments do NOT make positive statements about the premises.

ES:
No, my comments aren't about soundness. I indicated that your argument contains two premises and a conclusion, which means that we have three distinct propositions. This doesn't speak of the truth status of any these propositions.

Q: J's marital status
Q1: J is married
Q2: J is not married

Both Q1 and Q2 can be considered positive statements about J's marital status (that is a subject, not a premise), in the sense of saying, "It is the case that J is married," or "It is the case that J is not married." This is not however the same as saying that Q1 or Q2 is a 'true' statement about J's marital status.

POWELL:
If you say things like "It is the case that J is married" then you are into soundness, not merely validity. Validity says things like "if it were the case that J was married. . ."

ES:
Those are three different subjects. We don't infer the conclusion from the second premise. We infer the conclusion from both the first and second premises. That is M.P. by definition.

POWELL:
I disagree, for arguments that are claimed to be merely valid, not sound, you are inferring the conclusion from the initial conditional.

ES:
No, this is simply not the case. An M.P. argument does not infer its conclusion from its hypothetical. It infers its conclusion from its hypothetical 'and' the affirmation of the antecedent.

The hypothetical is one proposition and the affirmation of the antecedent is a different proposition. The conclusion (yet another proposition) is inferred from both of these propositions. That is the point I was making in my comments.

As I said, in order to prove circularity, you must demonstrate that the proposition of the conclusion is found in the premises that are proposed to lead to it.

POWELL:
I think I understand you, Eric.

Something you may not understand is the arbitrariness between true / false "propositions" and valid / invalid "deductive arguments" that allowed logicians to convert a circular argument into M.P.

Is the following an argument or a proposition?

JQ1. If if p then q then if p then q.

As it stands it appears to be a proposition, but it can be written as a series of propositions to make an argument. This is what a syllogism is good for, identifying the propositions of the argument. It is this power that allowed logicians to turn a circular argument into M.P.

One way is to convert it into a circular argument:

If "if p then q" then "if p then q"

To convert it into a syllogism, hide the first "if" in the inference and convert the middle "then" into "therefore."

(if) JQ2. if p then q
therefore
JQ3. if p then q

Here's another way to convert it into an argument:

If "if p then q" then if "p" then "q"

which has two possible meanings.

To convert this into a syllogism, hide the first and third "ifs" in the inference and convert both "thens" into "therefores."

(if) JQ4. if p then q
therefore
(if) JQ5. p
therefore
JQ6. q

This is sort of in between the circular argument and M.P.

Here's another interpretation of the second writing.

Suppress the second "then" as merely meaning "next proposition" or "and"

(if) JQ7. if p then q
(next proposition)
(if) JQ8. p
therefore
JQ9. q

This, of course, is M.P.

One thing this linguistic manipulation suggests is that I could convert any argument in long English whether it was circular, fallacious, or whatever into a single proposition. If I were to post what you consider to be a circular or invalid argument, I could convert it into a proposition and say, "it's not an argument at all, but a proposition." Putting arguments into syllogism form prevents this.

POWELL:
Let me expand what the conditional linguistically means to try to show this.

JP7. "If p then q" = "If you happen to have p isolated as a true premise then you must have q isolated as a true conclusion."

What this conditional means is that if "you happen to have p isolated as a true premise" then "you must have q isolated as a true conclusion."

In other words,

JP8. If "If you happen to have p isolated as a true premise then you must have q isolated as a true conclusion" then if "you happen to have p isolated as a true premise" then "you must have q isolated as a true conclusion."

or

JP9. If "if p then q" then if "p" then "q."

or

JP10. If "if p then q" then "if p then q."

This circularity claim doesn't seem to work for arguments claimed to be sound, however.

ES:
It doesn't work here either. All you are doing is drawing an inference from the hypothetical. What you infer from a hypothetical is another hypothetical. M.P. does not do this. See below.

As I said:

ES:
The problem however is that you are inferring a hypothetical from a hypothetical. That isn't what M.P. is about.

M.P. form is:

p -> q
p
.: q

Note that the THEN, i.e. the ‘therefore’ precedes q. Your formulation is something like:

(p -> q)
.: (p) -> (q)

(which would allow the inclusion of M.T.
(p -> q)
.: (p) -> (q) and (~q) -> (~p))

POWELL:
Ok.

POWELL:
Please write out in complete sentences in long English the translation of your symbolic representations above. When you use this syllogistic form I can't tell if you're claiming the argument is sound or merely valid. I need to see your "ifs" and "thens" to help show you when you jump from valid arguments to sound ones. Again, I am not claiming that M.P., when claimed to be sound, is circular, only when it is claimed to be merely valid.

ES:
There is nothing about the subject of soundness in my comments. The problem here is that you're not understanding the inference that M.P. makes.

In your English translation above, you are dealing only with the hypothetical and what you infer from that. M.P., on the other hand, deals with 'two' propositions, not just the one. This means that your translation doesn't reflect M.P.

To make it clear:

"Given the propositions (p -> q) and p, if (p -> q) and p were true, then q would be true."

There is nothing circular here. See below.

POWELL:
It doesn't look that way to you.

POWELL:
You think M.P. avoids circularity because linguistically you can use "and" instead of "then" after the first q and you are allowed to place quotation marks (or commas) where you like? In other words, you think that even though you are willing to concede that the following is a correct translation of M.P.

JP23. If "if p then q" then if "p" then "q"

ES:
You're missing the point here. I don't agree that this is a correct translation of M.P.

It reflects inferring a hypothetical from a hypothetical. M.P. nowhere infers a hypothetical. Of course the following is true:

JP25. If "if p then q" were true it would also be true that "if p then q."

But this is 'not' what M.P. is reduced to. See below.

POWELL:
I think it does. Let me indicate how the circular argument below is converted into M.P.

JQ10. If "if p then q" then "if p then q."

The first "if" is suppressed becoming part of the inference, namely "if premise 1"

The "if p then q" becomes the first premise.

The middle "then" becomes "next proposition"

The third "if" is suppressed becoming part of the inference, namely "if premise 2"

The last "p" becomes the second premise.

The last "then" becomes "therefore"

The last "q" becomes the conclusion.

(if) JQ11. if p then q.
(next proposition)
(if) JQ12. p.
- - - - therefore - - - -
JQ13. q.

If your argument is claimed to be merely valid then all you need are the conditionals, not the rest of M.P., because the rest follows from the conditional. If the conditional were true then it would have to also be true that if you have p then q would be true.

If, however, the argument is claimed to be sound, things are quite different.

For example,

JQ14. If God is an Omnibeing then God is all-good and all-powerful.
JQ15. If God is all-good then God should cause that there be no evil.
JQ16. If God is all-powerful then God could cause that there be no evil.
JQ17. If there is evil then God is either not all-good or not all-powerful.
- - - - - therefore - - - - -
JQ18. If there is evil then God is not an Omnibeing.

It is not necessary, unless you want this argument to be sound and to conclude that God is not an Omnibeing, to expand the last conditional into M.P. The conclusion JQ18 must be true if the premises are true, so the argument is valid.

Or, maybe you'll say it isn't valid because it doesn't follow one of the recognized valid forms. What do you say, Eric?

POWELL:
Interesting. Are you saying that M.P. is not circular by definition, by choice of how the terms are grouped?

ES:
It is not circular both by what the terms mean and how they are grouped. As I said, we are dealing with three different propositions. If you can show that the last proposition, the conclusion, is found in the former two, then you have circularity.

POWELL:
I see.

ES:
Yes, you are inferring a hypothetical from a hypothetical. That isn't what M.P. does.

POWELL:
Wait a minute. Are you saying that M.P. CANNOT BE JUSTIFIABLY TRANSLATED thusly:

JP26. If "if p then q" THEN if "p" then "q"

or, longer

JP27. If the conditional "if p then q" were true THEN if the antecedent "p" were true then the consequent "q" would be true?

ES:
That is what I have been saying, yes. You're still not understanding that your THEN is the point of inference in 'your' formulation. This means that your conclusion is a hypothetical. M.P.'s conclusion is not a hypothetical.

That is why the symbology actually makes things clearer.

p -> q
p
.: q

Here, it is obvious where the inference is being made. It is 'not' made after the hypothetical. It is made from 'both' the hypothetical and the second premise. The conclusion is not a hypothetical.

The only way this could be circular is if q was found in the preceding premises. It isn't.

(p -> q)
.: (p) -> (q)

Here, in your formulation, the inference is made from the hypothetical. Your conclusion ends up being a hypothetical. This doesn't properly reflect M.P.

Note your comment:

POWELL:
I'm asking you to see that M.P. is a correct rule of inference because of the linguistic meaning of the conditional "if p then q."

ES:
That is the problem in a nutshell. You are reducing M.P. to only be addressing the hypothetical. This isn't the case.

This is what M.P. is about :

p -> q (if this proposition were true, then if p was the case, q would be the case)
p (if this proposition were true, then p would be the case)
.: q

You see, you're stopping at the hypothetical, but that doesn't produce the conclusion. If (p -> q) and (p) were true, then q would be the case. There is nothing circular here.

POWELL:
Ok, let me try a different approach, Eric.

Is the following a circular argument?

If atheism is true then God does not exist. God does not exist because atheism is true.

If this one isn't circular then PLEASE give me a couple of different typical circular religious arguments IN COMPLETE ENGLISH SENTENCES, not in syllogistic or symbolic form.

John Powell

John Powell

April 29th 2003, 11:35 PM

POWELL:
To NOMAD.

POWELL:
I hope I didn't offend you for skipping this, Nomad. I felt I should respond first to the new people.

NOMAD:
not at all! i think we mostly understand each other anyways, so totally agreed.

POWELL:
Math certainly does have true and false. Usually, true =1 and false = 0.

NOMAD:
was that actually ever used as a convention? i thought assigning numerical values to true and false wasn't until the time of computers.

POWELL:
Well sure, probably not until computers.

NOMAD:
before that, it was just true and false (and really was in the realm of logic at that point, just like logic works with science as well).

POWELL:
Right. Science and math use logic. So, you're saying it's not technically part of math. Perhaps that's ok. It's logic, not math per se.

NOMAD:
some computers use -1 for true as well.

POWELL:
Interesting.

POWELL:
For example,

True or False: a^2 + b^2 = c^2 where a and b are the two shorter sides of a right triangle and c is the hypotenuse?

NOMAD:
well, the problem is that i'm trying to isolate math (as a theoretical language) without using logic, but it's turning out to be very difficult.

a^2 + b^2 = c^2 in a right triangle may be true or false, but what about the mere statement a^2 + b^2 = c^2? is it true or false? it is a valid equation, but neither true or false. and this, truly, is a purely theoretical statement.

POWELL:
A typical math question would be whether there were real or only complex solutions to the equation. If I asked a math teacher whether the equation was a "valid equation" they would probably say "yes" since it doesn't seem to "break any rules."

POWELL:
Good points, but I think the analogy isn't working in the way that I previously thought it might, but validity is more like learning the rules of math and soundness is more like applying them to real life problems.

NOMAD:
i think that is along the same lines.

POWELL:
Great! :yipee:

POWELL:
I hope my distinction given above for the x=3 problem helps to clarify how I'm thinking about this.

NOMAD:
it does. but i was trying to avoid commingling logic, at least for the purposes of example. i guess it is impossible to do that :)

POWELL:
Good point. Is the following proposition true or false?

P

If you won't say "true" then you should not use it in sound argument.

NOMAD:
is the following a sound argument?

P1: 'p->q' IS TRUE
P2: p IS TRUE
C: therefore, q IS TRUE

that is a sound argument. yet, p and q aren't anything 'real' - i can't go run a scientific experiment and see if p really is, in fact, true, because these are just theoretical statements.

POWELL:
No, it isn't a sound argument. Nor is the following

JP1. if p then q
JP2. p
- - - - - therefore - - - - -
JP3. q

You must replace p and q with linguistic variables before you have a chance for the argument to be sound. Then those linquistic variables must be true for the argument to be sound.

NOMAD:
as a scientist, this may seem really strange for me to claim that p is true when i don't even know what p represents, but it is perfectly valid inside theoretical logic examples to do so. you see this done a lot in math in proofs and such.

POWELL:
You should not. There should always be an "if" in front of those statements. Once you say "theoretical" that implies "if" in front of such statements.

NOMAD:
as an example, suppose i wanted to know what the angular velocity of the earth would be if it were a different mass, or in a different (say, more distant) orbit around the sun. i can plug those _theoretical_ values into the equations and get values that i can put some faith in. yet, since the assumptions i plugged into the equations do not correspond to the real world, the results don't match the real world either. yet, they may be useful in some sense, and perhaps not even just for proving concepts, but in testing theories.

POWELL:
This example would be more similar to validity. You're saying "if" things were different then what would happen. Such things cannot be closely associated with "sound."

In fact, science has a more difficult time dealing with hypotheticals like this then you seem to realize. The simple answer you calculate by assuming the only thing that would be changed by changing the mass are the variables in a certain angular relationship is not necessarily the correct answer. if the Earth had had a different mass then Jupiter may have thrown it out of the Solar System or into the Sun or something else.

As another example,

If the speed of light were only 300 m/s what would the world be like? This is too complicated a thing for scientists to come up with reliable answers. Perhaps relativistic effects would be observed by merely driving in cars. On the other hand, perhaps the universe could not exist.

Science does better with showing why certain scenarios do not work, such as if a violation of a law of nature occurs, rather than proposing how others would work if the circumstances or laws were very different. There are too many relationships that have to be considered.

Many of these "what if" questions are really philosophical rather than strictly scientific unless you can perform experiments or do observations testing the ideas.

POWELL:
Wait a minute, Nomad. In that case you would be saying "If P" or "Assuming P." That's in the regime of validity again. Until you will affirm "P" it should not be part of a sound argument. You cannot justifiably affirm P until you know what P corresponds to.

NOMAD:
ok, so this is exactly what i thought you were complaining about :) justifiably? maybe not, if 'justifiably' means 'i can back up my assertion of P with a scientific experiment in the real world'. but i can certainly say 'P is true' for the purposes of a theoretical investigation.

POWELL:
You could say that because you have free will, but what you should really mean is "if p were true."

NOMAD:
i see what you are getting at about soundness and validity though.

POWELL:
Great. My background is science too, but I have found philosophical logic fairly easy to pick up because science is so logical and I had a strong language background in my home.

POWELL:
This might be a useful analogy, however then wouldn't MT be "2 not = 3"?

NOMAD:
no. for a math equation, if you can reduce the equation to a 'tautology' (say, 1 = 1), that shows that for all substitutions of all variables, the equation remains true: the equals sign will return 'true' for all substitutions. this is equivalent to saying 'anytime you have what was originally on the left side of the equals side, you can replace it with what is on the right side of the equals side without reservation'. the parallel to MP is obvious.

if you reduce the equation and you end up with an impossibility (say, 1 = 2), that means that there is no value of any variable that will make the equation valid. the equals will always return false. this is equivalent to saying 'if you have what was originally on the left side of the equation, you can never replace it with what is on the right side, without reservation'. this parallels to MT in that if you have ~q, you can never have p. not directly perhaps, but that was my line of thought, as a parallel.

POWELL:
Ok. I think I see your point.

POWELL:
Even in math, the statement "x=1" is considered separate from "x^2 - 2x + 1 = 0." They are equivalent.

NOMAD:
ok, that works for me.

POWELL:
I don't think your pigs / cows conditional is an equality of the pigs and cows separately. Perhaps, you can justifiably consider it an equality if you claim the conditional is true. "If pigs oink then cows moo" = true.

NOMAD:
i think i am still not doing any good at expressing 'conceptual' equivalents. so i think i will stop trying, i don't know any different way to do it.

i don't mean it's an equality at all, i just mean by itself, it doesn't assert anything. 'x = y' is a valid equation: if you tell me the value of X, i can then tell you the value of Y. but right now, since i don't know the value for either X OR Y, i can't tell you what either of them are.

if you give me a specific X and Y though, i can tell you whether they fit the pattern.

POWELL:
Conditionals were a little harder for me to understand.

If a conditional like "if p then q" is true what that means is that either p = 1, q = 1 or p = 0, q = 0 or p = 0, q = 1. If the conditional is false that means p = 1, q = 0.

So, if I claim that the conditional "if pigs oink then cows moo" is true that means that either pigs oink and cows moo or pigs don't oink and it doesn't matter if cows moo. If the conditional is true then it also means that it cannot be the case that pigs oink but cows don't moo.

POWELL:
Again, you don't understand the truth table for a conditional. If the conditional "if p then q" is true that means that p=1,q=1; or p=0,q=0; or p=0,q=1; but NOT p=1, q=0. A false conditional is one in which p=1, q=0.

NOMAD:
let me try again: if we assert that 'p->q' is a true proposition, there are three valid solutions for (p,q) = (0, 0), (0, 1), (1, 1) and one invalid solution for (p, q) = (1, 0). IF (p->q) is true. so, if we say it's true, and then i tell you p is one, there is only coordinate (1,1) that fulfills the truth of the original proposition.

POWELL:
Yes. If p->q is true and p = 1 then q = 1.

POWELL:
I think we are progressing at understanding each other.

NOMAD:
i think we are getting closer. though, i am getting more confused :)

POWELL:
The conditional is a bit weird, I'll admit. All the conditional being true requires is that you CANNOT have p = 1 and q = 0, otherwise the conditional would be false.

John Powell

Hiramjr

April 30th 2003, 03:43 PM

To Powell

ES:
If an argument does not follow a valid argument form, then the argument is not valid.

In your example we have:

p: J is a husband
q: J is a married man

p -> q
~p
.: ~q

This is an argument and it is invalid.

POWELL:
I believe you are inconsistent about calling this an "argument" rather than an "argument form" and you are mistaken about its validity.

ES:
What you proposed was an argument. That argument follows a certain form. That form is shown by the symbolization. The symbolization is utilized to easily show why the argument is invalid.

Because I defined p and q, the symbolization constitutes an argument.

POWELL:
First, on the possible inconsistency. I have not specified what J represents. It's a linguistic variable that could have names like John, Jack, Joe, even female names starting with J, even names not starting with J.

ES:
It doesn't matter what J is. What matters is that your argument had a first premise, which was a hypothetical consisting of an antecedent and a consequent. Your argument had a second premise that denied the antecedent. This entails a fallacy of logic even if we never know what J means. Validity isn't determined by knowing J.

POWELL:
More inconsistency, I think, Eric. Let me rephrase your words relevant to denying the antecedent to show how they support the notion that M.P. is an argument, not just an argument form.

It doesn't matter what p and q are. What matters is that your argument had a first premise (if p then q), which was a hypothetical consisting of an antecedent (p) and a consequent (q). Your argument had a second premise (p). This entails a correct inference even if we never know what p and q mean. Validity isn't determined by knowing p or q.

I believe to be consistent in your destinction between argument and argument form you should have called my J syllogism also an argument form. To be an argument, according to your definition, J must be identified.

ES
There is nothing about J that has anything to do with the argument's form. The form of the argument is:

p -> q
~p
.: ~q

Regardless of what p and q represent, the form is invalid. Because the form is invalid, the argument is invalid. The argument is not itself an invalid argument form, rather it has been constructed according to an invalid argument form.

Just as a student may use the wrong format for his term paper, his term paper is not the format. His term paper follows that format.

You're confusing two different subjects.

S1: The syllogism that represents the argument
S2: The syllogism that represents the argument's form

When I say:

p: J is a husband
q: J is a married man

p -> q
~p
.: ~q

This is referring to your argument. I have defined p and q, and the symbology is merely a shorthand means of writing out your argument.

Now, after the argument has been written out (S1), the next subject (S2) is the argument's form. I could just as well use other symbols:

r -> w
~r
.: ~w

Here, I am referring to the pattern of your argument. This is dealing with the argument's form. It has nothing to do with what the premises actually state. The form is invalid for hypothetical syllogisms.

To use the term paper analogy again.

t: The term paper
p: "The Migration of Elephants"
q: Documentation regarding the migration of elephants
r: Bibliography

t =
1. r
2. q
3. p

Here, I am defining certain variables to represent certain subjects. For (1)-(3), I am indicating the order of those subjects as they appear in the term paper. The order is:

Bibliography
Documentation
Title

Now, I am dealing, not with the contents of the term paper, but with the format in which it has been written. I can compare this format with the one stipulated by the instructor. By comparing the formats I discover that the term paper is in the wrong format.

It should instead be:

Title
Documentation
Bibliography

Note that nowhere in this evaluation do I have to outline exactly what the term paper says regarding the migration of elephants. I am merely comparing the formats.

In a similar fashion, in your argument, because it is a hypothetical syllogism, we don't need to know what J refers to. J is a subject found within a proposition. We determine validity (of hypothetical syllogisms) based on what form the propositions follow, not on their content. See below.

POWELL:
Isn't that the reason you call M.P. an "argument form" rather than an "argument," because p and q are linguistic variables?

ES:
No. M.P. is an argument form by definition. That has nothing to do with how it is symbolized. In other words, it isn't an argument form because p and q are variables sometimes used to symbolized it. M.P. does not define p and q.

POWELL:
By definition? Absurd. Logicians didn't call it a "form" just because they liked the sound of the word, Eric.

ES
Nothing in what I said indicates that M.P. is "called" a form because logicians liked the sound of the word. This response makes no sense to me.

M.P. has a definition. Its definition indicates that it 'is' an argument form. Definitions aren't based on people liking the sounds of words.

POWELL:
Surely, M.P. is called an argument form because p and q are stand-ins for a nearly infinite number of possible linguistic terms like "it is raining" and "the roads are wet" that would produce a natural language argument rather than something that merely had the shape or structure of a natural language argument.

ES
M.P. is not defined by p and q. Any variable can be used to demonstrate what M.P. refers to. M.P. is defined as a pattern for certain arguments. It stipulates that principle that given (r -> w) and (r), if it were the case that both (r -> w) and (r) were true, then this would guarantee that w would be the case. That is a proposition, it is a definition.

The definition isn't based on the 'content' of r or w. It is based on the logical relationship between (r -> w) and (r), between a hypothetical and the affirmation of its antecedent. It is impossible for both to be true and w false. Thus, if an argument follows this form, then it is valid.

It is no different from saying that, given a title, documentation and a bibliography, if the bibliography follows the documentation and the documentation follows the title, then this is the proper format for a term paper. This is a proposition, it is a definition. It is not a term paper.

Any term paper that follows this pattern is a "valid" term paper, regardless of what is the subject of the paper.

POWELL:
Now, on the issue of validity. Are you saying, Eric, that if it is true that J is not a married man that you cannot be assured that J is not a husband, in other words J could be a husband even if J is not a married man? If yes, then what are your definitions for husband and married man?

ES:
The fact that an argument is invalid does not mean that its conclusion is false. It only means that the argument does not, for whatever reason, follow the rules of formal logic.

If a term paper is handed in and it doesn't follow the proper form, it is still a term paper. It simply needs to be put in the proper format.

POWELL:
That's not a very good definition of "valid," Eric.

ES
I am not defining "valid" in my above comments.

POWELL:
Are you saying that valid arguments are arguments which follow the rules for making valid arguments, but you can't really explain better than that?

ES
No, my point is that, in your above comments, you are not properly dealing with what validity deals with regard to a hypothetical syllogism. For this type of argument, validity is determined by its form, not its content (no, this does not mean that this is the case for each and every type of argument).

Contrary to this however, when you offer your hypothetical syllogism, you are determining its validity based on the content of its premises.

Given the proposition, "J is a married man," we know that J is a husband because of the conventional definition of a married man. We are not properly inferring that J is a husband, rather a married man = being a husband.

Thus,

p: J is a married man
q: J is a husband

p = q, and ~p = ~q.

Based on what it means for a person to be married, the following propositions are true:

P1: A person who is married 'is' a husband.

p . q
p
.: q

P2: A person who is not married is not a husband.

~p . ~q
~p
.: ~q

When you offer as your second premise that J is not married, you then conclude that he is not a husband. But this conclusion is not based on your hypothetical syllogism. It is based on the conventional definition of the word married, which entails P2.

You are inadvertently inserting a premise into your argument:

1. If J is married, then he is a husband
2. J is not married [2'. A person who is not married is not a husband (P2)]
3. Therefore, J is not a husband

The conclusion is not derived from (1) and (2). It is derived from (2) and (2') via tautology. So, one could argue that this is not an argument at all, but is merely a tautological statement, "J is not married and thus is not a husband."

The reason you think your argument is valid is because the conclusion would have to be true because of what it means to not be married. This makes (1) superfluous.

1' If a bird is in flight, then a bird is in the air
2. J is not married [2'. A person who is not married is not a husband (P2)]
3. Therefore, J is not a husband

Both (1') and (2) are true, but the conclusion is only derived from (2) and (2'). This is not a valid hypothetical syllogism.

Validity indicates that we are guaranteed to get to the conclusion if the premises were true. Think of it in terms of driving somewhere. If a set of directions is correct, then if you took that path, you would be guaranteed to reach your destination. This doesn't mean that you couldn't get to your destination by some other means.

For a hypothetical syllogism (a particular form of argument), validity is not determined by what the content of the premises mean. It is determined by its form (following the directions). This is why even the strangest arguments can be deemed valid.

a. If square circles don't exist, then the moon doesn't exist
b. Square circles don't exist
c. Therefore, the moon doesn't exist

The form of this argument is:

p -> q
p
.: q

The argument is valid. Its validity has nothing to do with the content of its premises. Now, for other types of arguments validity may be determined by the content of their premises, but for any argument that follows the form of M.P., its validity is defined by the definition of M.P.

POWELL:
Let me give you a better definition then. Read my first post in "Invalidating Validity" in this same philosophy section.

“ COPI & COHEN (pg. 42-43):

1.7 Deduction and Validity

. . . Thus we define "validity" as follows: A deductive argument is valid when, if its premisses are true, its conclusion must be true. . .
”

ES
This is correct. For an argument that follows the form of M.P., if both of its premises (note the plurality) were true, then its conclusion would be true. That is because, given (p -> q) and (p), if both premise were true, then q would have to be the case (i.e. it would rationally be determined to be true based on the truth of both premises, not just one), 'regardless' of the content of p and q.

POWELL:
According to this definition, my husband argument is valid, even though it follows the form of the invalid "denying the antecedent."

ES
No, the argument isn't valid. You have a valid inference in the argument, but the argument itself, proposed as a hypothetical syllogism is not valid.

POWELL:
Q. Is it true that if premise 1 were true "If J is a husband then J is a married man" and my original premise 2 were true "J is not a husband" then the conclusion would have be true, could not be false, 3 "J is not a married man."?

ES
This is true. This is not however what validity for a hypothetical syllogism means.

POWELL:
Is the following an argument or a proposition?

JQ1. If if p then q then if p then q.

ES
It is a proposition.

POWELL:
As it stands it appears to be a proposition, but it can be written as a series of propositions to make an argument. This is what a syllogism is good for, identifying the propositions of the argument. It is this power that allowed logicians to turn a circular argument into M.P.

One way is to convert it into a circular argument:

If "if p then q" then "if p then q"

To convert it into a syllogism, hide the first "if" in the inference and convert the middle "then" into "therefore."

(if) JQ2. if p then q
therefore
JQ3. if p then q

ES
I think this is where you've first gotten off track here. In converting JQ1 into a syllogism, you can't "hide the first 'if'." That 'if' is a component of JQ1. You might as well suggest that we hide the first 'p'.

When we are testing an argument to determine its validity, we add 'if' to its premises, but this does not mean that the 'if' is a component of the premises.

You are conflating two different subjects:

S1: The argument itself
S2: The test for its validity

The argument:

It is the case that if J is married then J is a husband, and it is the case that J is married, therefore J is a husband.

To use shorthand:

p: J is married
q: J is a husband

The following is the argument:

S1: (If p then q) and (p), therefore q

The following is a test for the validity of the argument:

S2: If ((if p then q) and (p)), therefore q

Both S1 and S2 are propositions. Each is either true or false. S1 contains only one 'if' (Note that it is not saying that if something is the case THEN if something else is the case, THEN something is the case). It is making three distinct propositions:

P1: "It is the case that If p then q" (p -> q)
P2: "It is the case that p" (p)
P3: "It is the case that P1 and P2 guarantee q, and q is the case" (.: q)

(Every premise of every argument implies the statement, "It is the case." This is because every premise is a proposition. This is not the same as saying that it is "true" that "It is the case")

When we are testing for validity, (i.e. determining whether S2 is true), we are asking whether or not it is true that if P1 and P2 were true, then P3 would have to be true.

S2 is true. There is no way for the antecedent to be true and the consequent false. That is why M.P. (S1 form) is a valid argument form, meaning that any argument that follows this form is valid. It doesn't matter what the content is.

There is nothing circular here. The conclusion is not in the premises.

POWELL:
Ok, let me try a different approach, Eric.

Is the following a circular argument?

If atheism is true then God does not exist. God does not exist because atheism is true.

ES
No.

If atheism is true, then God does not exist
Atheism is true
Therefore, God does not exist

If God exists, then atheism is not true
God exists
Therefore, atheism is not true

Neither is circular.

POWELL:
If this one isn't circular then PLEASE give me a couple of different typical circular religious arguments IN COMPLETE ENGLISH SENTENCES, not in syllogistic or symbolic form.

ES
"Pointless evil could only exist if God didn't exist. We know that God doesn't exist because pointless evil exists." (assumes knowledge that God doesn't exist and thus pointless evil exists, in order argue that the existence of pointless evil proves that God doesn't exist)

"We know that the Bible is not the word of God because there is no God. We know that there is no God because the Bible is not the word of God." (assumes knowledge that God doesn't exist and thus the Bible is not the word of God, in order argue that the Bible not being the word of God proves that God doesn't exist)

John Powell

April 30th 2003, 09:37 PM

POWELL:
I think I'm understanding better where we disagree.

POWELL:
I believe to be consistent in your destinction between argument and argument form you should have called my J syllogism also an argument form. To be an argument, according to your definition, J must be identified.

ES:
There is nothing about J that has anything to do with the argument's form. The form of the argument is:

p -> q
~p
.: ~q

Regardless of what p and q represent, the form is invalid. Because the form is invalid, the argument is invalid. The argument is not itself an invalid argument form, rather it has been constructed according to an invalid argument form.

Just as a student may use the wrong format for his term paper, his term paper is not the format. His term paper follows that format.

You're confusing two different subjects.

S1: The syllogism that represents the argument
S2: The syllogism that represents the argument's form

When I say:

p: J is a husband
q: J is a married man

p -> q
~p
.: ~q

This is referring to your argument. I have defined p and q, and the symbology is merely a shorthand means of writing out your argument.

Now, after the argument has been written out (S1), the next subject (S2) is the argument's form. I could just as well use other symbols:

r -> w
~r
.: ~w

Here, I am referring to the pattern of your argument. This is dealing with the argument's form. It has nothing to do with what the premises actually state. The form is invalid for hypothetical syllogisms.

To use the term paper analogy again.

<snipped>

In a similar fashion, in your argument, because it is a hypothetical syllogism, we don't need to know what J refers to. J is a subject found within a proposition. We determine validity (of hypothetical syllogisms) based on what form the propositions follow, not on their content. See below.

POWELL:
Your term paper analogy is getting more and more useful.

Now tell me Eric, what if I were to violate the teacher's order on writing the term paper. Would it NECESSARILY be a bad paper? The teacher might give it a bad grade for violating his instructions, but does that mean that it could not be one of the best papers ever written?

You seem to think that merely because an argument follows a certain form that it is or is not valid. That's not what defines whether an argument is valid or not. Surely what happened is that it was concluded by logicians that arguments that followed the M.P. form were always valid, always had the conclusion guaranteed true if the premises were true. It was not that they made up M.P. and then defined it to be a valid form without regard to whether it satisfied the usual conditions for validity, right?

You also seem to have an overly restrictive definition of "argument form." Think of a form letter. It's not necessarily one with a very abbreviated content showing broadly what needs to be filled in. It's usually one where EVERYTHING is already spelled out except for personal information of the target. My husband syllogism was similar. In that sense my statement

JR1. If J is a husband then J is a married man

is a proposition form. J is a variable that could be any individual. This proposition cannot justifiably be claimed to be true until J is identified, just like an argument in the M.P. form cannot be justifiably claimed to be sound until p and q are identified.

Your specialized definition of argument as opposed to argument form could be useful if you were consistent about this. I think what you mean to say is that only those series of statements in which everything is spelled out and could justifiably be a sound argument do you have an argument. If parts are not identified (for example if there are variable names) then it's not quite a full argument, but just an argument form.

Let me see where you make the change from "form" to argument.

Are the following arguments or just argument forms?

JR2. If p then snakes run
JR3. p
JR4. therefore, snakes run

JR5. If dogs fly then q
JR6. dogs fly
JR7. therefore, q

JR8. If dogs x then snakes y
JR9. dogs x
JR10. therefore, snakes y

JR11. If D fly then S run
JR12. D fly
JR13. therefore, S run

JR14. If D F then S R
JR15. D F
JR16. therefore, S R

POWELL:
Surely, M.P. is called an argument form because p and q are stand-ins for a nearly infinite number of possible linguistic terms like "it is raining" and "the roads are wet" that would produce a natural language argument rather than something that merely had the shape or structure of a natural language argument.

ES:
M.P. is not defined by p and q. Any variable can be used to demonstrate what M.P. refers to. M.P. is defined as a pattern for certain arguments.

POWELL:
Well, sure. Beginning algebra students learn that the variable doesn't have to be called "x."

ES:
It stipulates that principle that given (r -> w) and (r), if it were the case that both (r -> w) and (r) were true, then this would guarantee that w would be the case. That is a proposition, it is a definition.

The definition isn't based on the 'content' of r or w. It is based on the logical relationship between (r -> w) and (r), between a hypothetical and the affirmation of its antecedent. It is impossible for both to be true and w false. Thus, if an argument follows this form, then it is valid.

POWELL:
NOT NECESSARILY! It has been concluded by logicians that this is true about M.P., but that doesn't mean they were right.

ES:
It is no different from saying that, given a title, documentation and a bibliography, if the bibliography follows the documentation and the documentation follows the title, then this is the proper format for a term paper. This is a proposition, it is a definition. It is not a term paper.

Any term paper that follows this pattern is a "valid" term paper, regardless of what is the subject of the paper.

POWELL:
Yes, if you DEFINE a term paper to be what satisfies your arbitrary rules then anything that doesn't follow that pattern is disqualified by you. However, Eric, if I were to write a paper that did not follow those arbitrary rules could it still be one of the best papers ever written?

If I were to write an argument that did not follow one of the "valid" forms, in fact if it followed one of the invalid forms, could it still be valid in the sense that the conclusion would have to be true if the premises were true? You say no, but I presented one that is valid according to the rules.

Validity is NOT DEFINED by whether it follows a certain form, Eric, but whether it satisfies the definition that the conclusion must be true, cannot be false, if the premises are true.

POWELL:
Now, on the issue of validity. Are you saying, Eric, that if it is true that J is not a married man that you cannot be assured that J is not a husband, in other words J could be a husband even if J is not a married man? If yes, then what are your definitions for husband and married man?

ES:
The fact that an argument is invalid does not mean that its conclusion is false.

POWELL:
I never said it did.

ES:
It only means that the argument does not, for whatever reason, follow the rules of formal logic.

POWELL:
I deny that the definition of valid is any argument that follows the M.P., M.T., or other such forms.

If you have an authoritative source that DEFINES validity in this way, please post it.

ES:
If a term paper is handed in and it doesn't follow the proper form, it is still a term paper. It simply needs to be put in the proper format.

POWELL:
Does it HAVE TO be put in the format that the teacher requires to be a good paper?

POWELL:
That's not a very good definition of "valid," Eric.

ES:
I am not defining "valid" in my above comments.

POWELL:
Are you saying that valid arguments are arguments which follow the rules for making valid arguments, but you can't really explain better than that?

ES:
No, my point is that, in your above comments, you are not properly dealing with what validity deals with regard to a hypothetical syllogism. For this type of argument, validity is determined by its form, not its content (no, this does not mean that this is the case for each and every type of argument).

POWELL:
I don't think so, Eric. For this type of argument IT MAY BE USEFUL TO ASSUME that since it follows the M.P. form that it will be valid. Again, validity is not defined by whether it follows a form, but whether it satisfies the core definition that the conclusion must be true, cannot be false, if the premises are true.

As efficient humans we often come up with short-cuts. A short cut to identifying valid arguments is whether they follow the right form. If they do then they very probably are valid, if they follow an invalid form then they are probably invalid.

Just because certain arguments have claimed to be valid doesn't mean they are. I discuss this in the beginning posts of my "invalidating validity" thread.

ES:
Contrary to this however, when you offer your hypothetical syllogism, you are determining its validity based on the content of its premises.

POWELL:
That's how it should be done, unless you come up with a reliable short cut.

ES:
Given the proposition, "J is a married man," we know that J is a husband because of the conventional definition of a married man. We are not properly inferring that J is a husband, rather a married man = being a husband.

Thus,

p: J is a married man
q: J is a husband

p = q, and ~p = ~q.

Based on what it means for a person to be married, the following propositions are true:

P1: A person who is married 'is' a husband.

p . q
p
.: q

P2: A person who is not married is not a husband.

~p . ~q
~p
.: ~q

When you offer as your second premise that J is not married, you then conclude that he is not a husband. But this conclusion is not based on your hypothetical syllogism. It is based on the conventional definition of the word married, which entails P2.

You are inadvertently inserting a premise into your argument:

1. If J is married, then he is a husband
2. J is not married [2'. A person who is not married is not a husband (P2)]
3. Therefore, J is not a husband

The conclusion is not derived from (1) and (2). It is derived from (2) and (2') via tautology. So, one could argue that this is not an argument at all, but is merely a tautological statement, "J is not married and thus is not a husband."

The reason you think your argument is valid is because the conclusion would have to be true because of what it means to not be married. This makes (1) superfluous.

1' If a bird is in flight, then a bird is in the air
2. J is not married [2'. A person who is not married is not a husband (P2)]
3. Therefore, J is not a husband

Both (1') and (2) are true, but the conclusion is only derived from (2) and (2'). This is not a valid hypothetical syllogism.

POWELL:
Interesting. I'm trying to say that M.P. is similarly superfluous. All you need is the conditional, since the rest follows by linguistic definition.

The following is an invalid form, right?

JR17. p
JR18. therefore, q

But, here's a valid (by my definition) argument that follows that invalid form.

JR19. J is a married man
JR20. Therefore, J is a husband.

That reminds me that I forgot to ask you something. Is a circular argument valid, Eric?

ES:
Validity indicates that we are guaranteed to get to the conclusion if the premises were true. Think of it in terms of driving somewhere. If a set of directions is correct, then if you took that path, you would be guaranteed to reach your destination. This doesn't mean that you couldn't get to your destination by some other means.

POWELL:
You come up with some great analogies, Eric. Now tell me, if you were to do your best to follow the directions of the best and most honest direction giver in the universe who claimed they were correct directions would you NECESSARILY arrive at your destination or is it possible that even following those instructions you'd end up in a black hole that appeared suddenly?

In like manner, so-called valid deductive arguments do not absolutely guarantee the conclusion will be true even if the premises were true. They only guarantee that very probably the conclusion will be true if the premises were true.

ES:
For a hypothetical syllogism (a particular form of argument), validity is not determined by what the content of the premises mean. It is determined by its form (following the directions). This is why even the strangest arguments can be deemed valid.

POWELL:
You can use the form of the argument to ESTIMATE or PREDICT that the argument will or will not be valid, but that's not what defines validity.

ES:
a. If square circles don't exist, then the moon doesn't exist
b. Square circles don't exist
c. Therefore, the moon doesn't exist

The form of this argument is:

p -> q
p
.: q

The argument is valid. Its validity has nothing to do with the content of its premises. Now, for other types of arguments validity may be determined by the content of their premises, but for any argument that follows the form of M.P., its validity is defined by the definition of M.P.

POWELL:
It's not DEFINED to be valid because it follows M.P., Eric. It is ASSUMED to be valid because it follows M.P. Validity is not defined by the form of the argument, but rather whether the conclusion must be true if the premises are true.

POWELL:
Let me give you a better definition then. Read my first post in "Invalidating Validity" in this same philosophy section.

COPI & COHEN (pg. 42-43):

1.7 Deduction and Validity

. . . Thus we define "validity" as follows: A deductive argument is valid when, if its premisses are true, its conclusion must be true. . .

ES:
This is correct. For an argument that follows the form of M.P., if both of its premises (note the plurality) were true, then its conclusion would be true. That is because, given (p -> q) and (p), if both premise were true, then q would have to be the case (i.e. it would rationally be determined to be true based on the truth of both premises, not just one), 'regardless' of the content of p and q.

POWELL:
According to this definition, my husband argument is valid, Eric, even though it follows the form of the invalid "denying the antecedent."

ES:
No, the argument isn't valid.

POWELL:
What is the definition of valid, Eric? THE CONCLUSION MUST BE TRUE, CANNOT BE FALSE, IF THE PREMISES ARE TRUE.

You've agreed that this is the correct definition, Eric, so please don't use any other definition having to do with following logical forms or whatever unless you can quote an authority to match Copi and Cohen.

Doesn't my husband argument satisfy that defining condition, Eric? Isn't it true that if premise 1 (If J is a husband then J is a married man) were true and if premise 2 (J is not a husband) were true then the conclusion (J is not a married man) would have to be true, could not be false? Are you saying that the conclusion could be false even if the premises were true? If yes, then please show me how.

ES:
You have a valid inference in the argument, but the argument itself, proposed as a hypothetical syllogism is not valid.

POWELL:
If it's valid then it doesn't need to be rewritten with additional premises.

COPI & COHEN:
If a deductive argument is valid, no additional premisses could possibly add to the strength of that argument. For example, if all humans are mortal, and if Socrates is human, we may conclude without reservation that Socrates is mortal - - - and that conclusion will follow from those premisses no matter what else may be true in the world, and no matter what other information may be discovered or added. If we come to learn that Socrates is ugly, or that angels are immortal, or that cows give milk, neither those findings nor any other findings can have any impact on the validity of the original argument.

POWELL:
Doesn't it make you wonder, Eric, how you can write essentially the same argument in a "valid form" if it isn't valid in the first place? Perhaps your "all arguments following invalid forms are invalid" idea is misguided.

POWELL:
Q. Is it true that if premise 1 were true "If J is a husband then J is a married man" and my original premise 2 were true "J is not a husband" then the conclusion would have be true, could not be false, 3 "J is not a married man."?

ES:
This is true. This is not however what validity for a hypothetical syllogism means.

POWELL:
Then what defines validity, Eric? Please post your source.

POWELL:
Is the following an argument or a proposition?

JQ1. If if p then q then if p then q.

ES:
It is a proposition.

POWELL:
As it stands it appears to be a proposition, but it can be written as a series of propositions to make an argument. This is what a syllogism is good for, identifying the propositions of the argument. It is this power that allowed logicians to turn a circular argument into M.P.

One way is to convert it into a circular argument:

If "if p then q" then "if p then q"

To convert it into a syllogism, hide the first "if" in the inference and convert the middle "then" into "therefore."

(if) JQ2. if p then q
therefore
JQ3. if p then q

ES:
I think this is where you've first gotten off track here. In converting JQ1 into a syllogism, you can't "hide the first 'if'." That 'if' is a component of JQ1. You might as well suggest that we hide the first 'p'.

POWELL:
Now, we're getting somewhere. Your use of syllogisms has apparently led you to ignore the English translations of what you're arguing. There is an "if" in front of your syllogisms if you are claiming they are merely valid, not sound.

ES:
When we are testing an argument to determine its validity, we add 'if' to its premises, but this does not mean that the 'if' is a component of the premises.

POWELL:
It's probably best thought of as part of the inference, but it could be thought of as part of the premises. If you write out the syllogism into complete sentences you should see this. You can't ignore the "ifs" unless you claim the argument is sound.

ES:
You are conflating two different subjects:

S1: The argument itself
S2: The test for its validity

The argument:

It is the case that if J is married then J is a husband, and it is the case that J is married, therefore J is a husband.

POWELL:
You are confusing a valid argument with a sound argument. You are trying to claim that the argument itself is when it's treated as a sound argument. When you say things like "it is the case J is married" or "it is true that J is married" then you are treating the argument as sound. When you say things like "If it is the case that J is married" then you are treating the argument as merely valid.

ES:
To use shorthand:

p: J is married
q: J is a husband

The following is the argument:

S1: (If p then q) and (p), therefore q

The following is a test for the validity of the argument:

S2: If ((if p then q) and (p)), therefore q

Both S1 and S2 are propositions. Each is either true or false. S1 contains only one 'if' (Note that it is not saying that if something is the case THEN if something else is the case, THEN something is the case). It is making three distinct propositions:

P1: "It is the case that If p then q" (p -> q)
P2: "It is the case that p" (p)
P3: "It is the case that P1 and P2 guarantee q, and q is the case" (.: q)

POWELL:
Given your explanation, S1 is an argument claimed to be sound. S2 is an argument claimed or tested to be valid.

ES:
(Every premise of every argument implies the statement, "It is the case." This is because every premise is a proposition. This is not the same as saying that it is "true" that "It is the case")

POWELL:
I don't think so, Eric. Every premise of every SOUND argument implies the statement, "It is the case." Every premise of every MERELY VALID argument implies the statement "IF it were the case."

ES:
When we are testing for validity, (i.e. determining whether S2 is true), we are asking whether or not it is true that if P1 and P2 were true, then P3 would have to be true.

S2 is true. There is no way for the antecedent to be true and the consequent false. That is why M.P. (S1 form) is a valid argument form, meaning that any argument that follows this form is valid. It doesn't matter what the content is.

POWELL:
Unfortunately for logicians, this is not true. There are ways for M.P. form arguments to be invalid. See my discussion at "invalidating validity."

ES:
There is nothing circular here. The conclusion is not in the premises.

POWELL:
Ok, let me try a different approach, Eric.

Is the following a circular argument?

If atheism is true then God does not exist. God does not exist because atheism is true.

ES
No.

If atheism is true, then God does not exist
Atheism is true
Therefore, God does not exist

If God exists, then atheism is not true
God exists
Therefore, atheism is not true

Neither is circular.

POWELL:
If this one isn't circular then PLEASE give me a couple of different typical circular religious arguments IN COMPLETE ENGLISH SENTENCES, not in syllogistic or symbolic form.

ES:
"Pointless evil could only exist if God didn't exist. We know that God doesn't exist because pointless evil exists." (assumes knowledge that God doesn't exist and thus pointless evil exists, in order argue that the existence of pointless evil proves that God doesn't exist)

POWELL:
Thanks, Eric! Unfortunately I failed to say that I meant examples that begin with a conditional.

Anyway, doesn't this still follow the M.P.-form if I make a slight revision?

JR21. If pointless evil exists then God does not exist.
JR22. pointless evil exists.
JR23. therefore, God does not exist.

Wow, that circular argument turns out to be M.P. with only a slight modification!

ES:
"We know that the Bible is not the word of God because there is no God. We know that there is no God because the Bible is not the word of God." (assumes knowledge that God doesn't exist and thus the Bible is not the word of God, in order argue that the Bible not being the word of God proves that God doesn't exist)

POWELL:
This second one is like two M.P.'s in one.

JR24. If there is no God then the Bible is not the word of God.
JR25. there is no God.
JR26. therefore, the Bible is not the word of God.

JR27. If the Bible is not the word of God then God does not exist.
JR28. The Bible is not the word of God.
JR29. therefore, God does not exist.

By merely adding premises and conclusions derived directly from the conditionals, I turned a circular argument into two M.P.-form valid arguments! Wow.

I suspect that the person making that God-Bible circular argument was really trying to conclude that God does not exist and that the Bible is not the Word of God. He can do so in a valid (but not necessarily sound) way.

Now, Eric, could you give me a circular argument that begins with a conditional that I can't easily turn into something like M.P.? If such arguments can be so turned, doesn't that suggest to you that maybe M.P. is essentially a circular argument when claimed to be merely valid?

John Powell.

Hiramjr

May 1st 2003, 01:20 AM

To Powell

POWELL:
Your term paper analogy is getting more and more useful.

Now tell me Eric, what if I were to violate the teacher's order on writing the term paper. Would it NECESSARILY be a bad paper? The teacher might give it a bad grade for violating his instructions, but does that mean that it could not be one of the best papers ever written?

ES
I am using the analogy to highlight one essential point. That point is that if something follows a pattern, that thing is not the pattern itself.

The fact that the term paper doesn't follow the approved pattern only means that it doesn't follow the approved pattern. This says nothing about the content of the paper.

POWELL:
You seem to think that merely because an argument follows a certain form that it is or is not valid.

ES
The subject is arguments that follow the pattern of M.P. My comments have never been about 'all' arguments. A hypothetical syllogism that follows the pattern of M.P. is valid. It is valid because M.P. is a valid argument form.

POWELL:
That's not what defines whether an argument is valid or not. Surely what happened is that it was concluded by logicians that arguments that followed the M.P. form were always valid, always had the conclusion guaranteed true if the premises were true. It was not that they made up M.P. and then defined it to be a valid form without regard to whether it satisfied the usual conditions for validity, right?

ES
Yes. I haven't indicated anything otherwise.

POWELL:
You also seem to have an overly restrictive definition of "argument form."

ES
The subject has been about one argument form. I'm sorry but you really need to stay on topic and within the context of that topic. If the subject is one argument form and I make comments about that subject, then it is improper to assume that my comments somehow are about every argument form.

POWELL:
Think of a form letter. It's not necessarily one with a very abbreviated content showing broadly what needs to be filled in. It's usually one where EVERYTHING is already spelled out except for personal information of the target. My husband syllogism was similar. In that sense my statement

JR1. If J is a husband then J is a married man

is a proposition form. J is a variable that could be any individual. This proposition cannot justifiably be claimed to be true until J is identified, just like an argument in the M.P. form cannot be justifiably claimed to be sound until p and q are identified.

ES
The subject isn't about soundness.

POWELL:
Your specialized definition of argument as opposed to argument form could be useful if you were consistent about this. I think what you mean to say is that only those series of statements in which everything is spelled out and could justifiably be a sound argument do you have an argument. If parts are not identified (for example if there are variable names) then it's not quite a full argument, but just an argument form.

ES
Again, with hypothetical syllogisms, knowing everything about the premises is irrelevant to the subject of validity. It doesn't matter that J is undefined.

1. If fhujsl then trhgji
2. fhujsl
3. Therefore trhgji

This is a valid argument even if we have no idea what fhujsl or trhgji refer to. When variables are used 'in' propositions, the assumption is that they refer to some rational idea. That idea doesn't need to be known before determining validity.

POWELL:
Let me see where you make the change from "form" to argument.

Are the following arguments or just argument forms?

ES
M.P. is an argument form. M.T. is an argument form. Those argument forms are communicated through the use of variables.

p -> q
p
.: q

p -> q
~q
.: ~p

No definition is given to either p or q because the purpose for using the variables is simply to show what the forms are.

Now, when we construct arguments, we can use variables in at least two ways. One way is as a shorthand to represent whatever propositions are in our argument. Another way is to show the form of the argument.

1. If humans breathe air, then they can't breathe underwater
2. humans breathe air
3. Therefore, they can't breathe underwater

Another way of writing this is:

p: humans breathe air
q: they can't breathe underwater

1. If p then q
2. p
3. Therefore q

This use of symbology is simply a shorthand way of writing the argument. It represents the argument because the variables are defined.

The use of variables can also indicate the form of the argument.

1. p -> q
2. p
3. .: q

We can compare this form with the standard argument forms we have and we can easily see that this is an M.P. argument.

POWELL:
JR2. If p then snakes run
JR3. p
JR4. therefore, snakes run

ES
This is an argument. We can go into what p represents because we assume that it represents something.

ES:
It stipulates that principle that given (r -> w) and (r), if it were the case that both (r -> w) and (r) were true, then this would guarantee that w would be the case. That is a proposition, it is a definition.

The definition isn't based on the 'content' of r or w. It is based on the logical relationship between (r -> w) and (r), between a hypothetical and the affirmation of its antecedent. It is impossible for both to be true and w false. Thus, if an argument follows this form, then it is valid.

POWELL:
NOT NECESSARILY! It has been concluded by logicians that this is true about M.P., but that doesn't mean they were right.

ES
Without any proof to the contrary, this is what we go with.

POWELL:
I deny that the definition of valid is any argument that follows the M.P., M.T., or other such forms.

ES
I am not defining the term "valid." I am simply stating a fact. An argument that follows the pattern of M.P. is valid. Why? Because the M.P. form satisfies the criteria for validity, which is why it is a valid argument form.

POWELL:
The following is an invalid form, right?

JR17. p
JR18. therefore, q

ES
It is simply a proposition. p -> q

POWELL:
But, here's a valid (by my definition) argument that follows that invalid form.

JR19. J is a married man
JR20. Therefore, J is a husband.

ES
It is a true proposition. It is not a hypothetical syllogism.

POWELL:
That reminds me that I forgot to ask you something. Is a circular argument valid, Eric?

ES
Yes.

ES:
Validity indicates that we are guaranteed to get to the conclusion if the premises were true. Think of it in terms of driving somewhere. If a set of directions is correct, then if you took that path, you would be guaranteed to reach your destination. This doesn't mean that you couldn't get to your destination by some other means.

POWELL:
You come up with some great analogies, Eric. Now tell me, if you were to do your best to follow the directions of the best and most honest direction giver in the universe who claimed they were correct directions would you NECESSARILY arrive at your destination or is it possible that even following those instructions you'd end up in a black hole that appeared suddenly?

In like manner, so-called valid deductive arguments do not absolutely guarantee the conclusion will be true even if the premises were true. They only guarantee that very probably the conclusion will be true if the premises were true.

ES
You're getting into the realm of epistemology which is a different subject. It could be the case that we all are living in the Matrix reality where nothing is what it seems. That is a logical possibility.

There is a distinction between absolute certainty and virtual certainty. Absolute certainty involves affirming propositions such that ones affirmation can't be wrong and that which is affirmed can't be false. We don't live according to absolute certainty.

We live according to virtual certainty, which entails affirming propositions such that ones affirmation is believed to be rational beyond an epistemological doubt, and the proposition that is affirmed is believed to be true beyond this reasonable doubt.

Yes, we 'could' be living in the Matrix, but we have no reason to believe this is the case. We live according to epistemological preconditions (essential assumptions), such as the "laws of logic" obtain and our perception and reasoning abilities are reliable.

Thus, a given argument is believed to be valid, its premises are believed to be true, and it is believed to be sound. Could that belief be false? Yes.

ES:
You are conflating two different subjects:

S1: The argument itself
S2: The test for its validity

The argument:

It is the case that if J is married then J is a husband, and it is the case that J is married, therefore J is a husband.

POWELL:
You are confusing a valid argument with a sound argument. You are trying to claim that the argument itself is when it's treated as a sound argument. When you say things like "it is the case J is married" or "it is true that J is married" then you are treating the argument as sound. When you say things like "If it is the case that J is married" then you are treating the argument as merely valid.

ES
No John. I'm sorry, but please listen. An argument has to be proposed before it can be deemed to be valid or sound. Validity and soundness are assessments of the argument. For Every argument that is proposed it is assumed that the proponent claims that the argument is valid, its premises are true and thus is sound. Each of these subjects is addressed when we evaluate the argument to determine whether or not these claims are true.

The argument above, at this point, is merely an argument. It is not a "valid argument" until it is demonstrated to be so. It is not a "sound argument" until it is demonstrated to be so.

We have to start with S1 before addressing S2.

POWELL:
Given your explanation, S1 is an argument claimed to be sound. S2 is an argument claimed or tested to be valid.

ES
No. S1 is merely an argument. That it is claimed to be valid, its premises true and is sound is irrelevant. S2 indicates how the argument is being tested for validity. If S2 is true, then the argument is valid.

The point is that when we evaluate an argument, we have to evaluate the argument. S1 is the argument. S2 is not the argument.

POWELL:
If this one isn't circular then PLEASE give me a couple of different typical circular religious arguments IN COMPLETE ENGLISH SENTENCES, not in syllogistic or symbolic form.

ES:
"Pointless evil could only exist if God didn't exist. We know that God doesn't exist because pointless evil exists." (assumes knowledge that God doesn't exist and thus pointless evil exists, in order argue that the existence of pointless evil proves that God doesn't exist)

POWELL:
Thanks, Eric! Unfortunately I failed to say that I meant examples that begin with a conditional.

Anyway, doesn't this still follow the M.P.-form if I make a slight revision?

JR21. If pointless evil exists then God does not exist.
JR22. pointless evil exists.
JR23. therefore, God does not exist.

Wow, that circular argument turns out to be M.P. with only a slight modification!

ES
The argument is circular because of what the second premise means. It isn't circular because of the argument form. The fact that you can take a circular argument and put it into a given argument form does not somehow prove that the argument form is circular.

POWELL:
Now, Eric, could you give me a circular argument that begins with a conditional that I can't easily turn into something like M.P.? If such arguments can be so turned, doesn't that suggest to you that maybe M.P. is essentially a circular argument when claimed to be merely valid?

ES
I'm not sure what point you're trying to prove here. If I invent an argument that contains fifteen propositions and a conclusion, and it is the case that the conclusion is found somewhere in the premises, and it is also the case that this argument can't be reduced to two premises and a conclusion, then what exactly would this prove?

Woman

May 1st 2003, 02:08 AM

Eric,

Is this circular logic? It seems to have the conclusion in the second premise. This is an argument we hear a lot around here and although skeptics believe it is just so much smoke and mirrors, the believers have a priori that the Bible is the word of God. Just interested in your comments. I have enjoyed this discussion tremendously. John brought up some great questions I would have asked myself.

If the Bible is divinely inspired, then Christ rose
Christ said that the Bible was divinely inspired
Therefore Christ rose

W.

Socrates

May 1st 2003, 02:27 AM

Woman:If the Bible is divinely inspired, then Christ rose
Christ said that the Bible was divinely inspired
Therefore Christ roseIt is an application of presuppositional thinking. Every philosophical system starts with axioms, which by definition cannot be proven. Here, the axiom is that the Bible is divinely inspired, and this axiom makes much sense of the evidence of the Resurrection of Christ, as well as Earth history and even the ability to think rationally in the first place.

It is, however, possible to argue on the following lines, like the evidentialist John Warwick Montgomery:

The New Testament, even without a presupposition of divine authorship, is historically reliable by all the normal criteria of historical assessment.

The New Testament evidence is overwhelming that the man Jesus of Nazareth rose from the dead on the third day.

The same NT also records that Jesus identified Himself with the god of Israel. The Resurrection is strong validation for these claims.

Therefore Jesus really was who He claimed to be.

And these same reliable NT documents record that He said "Scripture cannot be broken" and used "Scripture said" and
"God said" interchangeably. Further, Jesus explicitly affirmed the historicity of Scripture in the most common places that biblioskeptics and their compromising churchian allies love to attack it -- recent Creation, the Flood and Ark, Jonah and the great sea creature. (See The Authority of Scripture (http://www.answersingenesis.org/docs2/4306apol_v3n21994.asp) for further explanation as well as demolishing claims of circularity).

Therefore on these grounds, although merely starting with the NT as historically reliable, one can deduce Biblical inerrancy.

Hiramjr

May 1st 2003, 12:17 PM

To Woman:

W:
Is this circular logic? It seems to have the conclusion in the second premise. This is an argument we hear a lot around here and although skeptics believe it is just so much smoke and mirrors, the believers have a priori that the Bible is the word of God. Just interested in your comments. I have enjoyed this discussion tremendously. John brought up some great questions I would have asked myself.

If the Bible is divinely inspired, then Christ rose
Christ said that the Bible was divinely inspired
Therefore Christ rose

ES
It can be circular.

First of all, we have distinguish between two different subjects:

S1: The resurrection of Christ
S2: The divine inspiration of the Bible

S1 is a subject of history, while S2 is a subject of authority.

When any historical event is proposed, particularly involving people and their actions, it is either believed or not believed based on the testimony provided to support it. Socrates either taught people his ideas or he didn't. We weren't there, so when we read accounts that say that this is true, we either believe those accounts or we don't.

The accounts don't have to be divinely inspired before we believe them. With history, we have to rely upon certain assumptions about the authors. We assume that some degree of authority is associated with their accounts such that they are believable.

As long as there is no reasonable doubt associated with the authors or their accounts, then we believe them, i.e. we trust that the authors are seeking to honestly communicate that certain events occurred and that those events actually occurred, until given sufficient reason to believe otherwise. This is an exercise of (secular) faith.

The subject of divine inspiration, in this context, means that the reason we can trust that certain historical accounts are correct and thus the events of history recorded actually occurred is because the author is God.

Again, we already believe that some historical events occurred because of our trust in those who recorded those events, even though those authors may have no affiliation with God. So, the introduction of divine inspiration is adding credibility to the biblical authors. It is introducing a guarantee. This introduction however is not required before a person can believe that the authors communicated factual events.

What the above argument seeks to prove, in part, is that the proposition, "Christ rose from the dead," is true because the authority of the account that records it guarantees that it is true.

This means that, for example, if a non-inspired account said that X occurred, this could provide grounds for believing that X occurred, but it could be the case that X didn't occur. If however an inspired account said that X occurred, then X occurred (i.e., it is believable beyond a reasonable doubt). The factor of inspiration affords the greater confidence that X occurred.

1. If the Bible is divinely inspired, then every historical event it records actually occurred.
2. The Bible is divinely inspired.
3. Hence, every historical event it records occurred.
4. The resurrection of Christ is an event recorded in the Bible.
5. Therefore, the resurrection of Christ occurred.

This argument depends on the truth of (2). The original argument (for the sake of argument) seeks to substantiate (2). The problem occurs with how it goes about doing this.

P1: Christ said that the Bible was divinely inspired

The question is, How does Christ saying that the Bible is inspired somehow prove that it is inspired? Some degree of authority is being associated with Christ. If that is authority is grounded in the assumption that the Bible is inspired, then the original argument is circular.

[The Bible is inspired.
The Bible records that] Christ said that the Bible is inspired.
Therefore, the Bible is inspired.

This is how the average nontheist (and even the theist) reads the original argument.

But it doesn't necessarily have to read this way. (There are other issues associated with the original argument, but I am here only dealing with the issue of circularity)

Suppose we are digging in a certain area and we uncover some interesting rocks. We show them to person who looks at them and announces that they are valuable diamonds. The question arises, Why should we believe him?

Suppose he provides credentials to demonstrate that he is an expert diamond merchant. We then associate a degree of authority to him. We believe his pronouncement based on what he has done to demonstrate that he knows what he is talking about.

We don't require divine inspiration before we can place our trust in the man's pronouncement.

A similar situation is associated with Christ. During the days of His ministry on earth, the immediate assumption about Him was not that He was the Son of God. He pointed to His works to substantiate His claims.

John 10
37 "If I do not do the works of My Father, do not believe Me; 38 but if I do them, though you do not believe Me, believe the works, so that you may know and understand that the Father is in Me, and I in the Father."

When a person reads the accounts of history recorded in the Bible, there does not first have to be the assumption that the Bible is inspired. The Bible is an anthology of different historical records.

6. If Christ performs miracles to substantiate what He says, then what He says is true.
7. Christ performed miracles to substantiate to substantiate what He said.
8. Hence, what He said is true.
9. Christ said that the Bible was inspired.
10. Therefore, the Bible is inspired.

The substantiation for (7) is not inspiration, rather it is the historical records of the NT. Inspiration is a conclusion attributed to the records (in the context fo the argument), but the primary source of data is the history.

Now, the nontheist does not believe that the NT or OT records are true or that they are inspired, but this is immaterial to the structure of the argument. It only means that he would deny (7). Okay, fine, but that doesn't mean that the argument is circular.

But ultimately, believing in God and in the inspiration of the Bible is not a matter conventional evidential belief. It is not an "a priori" belief either.

John 6
44 "No one can come to Me unless the Father who sent Me draws him; and I will raise him up on the last day. 45 "It is written in the prophets, 'And they shall all be taught of God.' Everyone who has heard and learned from the Father, comes to Me.

John 8
47 "He who is of God hears the words of God; for this reason you do not hear them, because you are not of God."

Evidential arguments are tools that can be used to turn a person's attention toward God, but the ground of a person's faith is the apprehension of God via His Spirit. That isn't something that can be put in a bottle and given to someone.

Woman

May 1st 2003, 05:11 PM

Hiram,

I sincerely appreciate your studied and thoughtful response. It answers many questions. Thank you for taking the time to address my quiery so thoroughly.

W.

John Powell

May 1st 2003, 06:04 PM

POWELL:
I appreciate your participation, Eric.

POWELL:
Your term paper analogy is getting more and more useful.

Now tell me Eric, what if I were to violate the teacher's order on writing the term paper. Would it NECESSARILY be a bad paper? The teacher might give it a bad grade for violating his instructions, but does that mean that it could not be one of the best papers ever written?

ES:
I am using the analogy to highlight one essential point. That point is that if something follows a pattern, that thing is not the pattern itself.

The fact that the term paper doesn't follow the approved pattern only means that it doesn't follow the approved pattern. This says nothing about the content of the paper.

POWELL:
Right.

Perhaps what you're calling the pattern or the form, namely

p -> q, p, therefore q

is itself an argument in the M.P. form. Perhaps this is similar to drawing the ideal circle. That physically can't be done, yet we have an idea of what it would be like. Perhaps anytime you try to represent the argument form you will necessarily be creating an argument itself.

A problem I have with this distinction of yours is your insistence that what you call an "argument form" cannot be considered a valid argument itself. That seems to be an unwise distinction.

POWELL:
You seem to think that merely because an argument follows a certain form that it is or is not valid.

ES:
The subject is arguments that follow the pattern of M.P. My comments have never been about 'all' arguments. A hypothetical syllogism that follows the pattern of M.P. is valid. It is valid because M.P. is a valid argument form.

POWELL:
That's not what defines whether an argument is valid or not. Surely what happened is that it was concluded by logicians that arguments that followed the M.P. form were always valid, always had the conclusion guaranteed true if the premises were true. It was not that they made up M.P. and then defined it to be a valid form without regard to whether it satisfied the usual conditions for validity, right?

ES:
Yes. I haven't indicated anything otherwise.

POWELL:
You also seem to have an overly restrictive definition of "argument form."

ES:
The subject has been about one argument form. I'm sorry but you really need to stay on topic and within the context of that topic. If the subject is one argument form and I make comments about that subject, then it is improper to assume that my comments somehow are about every argument form.

POWELL:
I'm sorry to appear so argumentative, but I suspected that you were being inconsistent in your definitions and the discussion seems to bear this out in some cases, but not all those I thought.

POWELL:
Think of a form letter. It's not necessarily one with a very abbreviated content showing broadly what needs to be filled in. It's usually one where EVERYTHING is already spelled out except for personal information of the target. My husband syllogism was similar. In that sense my statement

JR1. If J is a husband then J is a married man

is a proposition form. J is a variable that could be any individual. This proposition cannot justifiably be claimed to be true until J is identified, just like an argument in the M.P. form cannot be justifiably claimed to be sound until p and q are identified.

ES:
The subject isn't about soundness.

POWELL:
Then I wish you would stop speaking in terms that imply to me that you're speaking about soundness.

If it's not about soundness then we should avoid saying things like "It is the case . . ." and "It is true that . . ." with respect to premises and conclusions of the arguments and remember to say "If it is the case . . ." and "If it were true that. . ."

POWELL:
Your specialized definition of argument as opposed to argument form could be useful if you were consistent about this. I think what you mean to say is that only those series of statements in which everything is spelled out and could justifiably be a sound argument do you have an argument. If parts are not identified (for example if there are variable names) then it's not quite a full argument, but just an argument form.

ES:
Again, with hypothetical syllogisms, knowing everything about the premises is irrelevant to the subject of validity. It doesn't matter that J is undefined.

1. If fhujsl then trhgji
2. fhujsl
3. Therefore trhgji

This is a valid argument even if we have no idea what fhujsl or trhgji refer to.

POWELL:
Then why isn't it a valid argument if I use p and q or r and w in place of fhujsl and trhgji? I have no idea what p and q refer to either.

ES:
When variables are used 'in' propositions, the assumption is that they refer to some rational idea. That idea doesn't need to be known before determining validity.

POWELL:
That is what I assume when I use p and q. Could it be, Eric, that M.P. when written with p's and q's is an argument, but it is also representative of an argument form just like your fhujsl / trhgji example?

POWELL:
Let me see where you make the change from "form" to argument.

Are the following arguments or just argument forms?

ES:
M.P. is an argument form. M.T. is an argument form. Those argument forms are communicated through the use of variables.

p -> q
p
.: q

p -> q
~q
.: ~p

No definition is given to either p or q because the purpose for using the variables is simply to show what the forms are.

Now, when we construct arguments, we can use variables in at least two ways. One way is as a shorthand to represent whatever propositions are in our argument. Another way is to show the form of the argument.

1. If humans breathe air, then they can't breathe underwater
2. humans breathe air
3. Therefore, they can't breathe underwater

Another way of writing this is:

p: humans breathe air
q: they can't breathe underwater

1. If p then q
2. p
3. Therefore q

This use of symbology is simply a shorthand way of writing the argument. It represents the argument because the variables are defined.

The use of variables can also indicate the form of the argument.

1. p -> q
2. p
3. .: q

We can compare this form with the standard argument forms we have and we can easily see that this is an M.P. argument.

POWELL:
You seem to have gone back to the idea that a syllogism only counts as an argument if the variables are identified. However, fhujsl and trhgji have not been identified, so how can you call a syllogism using them part of an argument rather than merely an argument form?

POWELL:
JR2. If p then snakes run
JR3. p
JR4. therefore, snakes run

ES
This is an argument. We can go into what p represents because we assume that it represents something.

POWELL:
How is that significantly different from using p and q? There also we assume they represent something don't we?

ES:
It stipulates that principle that given (r -> w) and (r), if it were the case that both (r -> w) and (r) were true, then this would guarantee that w would be the case. That is a proposition, it is a definition.

The definition isn't based on the 'content' of r or w. It is based on the logical relationship between (r -> w) and (r), between a hypothetical and the affirmation of its antecedent. It is impossible for both to be true and w false. Thus, if an argument follows this form, then it is valid.

POWELL:
NOT NECESSARILY! It has been concluded by logicians that this is true about M.P., but that doesn't mean they were right.

ES:
Without any proof to the contrary, this is what we go with.

POWELL:
YES! Thank you, Eric.

I have presented in the thread "invalidating validity" discussion / arguments supporting the idea that so-called valid deductive arguments are not the "certain" things they're advertised to be by introductory logic texts. Until those arguments are adequately rebutted by you then for you to claim otherwise at this point would suffer the fallacies of argument by assertion, argument by ignorance and / or argumentum ad verecundiam.

Actually, your comments below about "virtual" rather than "absolute" suggest you are already in considerable agreement with me.

POWELL:
I deny that the definition of valid is any argument that follows the M.P., M.T., or other such forms.

ES:
I am not defining the term "valid." I am simply stating a fact. An argument that follows the pattern of M.P. is valid. Why? Because the M.P. form satisfies the criteria for validity, which is why it is a valid argument form.

POWELL:
Excellent. What if it doesn't satisfy the criterion, Eric?

POWELL:
The following is an invalid form, right?

JR17. p
JR18. therefore, q

ES:
It is simply a proposition. p -> q

POWELL:
What a minute, Eric. I clearly identified the premise and the conclusion in a syllogism, therefore it's an argument or at least an argument form. It's not a proposition unless I put it all in a single line of the syllogism, right?

I'm claiming

If premise p were true then it must be true that the conclusion q is true.

If I can't do this, Eric, then I can claim that the "p" and "therefore q" of M.P. is also only a proposition, right?

It's true I could have made it a conditional, but I didn't.

POWELL:
But, here's a valid (by my definition) argument that follows that invalid form.

JR19. J is a married man
JR20. Therefore, J is a husband.

ES:
It is a true proposition. It is not a hypothetical syllogism.

POWELL:
What do I have to do to make it an argument with a single premise and a single conclusion?

POWELL:
That reminds me that I forgot to ask you something. Is a circular argument valid, Eric?

ES:
Yes.

POWELL:
Good.

ES:
Validity indicates that we are guaranteed to get to the conclusion if the premises were true. Think of it in terms of driving somewhere. If a set of directions is correct, then if you took that path, you would be guaranteed to reach your destination. This doesn't mean that you couldn't get to your destination by some other means.

POWELL:
You come up with some great analogies, Eric. Now tell me, if you were to do your best to follow the directions of the best and most honest direction giver in the universe who claimed they were correct directions would you NECESSARILY arrive at your destination or is it possible that even following those instructions you'd end up in a black hole that appeared suddenly?

In like manner, so-called valid deductive arguments do not absolutely guarantee the conclusion will be true even if the premises were true. They only guarantee that very probably the conclusion will be true if the premises were true.

ES:
You're getting into the realm of epistemology which is a different subject. It could be the case that we all are living in the Matrix reality where nothing is what it seems. That is a logical possibility.

There is a distinction between absolute certainty and virtual certainty. Absolute certainty involves affirming propositions such that ones affirmation can't be wrong and that which is affirmed can't be false. We don't live according to absolute certainty.

We live according to virtual certainty, which entails affirming propositions such that ones affirmation is believed to be rational beyond an epistemological doubt, and the proposition that is affirmed is believed to be true beyond this reasonable doubt.

Yes, we 'could' be living in the Matrix, but we have no reason to believe this is the case. We live according to epistemological preconditions (essential assumptions), such as the "laws of logic" obtain and our perception and reasoning abilities are reliable.

Thus, a given argument is believed to be valid, its premises are believed to be true, and it is believed to be sound. Could that belief be false? Yes.

POWELL:
THANK YOU!

I have a beef with introductory logic texts that don't make this clear to their students which I think has contributed to lots of philosophy students claiming things about valid deductive arguments that just isn't so.

Copi & Cohen:
When an argument makes the claim that its premisses (if true) provide irrefutable grounds for the truth of its conclusion, that claim will be either correct or not correct. If it is correct, that argument is valid. If it is not correct (that is, if the premisses when true fail to establish the conclusion irrefutably), that argument is invalid.

For logicians, therefore, the term validity is applicable only to deductive arguments. To say that a deductive argument is valid is to say that it is not possible for its conclusion to be false if its premisses are true. Thus we define "validity" as follows: A deductive argument is valid when, if its premisses are true, its conclusion must be true.

. . .

A deductive argument is one whose conclusion is claimed to follow from its premisses with absolute necessity.

POWELL:
I doubt that Copi & Cohen are alone in these exaggerated claims. In place of the bold text they probably should have said things like "provide VIRTUALLY irrefutable grounds" and "is VIRTUALLY IMPOSSIBLE for its conclusion to be false" and "with VIRTUALLY absolute necessity." However, if they did that then they might have to call their deductive arguments, statistical arguments instead, which is one of my major conclusions of the "invalidating validity" discussion.

ES:
You are conflating two different subjects:

S1: The argument itself
S2: The test for its validity

The argument:

It is the case that if J is married then J is a husband, and it is the case that J is married, therefore J is a husband.

POWELL:
You are confusing a valid argument with a sound argument. You are trying to claim that the argument itself is when it's treated as a sound argument. When you say things like "it is the case J is married" or "it is true that J is married" then you are treating the argument as sound. When you say things like "If it is the case that J is married" then you are treating the argument as merely valid.

ES:
No John. I'm sorry, but please listen. An argument has to be proposed before it can be deemed to be valid or sound. Validity and soundness are assessments of the argument. For Every argument that is proposed it is assumed that the proponent claims that the argument is valid, its premises are true and thus is sound. Each of these subjects is addressed when we evaluate the argument to determine whether or not these claims are true.

The argument above, at this point, is merely an argument. It is not a "valid argument" until it is demonstrated to be so. It is not a "sound argument" until it is demonstrated to be so.

We have to start with S1 before addressing S2.

POWELL:
I should have realized this problem might come up earlier since the philosopher Tim Holt said something very similar to me. You are correct that VERY MUCH USUALLY when an argument is presented, it is presented in the sense of "It is true that . . .," The rare counter-examples would be where the nature of valid and sound arguments and such things are under discussion, such as in an introductory logic class. However, Eric, when it comes to debating things like religion between theists and atheists whose beliefs are so diametrically opposed this assumption that propositions are claimed to be true is MUCH LESS SELDOM the case.

For example, if I, someone who does not believe the Jesus of the Bible ever existed, were to make the following argument to you, a theist,

JS1. If Jesus said what is recorded in John 18:20 then Jesus lied.
JS2. Jesus said what is recorded in John 18:20.
JS3. therefore, Jesus lied.

you would be unwise to assume that I am claiming that Jesus lied when he spoke the words in John 18:20. I would be claiming that this is a valid argument and that you, as a theist who believes the Bible, should conclude that it's a sound argument and, therefore, that Jesus lied.

You cannot justifiably assume that the religious arguments I present are believed by me to be sound, nor I with those you present to atheists such as myself.

POWELL:
Given your explanation, S1 is an argument claimed to be sound. S2 is an argument claimed or tested to be valid.

ES:
No. S1 is merely an argument. That it is claimed to be valid, its premises true and is sound is irrelevant. S2 indicates how the argument is being tested for validity. If S2 is true, then the argument is valid.

The point is that when we evaluate an argument, we have to evaluate the argument. S1 is the argument. S2 is not the argument.

POWELL:
I still disagree. It should not be assumed at forums like tweb that propositions in arguments are claimed to be true.

Is the following a valid argument, Eric?

JS4. If dogs fly then snakes sing opera.
JS5. dogs fly.
JS6. therefore, snakes sing opera.

Yes, right?

However, Eric, do you seriously think that I or anyone else by proposing this syllogism claim that dogs fly or snakes sing opera? OF COURSE NOT. Therefore, merely presenting an argument does NOT NECESSARILY mean that the person is asserting the premises and conclusion are true. You should ASK THEM whether they are doing so if there's reason to think this might be an unusual situation.

That's a weakness of the syllogism method. It doesn't indicate whether the argument is claimed to be sound or merely valid.

POWELL:
If this one isn't circular then PLEASE give me a couple of different typical circular religious arguments IN COMPLETE ENGLISH SENTENCES, not in syllogistic or symbolic form.

ES:
"Pointless evil could only exist if God didn't exist. We know that God doesn't exist because pointless evil exists." (assumes knowledge that God doesn't exist and thus pointless evil exists, in order argue that the existence of pointless evil proves that God doesn't exist).

POWELL:
Thanks, Eric! Unfortunately I failed to say that I meant examples that begin with a conditional.

Anyway, doesn't this still follow the M.P.-form if I make a slight revision?

JR21. If pointless evil exists then God does not exist.
JR22. pointless evil exists.
JR23. therefore, God does not exist.

Wow, that circular argument turns out to be M.P. with only a slight modification!

ES:
The argument is circular because of what the second premise means. It isn't circular because of the argument form. The fact that you can take a circular argument and put it into a given argument form does not somehow prove that the argument form is circular.

POWELL:
Eric, if circular arguments can be so easily turned into valid M.P.-type arguments, then doesn't that suggest that M.P. is an essentially circular argument?

POWELL:
Now, Eric, could you give me a circular argument that begins with a conditional that I can't easily turn into something like M.P.? If such arguments can be so turned, doesn't that suggest to you that maybe M.P. is essentially a circular argument when claimed to be merely valid?

ES:
I'm not sure what point you're trying to prove here. If I invent an argument that contains fifteen propositions and a conclusion, and it is the case that the conclusion is found somewhere in the premises, and it is also the case that this argument can't be reduced to two premises and a conclusion, then what exactly would this prove?

POWELL:
All I want is one conditional and what is needed to produce what you consider a circular argument relative to that conditional so that I can demonstrate again how easily it is to convert it into M.P.

I think it helps to show that M.P. when claimed to be merely valid, not sound, is an essentially circular argument.

Here let me.

If atheism is true then God does not exist. God does not exist because atheism is true.

The circular form:

JS7. If atheism is true then God does not exist.
- - - - therefore - - - -
JS8. God does not exist because atheism is true.

Or, our old friend, M.P.:

JS9. If atheism is true then God does not exist.
Js10. Atheism is true.
- - - - - therefore - - - - -
JS11. God does not exist.

John Powell

John Powell

May 1st 2003, 08:17 PM

WOMAN (to Eric):
Is this circular logic? . . .

If the Bible is divinely inspired, then Christ rose Christ said that the Bible was divinely inspired Therefore Christ rose

POWELL:
That's a good question. Here's the argument in syllogism form:

1. If the Bible is divinely inspired then Christ rose.
2. Christ said that the Bible was divinely inspired.
- - - - - therefore - - - - -
3. Christ rose.

This is not even a valid argument as written, since there is no premise declaring that what Christ says must be true. so it can't very well be a circular argument since circular arguments are valid.

By adding the missing premise, the argument becomes valid. I think the revised argument is essentially circular if claimed to be merely valid, not sound, because it includes only M.P.-like structure.

4. If the Bible is divinely inspired then Christ rose.
5. If Christ said the Bible is divinely inspired then the Bible is divinely inspired.
6. Christ said the Bible is divinely inspired.
7. therefore (by 5, 6), the Bible is divinely inspired.
8. therefore (by 4, 7), Christ rose.

Most skeptics would deny premise 5, but I would even deny premise 6 since I don't believe Jesus existed.

With slight revision it becomes valid, but possibly unsound, M.P. in two different ways.

9. If the Bible is divinely inspired and it says Christ rose then Christ rose.
10. The Bible is divinely inspired and it says that Christ rose.
- - - - - therefore - - - - -
11. Christ rose.

Here's the other way:

12. If Christ says the Bible is inspired and the Bible says that Christ rose then Christ rose.
13. Christ says the Bible is inspired and the Bible says that Christ rose.
- - - - - therefore - - - - -
14. Christ rose.

I'm surprised that Eric HIRAMJR and Socrates looked as hard as they did for ways to see the argument as non-circular.

John Powell

Hiramjr

May 1st 2003, 10:54 PM

To Powell

POWELL:
Perhaps what you're calling the pattern or the form, namely

p -> q, p, therefore q

is itself an argument in the M.P. form.

ES
Just as context determines the meaning of words, context determines the meaning of the use of variables. As I have already said, if we define what the variables refer to, then we are dealing with an argument. If the variables are used merely to show the logical order of the argument, then we are dealing with the argument's form. We can take that form and compare it to the existing valid argument forms we have.

I didn't make up the concept of a valid argument form. A valid argument form is a pattern whereby if an argument fits that pattern, the argument is valid. It is valid because everything we know of logic and rational thought tells us that, given (p -> q) and (p), if both propositions were both true, then there is no way for q to be false.

We therefore have three distinct subjects:

S1: The argument
S2: The argument's form
S3: The valid argument forms of formal logic

I don't think there is really much more I can say about this. I don't see the difficulty.

ES
The subject isn't about soundness.

POWELL:
Then I wish you would stop speaking in terms that imply to me that you're speaking about soundness.

If it's not about soundness then we should avoid saying things like "It is the case . . ." and "It is true that . . ." with respect to premises and conclusions of the arguments and remember to say "If it is the case . . ." and "If it were true that. . ."

ES
As I have already said, every argument entails that its propositions are by implication worded, "It is the case that..." This does not mean that it is true "It is the case that..."

We can't find ourselves looking only at 'sentences' to the exclusion of the context in which they are written. If the topic of this thread is about M.P. and validity, then it makes no sense to look at a sentence and assume that it must be dealing with soundness because it "looks" like it does.

I think this is a recurring problem throughout this thread. You're not reading words according to the context in which they are presented.

You say: "That's a weakness of the syllogism method. It doesn't indicate whether the argument is claimed to be sound or merely valid."

The "syllogism method" is not designed to deal with whatever claim is being made about an argument. It is designed to logically order and test whatever claim is made about an argument. The context in which the argument is presented indicates what claim is being made about the argument.

POWELL:
You seem to have gone back to the idea that a syllogism only counts as an argument if the variables are identified. However, fhujsl and trhgji have not been identified, so how can you call a syllogism using them part of an argument rather than merely an argument form?

ES
Those are intended to be words, not variables.

POWELL:
The following is an invalid form, right?

JR17. p
JR18. therefore, q

ES:
It is simply a proposition. p -> q

POWELL:
What a minute, Eric. I clearly identified the premise and the conclusion in a syllogism, therefore it's an argument or at least an argument form. It's not a proposition unless I put it all in a single line of the syllogism, right?

I'm claiming

If premise p were true then it must be true that the conclusion q is true.

If I can't do this, Eric, then I can claim that the "p" and "therefore q" of M.P. is also only a proposition, right?

ES
If you are claiming, if p then q, then all you have is a proposition. p -> q

p
.: q

This isn't any kind of an argument form. There is nothing indicated about p from which to make the inference to q.

A deductive argument is one whose conclusion is claimed to follow from its premisses with absolute necessity.

POWELL:
I doubt that Copi & Cohen are alone in these exaggerated claims. In place of the bold text they probably should have said things like "provide VIRTUALLY irrefutable grounds" and "is VIRTUALLY IMPOSSIBLE for its conclusion to be false" and "with VIRTUALLY absolute necessity." However, if they did that then they might have to call their deductive arguments, statistical arguments instead, which is one of my major conclusions of the "invalidating validity" discussion.

ES
Although I understand your concerns here, I think that you're just not recognizing the conventional meaning of words.

Suppose I have a bucket and I fill it with water. The bucket is absolutely filled with water. The modifier "absolutely" is related to the size of the bucket. The claim is not that absolutely all water is in the bucket.

When we are dealing with logic, we are dealing with the "size" of our rational abilities. In other words, if we as subjective observers and logicians are limited in what we can truly know with certainty, then to say that we know something "absolutely" is not necessarily to claim that we have attained to absolute certainty (our "knowing" cannot be wrong and what we know cannot be false).

To claim that we logically know something "absolutely" generally means that we know it to the full extent of our abilities. It means that if our rational abilities allow for us to attain to virtual certainty, then any subject that is known with virtual certainty is known "absolutely," i.e. known to the full extent of our rational abilities.

When we say that our confidence is less than absolute, this means that we don't know something to the full extent of our rational abilities. This generally means that there is some reasonable doubt that prevents "knowing" with absolute virtual certainty, if you will.

POWELL:
Eric, if circular arguments can be so easily turned into valid M.P.-type arguments, then doesn't that suggest that M.P. is an essentially circular argument?

ES
Of course not. If a largely incoherent term paper can follow a proper format, does this make that format incoherent?

POWELL:
Here let me.

If atheism is true then God does not exist. God does not exist because atheism is true.

The circular form:

JS7. If atheism is true then God does not exist.
- - - - therefore - - - -
JS8. God does not exist because atheism is true.

ES
The form of the argument is the following:

p -> q
q
.: p

1. If atheism is true, then God does not exist
2. God does not exist (because atheism is true)
3. Therefore, atheism is true

The argument is circular because the conclusion is found in the second premise. Now, does the fact that this argument is circular mean that every argument that follows M.P. form is circular? Of course not. The argument’s form is invalid. Does this mean that M.P. itself somehow incorporates circular reasoning? No. M.P. operates according to logical principles. Given (p -> q) and (p), if both propositions were true, then q would be true. There is nothing circular here.

Hiramjr

May 1st 2003, 11:03 PM

WOMAN (to Eric):
Is this circular logic? . . .

If the Bible is divinely inspired, then Christ rose Christ said that the Bible was divinely inspired Therefore Christ rose

Powell
I'm surprised that Eric HIRAMJR and Socrates looked as hard as they did for ways to see the argument as non-circular.

ES
I indicated that the argument would be circular in one context but not another. Circularity is an informal fallacy not a formal fallacy. This means that we determine circularity by examining what the propositions mean.

nomad

May 2nd 2003, 10:13 AM

hey john, just wanted to say thanks for the conversation, and i haven't forgotten about you but i think we're close enough to agreement i'm just going to read along now :)

John Powell

May 4th 2003, 12:57 AM

POWELL:
Perhaps what you're calling the pattern or the form, namely

p -> q, p, therefore q

is itself an argument in the M.P. form.

ES:
Just as context determines the meaning of words, context determines the meaning of the use of variables. As I have already said, if we define what the variables refer to, then we are dealing with an argument. If the variables are used merely to show the logical order of the argument, then we are dealing with the argument's form. We can take that form and compare it to the existing valid argument forms we have.

POWELL:
This seems to be good.

ES:
I didn't make up the concept of a valid argument form. A valid argument form is a pattern whereby if an argument fits that pattern, the argument is valid. It is valid because everything we know of logic and rational thought tells us that, given (p -> q) and (p), if both propositions were both true, then there is no way for q to be false.

POWELL:
Ok.

ES:
We therefore have three distinct subjects:

S1: The argument
S2: The argument's form
S3: The valid argument forms of formal logic

I don't think there is really much more I can say about this. I don't see the difficulty.

POWELL:
I was not used to having M.P. denied as a valid argument. You were the first. I suspect that the vast majority of former logic students, if asked the following question

- - - - -
Is the following syllogism a valid argument?

JT1. If p then q.
JT2. p.
JT3. therefore, q.
- - - - -

and given only the choices "yes" or "no," would answer "yes." Don't you agree, Eric?

ES:
The subject isn't about soundness.

POWELL:
Then I wish you would stop speaking in terms that imply to me that you're speaking about soundness.

If it's not about soundness then we should avoid saying things like "It is the case . . ." and "It is true that . . ." with respect to premises and conclusions of the arguments and remember to say "If it is the case . . ." and "If it were true that. . ."

ES:
As I have already said, every argument entails that its propositions are by implication worded, "It is the case that..." This does not mean that it is true "It is the case that..."

We can't find ourselves looking only at 'sentences' to the exclusion of the context in which they are written. If the topic of this thread is about M.P. and validity, then it makes no sense to look at a sentence and assume that it must be dealing with soundness because it "looks" like it does.

POWELL:
When something is written in a syllogism form it might look like the statements are all affirmative to you (and so I would say claimed to be sound), but that's not what they necessarily look like to me. For normal arguments I would agree with you, but not necessarily when discussing highly controversial topics like theism-atheism or when discussing whether M.P. is circular or whether so-called valid arguments really are. In those cases and others you should not assume statements are affirmative "it is the case . . .", but merely hypothetical "if it were the case . . ."

ES:
I think this is a recurring problem throughout this thread. You're not reading words according to the context in which they are presented.

POWELL:
I have read more into some of your words than intended. I'm sorry.

ES:
You say: "That's a weakness of the syllogism method. It doesn't indicate whether the argument is claimed to be sound or merely valid."

The "syllogism method" is not designed to deal with whatever claim is being made about an argument. It is designed to logically order and test whatever claim is made about an argument. The context in which the argument is presented indicates what claim is being made about the argument.

POWELL:
But, Eric, don't you assume that when an argument is put into syllogism form that the statements are all affirmative? In other words, If I were to write,

JT4. If dogs fly then snakes sing opera.
JT5. dogs fly.
JT6. therefore, snakes sing opera.

wouldn't you assume, given what you've said, that I'm claiming that the conditional IS TRUE and the premise "dogs fly" IS TRUE and the conclusion "snakes sing opera" IS TRUE? However, can't you see that making that assumption would be unwise in this case? Surely, you should assume that I'm saying IF the conditional were true and IF "dogs fly" were true THEN "snakes sing opera" would be true, right?

POWELL:
You seem to have gone back to the idea that a syllogism only counts as an argument if the variables are identified. However, fhujsl and trhgji have not been identified, so how can you call a syllogism using them part of an argument rather than merely an argument form?

ES:
Those are intended to be words, not variables.

POWELL:
That makes sense.

POWELL:
The following is an invalid form, right?

JR17. p
JR18. therefore, q

ES:
It is simply a proposition. p -> q

POWELL:
What a minute, Eric. I clearly identified the premise and the conclusion in a syllogism, therefore it's an argument or at least an argument form. It's not a proposition unless I put it all in a single line of the syllogism, right?

I'm claiming

If premise p were true then it must be true that the conclusion q is true.

If I can't do this, Eric, then I can claim that the "p" and "therefore q" of M.P. is also only a proposition, right?

ES:
If you are claiming, if p then q, then all you have is a proposition. p -> q

p
.: q

This isn't any kind of an argument form. There is nothing indicated about p from which to make the inference to q.

POWELL:
I will claim that this is an INVALID ARGUMENT FORM, Eric.

Now to try to use your words against your position, there is nothing indicated about p and q from which to make a JUSTIFIED inference to "not q" in a "denying the antecedent" invalid argument form either, Eric, but that does not mean that "denying the antecedent" is NOT an argument form. It's just not a valid argument form.

COPI & COHEN:
A deductive argument is one whose conclusion is claimed to follow from its premisses with absolute necessity.

POWELL:
I doubt that Copi & Cohen are alone in these exaggerated claims. In place of the bold text they probably should have said things like "provide VIRTUALLY irrefutable grounds" and "is VIRTUALLY IMPOSSIBLE for its conclusion to be false" and "with VIRTUALLY absolute necessity." However, if they did that then they might have to call their deductive arguments, statistical arguments instead, which is one of my major conclusions of the "invalidating validity" discussion.

ES:
Although I understand your concerns here, I think that you're just not recognizing the conventional meaning of words.

Suppose I have a bucket and I fill it with water. The bucket is absolutely filled with water. The modifier "absolutely" is related to the size of the bucket. The claim is not that absolutely all water is in the bucket.

POWELL:
Fine.

ES:
When we are dealing with logic, we are dealing with the "size" of our rational abilities. In other words, if we as subjective observers and logicians are limited in what we can truly know with certainty, then to say that we know something "absolutely" is not necessarily to claim that we have attained to absolute certainty (our "knowing" cannot be wrong and what we know cannot be false).

To claim that we logically know something "absolutely" generally means that we know it to the full extent of our abilities. It means that if our rational abilities allow for us to attain to virtual certainty, then any subject that is known with virtual certainty is known "absolutely," i.e. known to the full extent of our rational abilities.

When we say that our confidence is less than absolute, this means that we don't know something to the full extent of our rational abilities. This generally means that there is some reasonable doubt that prevents "knowing" with absolute virtual certainty, if you will.

POWELL:
This seems similar to something Tim Holt told me. He seemed to be defining valid deductive arguments as those where the certainty in the conclusion was matched to the certainty of the premises or something like that. That definition might salvage deductive arguments from my efforts to classify them as "very probable" statistical arguments.

My point then is that, to the full extent of MY rational abilities, if the premises of so-called valid deductive arguments are true then the conclusions are not "certainly true," they are merely "very probably true." I think logic teachers should concede this limitation to their logic students like science teachers should concede the major limitations of scientific conclusions to their science students.

POWELL:
Eric, if circular arguments can be so easily turned into valid M.P.-type arguments, then doesn't that suggest that M.P. is an essentially circular argument?

ES:
Of course not. If a largely incoherent term paper can follow a proper format, does this make that format incoherent?

POWELL:
No.

POWELL:
Here let me.

If atheism is true then God does not exist. God does not exist because atheism is true.

The circular form:

JS7. If atheism is true then God does not exist.
- - - - therefore - - - -
JS8. God does not exist because atheism is true.

ES:
The form of the argument is the following:

p -> q
q
.: p

POWELL:
I don't think so, Eric.

When you say "q because p" then p is the premise and q is the conclusion, right?

The conclusion of "If atheism is true then God does not exist. God does not exist because atheism is true." appears to be "God does not exist." This conclusion appears to be inferred from the premises "atheism is true" and "if atheism is true then God does not exist." The argument appears to be modus ponens to me, but when I wrote it as JS7 and JS8 it looks like a circular argument to me.

JS8 is a conclusion that "God does not exist because atheism is true" not a conclusion that "atheism is true."

What if I write the syllogism this way then:

JT7. If atheism is true then God does not exist.
- - - - - therefore - - - - -
JT8. If atheism is true then God does not exist.

Would you now accept that it is circular?

Or, would it be in the Modus Ponens form?

ES:
1. If atheism is true, then God does not exist
2. God does not exist (because atheism is true)
3. Therefore, atheism is true

The argument is circular because the conclusion is found in the second premise.

POWELL:
I think you've revised the argument too much different from what it appears to be initially. Let me try it a different way then.

If theism is true then God exists. God exists because theism is true.

Will you say this is a circular argument with conclusion "theism is true" rather than conclusion "God exists"?

ES:
Now, does the fact that this argument is circular mean that every argument that follows M.P. form is circular? Of course not. The argument’s form is invalid. Does this mean that M.P. itself somehow incorporates circular reasoning? No. M.P. operates according to logical principles. Given (p -> q) and (p), if both propositions were true, then q would be true. There is nothing circular here.

POWELL:
I agree that arguments of the M.P. form are not necessarily circular when claimed to be sound, when it is asserted that "p -> q" is true and "p" is true and "q" is true. However, I still disagree when they are merely claimed to be valid. Perhaps your answers to this post will help show me what I might try next to persuade you or be persuaded by you.

John Powell