Valid-only Modus Ponens is essentially circular

[John Powell]

POWELL:

MAJOR ASSERTION:
Modus Ponens, when claimed to be merely valid, not sound, is essentially a circular argument rearranged in such a way that the circularity is disguised.

DEMONSTRATION:
Because the syllogism form is ambiguous between sound or merely valid, it obscures, rather than illuminates the facts in this case. Consequently, the syllogism form won't be used initially.

Clearly circular form:

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

Expanded:

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

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

Expanded:
If the conditional "if p then q" is true then (or and) if "p" is true then "q" is true.

In Syllogism form:
1) if p then q
2) p
3) therefore q

Expanded:
If the premise conditional "if p then q" is true and if "p" is true then (or therefore) "q" is true.

EXPLANATION:
Modus Ponens when claimed to be merely valid, not sound, is essentially a circular argument in which the quotation marks are switched around. The second premise and conclusion is essentially a linguistic restatement of the original conditional.

If the conditional "if p then q" is true then this linguistically means that if you have p then you'll have q.

In terms of the syllogism, what happens is more involved.

1) the conclusion proposition "if p then q" is split into two parts "if p" and "then q,"

2) the "if p" is treated as the second premise proposition and the "then q" is left as the conclusion proposition

3) the "if" in front of "if p" and the "then" in front of the "then q" are taken from being part of the propositions to being part of the inference.

4) The logical connection between the premise 1 and 2 is switched from being "then" to being "and"

5) The inference conclusion "then" is switched to be "therefore"

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.

Analysis:
Modus Ponens as a merely valid, not sound, argument form appears to be merely a linguistic restatement of the conditional premise.

OPINIONS / REFLECTIONS:
Rather than accepting that their deductively valid arguments are circular, I suspect that too many philosophers have rearranged things to make it look like they aren't. I believe that the conditional "if p then q" by itself is enough to serve as a useful argument. If the listener accepts the conditional "if p then q", then the rest of M.P. follows by identity, A = A, by circularity

Of course, circular arguments are valid.

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.

Comments?

John Powell.
An athe-ist or strong atheist.

[Gavin]

Wouldn't this throw modus tolens out the window as well?

[John Powell]

Gavin:
Wouldn't this throw modus tolens out the window as well?

POWELL:
I'm still waiting for some rebuttals to my arguments. Don't count M.P. out so soon.

Nevertheless, I don't think you fully understand my arguments, Gavin. I'm claiming that deductive valid arguments of the M.P. form are circular, not that they aren't persuasive or not useful. On the contrary, they are very persuasively useful.

What could be more persuasive than a circular argument? If A is accepted by our listener to be true then they must accept A to be true, don't you agree?

I think it's philosophers who have drummed into our heads that circular arguments are bad. Scientists use equalities, A = A, with great relish.

Remember that this only applies to the valid-only form of M.P. Most people presenting arguments of the M.P. form are claiming their arguments are sound. Those sound arguments are not necessarily circular. However, when atheists debate these issues they are seldom, if ever, claiming the arguments they use are sound, because they don't believe in all the premises. Thus, the M.P. forms of religious-type arguments made by atheists are usually circular.

If I'm correct then I may have given theists a shield against a weapon that was needlessly feared by them, valid deductive religious arguments of the M.P. form posed by atheists.

I've only looked at this circularity issue briefly with respect to M.T., so I don't know yet. It's possible that it will also be circular, merely a linguistic restatement of "if p then q," but it might suffer a different problem. When philosophers say "if p then q" in M.T. they might mean "if p then absolutely, with no ifs, ands, or buts. there must be q" This is NOT, in my opinion, the necessary linguistic meaning of "if p then q." I might be persuaded to think otherwise upon further reflection.

Perhaps you can look at this issue and advise. I plan to study it eventually.

John Powell
An athe-ist or strong atheist.

[Gavin]

Hey John.

It seems to me that modus tolens and modus polens stand and fall together, since one the former is essentially the same as the latter, except negated.

I am not sure that I understand your argument either. How is modus ponens circular? Its seems like you start with A and then end up with B, not A.

A horseshoe B
A
ergo B

[John Powell]

Gavin:

Hey John.

It seems to me that modus tolens and modus polens stand and fall together, since one the former is essentially the same as the latter, except negated.

POWELL:
That could very well be true, Gavin.

It appears to me, however, that if one adopts reasonable meanings for "if p then q" other than "if p then absolutely with no ifs, ands, or buts, must have q" then M.T. is not necessarily valid.

M.P. does not seem to suffer that problem because, presumaby, whatever the meaning of "if p then q" if "p" then "q" should follow. For example if "if p then q" means "if p then almost certainly q" then M.P. could mean if "if p then almost certainly q" and if "p" then "almost certainly q"

Relative to M.T., consider that "if p then q" means "if p then almost certainly q." In that case, one cannot be absolutely certain that if you almost certainly don't have q or even if you absolutely don't have q that you cannot have p. In other words, M.T. would fail as a valid inference in that case, don't you agree? There is nothing I see in the phrase "if p then q" that DEMANDS it mean the absolute thing philosophers seem to think.

GAVIN:
I am not sure that I understand your argument either. How is modus ponens circular? Its seems like you start with A and then end up with B, not A.

A horseshoe B
A
ergo B

POWELL:
Is this syllogism merely valid or sound? One thing I'm claiming is that the syllogism form obscures this issue of circularity. Adopting logical symbols instead of the language equivalents might be even worse. If the argument is merely valid, what the M.P. syllogism means is

If "if A then B" and if "A" then "B" .

I think, this can also be stated as
If "if A then B" THEN if "A" then "B."

If you now rearrange the quotes you can form
If "if A then B" then "if A then B" which is clearly circular.

I would submit that all you need as a persuasive argument is the conditional. If your listener accepts "if A then B" to be true, you probably don't need M.P. for anything really unless the listener doesn't understand what "if A then B" means. You really haven't said anything more that isn't linguistically contained in the conditional by then giving the second premise and conclusion:

then if "A" then / therefore/ ergo "B"

since that's what the conditional linguistically means. At least that's how it looks to me.

The M.P. form might not be circular if it's treated as a sound argument.

John Powell

[Gavin]

wow this logic stuff really goes over my head sometimes.

[Gavin]

I hope you will find someone who will be better equiped to talk about this with you, John, cuz I am kind of a novice in formal logic.

[John Powell]

GAVIN:
I hope you will find someone who will be better equiped to talk about this with you, John, cuz I am kind of a novice in formal logic.

POWELL:
I'm a novice too, Gavin. However, I have a good mind that is even better since I stopped compartmentalizing religous-think separate from science-think. Also, I was reasonably well trained to think logically in my science classes and encouraged to avoid some forms of philosophical thinking.

Tim Holt has been the best in helping me to better understand philosophical logic. That doesn't mean Tim agrees with me on any specific issue. I've tried to get Doug Krueger, a regular at II Errancy, to discuss such things with me while he's been at www.jcsm.org, but he doesn't seem very cooperative. Perhaps it's because he knows I have an ax to grind with those at II Errancy relative to logic and he doesn't want to be the one to give me more ammunition or be the one hit.

GAVIN:
wow this logic stuff really goes over my head sometimes.

POWELL:
Then perhaps I did an inadequate job of explaining myself. I had no intention of obscuring or complicating things.

I tried to be as succinct as I could in my "proof" to give me the greatest chance of being able to defend it against critics. However, I'm willing to elaborate as necessary. Ask what you're not understanding, Gavin, and I'll try to better explain my reasoning.

John Powell

[John Powell]

Gavin,

I thought some more about what you said about M.T. having to fall to being circular if M.P. falls. I planned on dealing with M.T. later, but your questions have encouraged me to work on M.T. earlier than expected.

Now, I realize that M.T. COULD work even if "if p then q" means "if p then almost certainly q." Premise 2 could be "not q". The conclusion could then be "almost certainly not p" which would be considered, I think, to be a valid deductive argument if "almost certainly" referred to the exact same precisely defined probability in both the conditional and the inference, such as 99%.

I don't see that this is what "if p then almost certainly q" must necessarily mean, however. As the conditional is worded, there's no reason I can see that the "almost certainly" must go with the inference, except perhaps to form a valid deductive argument. I think the "almost certainly" could justifiably be attached to the "q" rather than to the inference. This would make premise 2 "almost certainly not q" and conclusion "not p" which would not be a valid deductive argument.

Consequently, I have doubts that one should consider M.T. to be valid in the first place unless one adopts that "if p then q" means something like "if you have p then absolutely with no ifs, ands, or buts you must have q."

Nevertheless, it's still possible that M.T. is just a linguistic restatement of "if p then q," and circular, but that's harder for me to see than with M.P.

To demonstrate this circularity, I would probably have to essentially argue that "if p then q" means "if not q then not p" which isn't obviously true to normal language speakers except, perhaps, to speakers trained in logic who already accept M.T. as a valid deductive argument. With that substitution, M.T. becomes M.P. and, therefore, circular.

Here's the noncircular argument:

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.

To try to turn this into a circular deductively valid argument add

5) M.P. and M.T. are both valid deductive arguments.
6) therefore (by 1) "if p then q" is equivalent to or means "if not q then not p."
7) the "if p then q" in M.T. is replaced with "if not q then not p"
8) therefore (by 2) M.T. becomes (i.e., is) "M.T. converted into M.P."
9) M.P. is circular (argued elsewhere).
10) therefore, (by 3 and 9) "M.T. converted into M.P." is circular.
11) therefore, (by 4 and 10) M.T. is circular.

I'm not sure this is valid, partly because of the use of "becomes" in 8, but not 10. "Is" and "becomes" are an equality of sorts, so maybe it's ok. The argument seems to be saying that "M.T. converted into M.P." is both M.T. and M.P. It's saying A=B and B=C, therefore A = C.

These two forms of the argument (noncircular conditionals only and circular form) might persuade someone who believes that M.P. and M.T. are both valid deductive arguments and that M.P. is a circular argument. It doesn't persuade me because I'm not prepared to accept that M.T. is a valid deductive argument (premise 1) yet.

John Powell

[Gavin]

I'm a novice too, Gavin.

You could have fooled me!

Then perhaps I did an inadequate job of explaining myself. I had no intention of obscuring or complicating things.

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

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?

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?

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.

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.

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

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.

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

Thanks John.

[Gavin]

ps I could not find this site: www.jcsm.org

just to let you know.

Thanks again.

[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.

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.

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. 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). 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)). 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. 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.

Now, the atheist argument you presented would be false for reasons other than badgering the Modus Ponens. 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). It is the hypothetical statement itself that is to be questioned, not the form of the argument. Premise 1 assumes that foreknowledge is logically exclusive to free will, which it clearly is not. 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

[John Powell]

Gavin:

You could have fooled me!

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]

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.

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]

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