Valid-only Modus Ponens is essentially circular

[Hiramjr]

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]

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]

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]

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

[John Powell]

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.

POWELL:
What?

Are you saying the following argument is NOT in a circular FORM, that regardless of what "p" is, an argument of this form will NOT NECESSARILY be circular, but it will depend on what "p" stands for?

1. p
- - - - - therefore - - - - -
2. p

John Powell

[Hiramjr]

To Powell:


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
You're misunderstanding what was said. M.P. is an argument form. I said that M.P. is not an argument. That is true. M.P. defines a particular argument form.

If you ask logic students whether the above argument is valid, they would indeed say yes. Now, why is it valid? It is valid because it follows the M.P. argument form. Why does that make it valid? Because the definition of M.P. indicates that any argument that follows this form is valid.

Suppose we say that a square is an object with four right angles. What have we just done? We have defined a word. Is the word "square" a square? The answer is no. Is the definition of a "square" a square? No. Is the definition an argument for a square? No. Anything that fits that definition/description is a square.

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?

ES
No, given what I said, I wouldn't make any such assumption because I interpret the syllogism by the context in which it is presented. The context of your comments indicates whether or not you are presenting this as an argument you believe to be sound. There is nothing in your comments that indicates that I should assume that you are presenting the argument as something that is sound.

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.

ES
I really don't know what else to say here. If an argument is circular then its conclusion is found in its premises. M.P. isn't an argument. An argument either follows M.P. form or it doesn't. If it follows M.P. form, then its circularity is determined by an analysis of its premises, not by its form.

p -> q
p
.: q

There is absolutely nothing circular about this form.

The reason why this form is valid is because the following proposition is true:

MP: If (p -> q) and (p), then q

Here, MP is not an argument. It is a proposition that constitutes a valid argument form.

[John Powell]

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?

ES:
No, given what I said, I wouldn't make any such assumption because I interpret the syllogism by the context in which it is presented. The context of your comments indicates whether or not you are presenting this as an argument you believe to be sound. There is nothing in your comments that indicates that I should assume that you are presenting the argument as something that is sound.

POWELL:
How about this one then.

1. If qetuo then adgjl
2. qetuo
3. therefore, adgjl

By displaying that syllogism should you assume I think the argument is sound, that I believe premise 1 and 2 are true or that I think it's at least valid, but maybe also sound?

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.

ES:
I really don't know what else to say here. If an argument is circular then its conclusion is found in its premises. M.P. isn't an argument. An argument either follows M.P. form or it doesn't. If it follows M.P. form, then its circularity is determined by an analysis of its premises, not by its form.

p -> q
p
.: q

There is absolutely nothing circular about this form.

The reason why this form is valid is because the following proposition is true:

MP: If (p -> q) and (p), then q

Here, MP is not an argument. It is a proposition that constitutes a valid argument form.

POWELL:
Now your calling single propositions argument forms too?

Can you give me a circular argument, Eric, that begins with a conditional that I can't easily turn into something like M.P.?

John Powell