Then you'd argue incorrectly — TonesInDeepFreeze

This is where we disgree.

A --> ~A <> A --> ~ B because A-->~A = ~A, yet A-->~B <> ~A.

It's a valid argument only if you allow that A --> ~A is of the form A-->~B. — Hanover

That is incorrect. Validity is semantic.
A -> ~A
A
therefore ~A

is valid since there are no interpretations in which the premises are true and the conclusion is false.

As to form, we prove that anything in the form of modus ponens is valid.

I don't think it follows proper modus ponens syntax. The antecdent and consequent cannot be the same because if they are then it is reducible to simply ~A. — Hanover

(1) It is valid whether viewed as modus ponens or viewed by consideration of the fact that the premises are not satisfiable.

(2) You have a serious misconception of modus ponens,

Modus ponens is any argument of this form:

P -> Q
P
therefore Q

There is no restriction on what P and Q can be.

That includes taking P to be A, and taking Q to be ~A.

A -> ~A
A
therefore ~A

is most certainly an instance of modus ponens.

You are welcome to state an alternative logic, but in ordinary truth-functional logic:

If P is false, then P -> ~P is true.

Your error lies in equating A --> ~ A to A-->~B because A-->~A = ~A and A-->~B doesn't equal ~A. They're logically different statements.

This is where we disgree. — Hanover

It's where you disagree with the definition of 'modus ponens'.

If P is false, then P -> ~P is true. — TonesInDeepFreeze

If P is false then if P is true then it is true that P is true is a contradiction pretty plain and simple.

It's where you disagree with the definition of 'modus ponens'. — TonesInDeepFreeze

Nope, we're in agreement with MP. We're in disagreement that P--> Q = P --> P. The former is a conditional, the latter a tautology.

You're confused. I'm not "equating" A -> ~A to A -> B.

Let P and Q be metavariables over formulas. Then modus ponens is any argument of the form:'

P -> Q
P
therefore Q

Instantiate P to A. Instantiate Q to ~A. There is no restriction against such an instatiation.

So

A -> ~A
A
therefore ~A

is an instance of modus ponens.

If P is false then if P is true then it is true that P is true is a contradiction pretty plain and simple. — Hanover

You're confused.

Look at the truth table by which you will see that if P is false, then P -> ~P is true.

It's ridiculous to argue about it. Just look at it.

You're confused. I'm not "equating" A -> ~A to A -> B.

Let P and Q be metavariables over formulas. Then modus ponens is any argument of the form:'

P -> Q
P
therefore Q

Instantiate P to A. Instantiate Q to ~A. There is no restriction against such an instatiation.

So

A -> ~A
A
therefore ~A

is an instance of modus ponens. — TonesInDeepFreeze

Again, this is incorrect. You cannot substitute P and Q to be a statement with the exact same truth value and maintain logical equivalence because once P and Q are the same, you have a different logical statement.

A -> ~A = ~A. That is, it is reducible to that.
A->~B is not reducible to ~A.

Therefore: A-->~A is not logically equivalent to A --~B.

It's like saying A+A = 4 and since it's generic, I can also say A+B=4. In the first case, A=2. In the second, we don't know what A or B equals.

We're in disagreement that P--> Q = P --> P. The former is a conditional, the latter a tautology. — Hanover

You're confused.

I did not say "P--> Q = P --> P". I said that

A -> ~A is an instance of P -> Q.

Nothing about equality, only instancehood.

And both P -> Q and P -> P are conditionals. The fact that P -> P is a tautology doesn't make it not a conditional.

You cannot substitute P and Q to be — Hanover

You can instantiate P and Q to whatever formulas you want.

You somehow got in your head a wrong notion.

maintain logical equivalence — Hanover

I said nothing about logical equivalence.

Read what I wrote.

A -> ~A = ~A — Hanover

Actually, the notation is:

(A -> ~A) <-> ~A

(A -> ~A) is not equal to ~A. They are not the same formula. Rather they are materially equivalent. Equality and material equivalence are not the same. The distinction is important.

A->~B is not reducible to ~A. — Hanover

I said nothing about "reducible".

Again, read what I wrote.

A-->~A is not logically equivalent to A --~B. — Hanover

I didn't say they are. Read what I wrote.

It's like saying A+A = 4 and since it's generic — Hanover

No, it's nothing like that. I made no such argument.

You somehow got in your head a wrong notion. — TonesInDeepFreeze

Well, one of us does.

Sure. I am just referring to the truth table

You need to reevaluate your mistaken notion about substitutions. [EDIT: replace 'substitutions' with 'instantiations', which is more strictly correct.]

Let P and Q be meta-variables (read as 'phi' and 'psi' if you like) ranging over sentences.

Modus ponens is any argument:

P -> Q
P
therefore Q.

Let A be a sentence letter or any sentence.

Instantiate P to A. Instantiate Q to ~A. Those are perfectly legal instantiations. There is no rule that disallows them. Look in any logic book or ask any logician.

So
A -> ~A
A
therefore ~A

is an instance of modus ponens.

/

And look at the truth table for

A -> (A -> ~A)

to see that it is true when A is false.

/

And, you said, "If A is true, then A is false" is a necessarily false statement.

That's incorrect.

If "A is false" is true, then "If A is true, then A is false" is true.

The antecedent is "If A is true" and the consequent is "A is false".

If "A is false" is true, then the antecedent is false and the consequent is true, so the conditional is true.

So "If A is true, then A is false" is not necessarily false, since there is an interpretation (viz. when ""A is false" is true" in which it is true.

The correct statements are:

(If A is true then A is false) then A is false.

If A is false then (If A is true then A is false).

A is false if and only if (If A is true then A is false).

Yes, that is the truth table.

One-third of folk here think the argument invalid. Odd.

Chatgpt:

"is this modus ponens:

A-> ~A
A
~A"

ChatGPT said:

"No, this is not an example of modus ponens. Modus ponens has the form:

→
A→B (If A, then B)

A (A is true)
Therefore,

B (B is true)

In your example, you have
→ ¬
A→¬A (If A, then not A), which leads to a contradiction when assuming

So it's not a valid application of modus ponens. Instead, it illustrates a logical inconsistency."

More evidence of ChatGPT's incompetence.

Or someone else's.

Amazing that someone would take the word of a bot on such a question. One could get bots to generate misinformation over and over again.

But not amazing that bots regularly get things quite wrong.

The bot does not understand substitution. And the bot can't even write formulas or English correctly: [EDIT: replace 'substitution' with 'instantiation', which is more strictly correct.]

"In your example, you have
→ ¬
A→¬A (If A, then not A), which leads to a contradiction when assuming"

(1) -> ~

is not well formed

(2) "assuming" doesn't end a sentence there.

(3) What the bot must mean is:

A -> ~A and A lead to a contradiction.

That is correct. But it doesn't show that

A -> ~A
A
therefore, ~A

is not an instance of modus ponens.

The bot incorrectly reasons that the inconsistency of the premises disallows the argument from being modus ponens. But it is not disallowed the premises of a modus ponens argument may be inconsistent

Here is correct information:

Let P and Q be meta-variables (read as 'phi' and 'psi' if you like) ranging over sentences.

Modus ponens is any argument:

P -> Q
P
therefore Q.

Let A be a sentence letter or any sentence.

Instantiate P to A. Instantiate Q to ~A. Those are perfectly legal instantiations. There is no rule that disallows them. Look in any logic book or ask any logician.

So
A -> ~A
A
therefore ~A

is an instance of modus ponens.

AGAIN: There is no rule of logic that prohibits substituting A for P and ~A for Q. [EDIT: replace 'substituting' with 'instantiating', which is more strictly correct.]

ChatGPT is just slamming text together that tends to flow together. Something with P and ~P is going to cause it to talk about contradictions because that's where the text usually appears.

It is bad at logic and uncommon programing languages like Prolog. It is actually surprisingly good at Java and Python, but still sometimes comically bad. I am waiting for the first financial meltdown of a sizeable business based on people using ChatGPT to code spreadsheets or dashboards.

Although I hear they are working on some that will do math well. I'll believe it when I see it.

That bit from the bot is atrocious confusion and misinformation. And it is intellectually shameful for a poster to post a confused and misinformational bot quote as if it is correct and settles a discussion about the logical matter. And risible that a poster quoting a bot doesn't understand that such bots compose text that seems like something that might be said, without fact checking itself that it is actually correct.

Get outta here with that bot garbage!

How pathetic that a philosophy forum is sidetracked by a poster not understanding the basic logic he is so adamantly making claims about.

It should not have to be said more than this:

The rule of modus ponens is:

If P and Q are ANY statements, then the following is modus ponens:

P -> Q
P
therefore Q

Since P and Q may be ANY statements, and A and ~A are statements we have:

A -> ~A
A
therefore ~A

is an instance of modus ponens.

Period.

And these also are instances of modus ponens, even though odd:

A -> A
A
therefore A

~A -> ~A
~A
therefore ~A

Period.

This is NOT the rule of modus ponens:

If P and Q are any statements except Q is not the negation of P, then the following is modus ponens:

P -> Q
P
therefore Q

And this is NOT the rule of modus ponens:

If P and Q are any statements and {P, P -> Q} is consistent then the following is modus ponens:

P -> Q
P
therefore Q

/

One more time, since the poster is presenting as seriously obtuse:

The rule of modus ponens is:

If P and Q are ANY statements, then the following is modus ponens:

P -> Q
P
therefore Q

Since P and Q may be ANY statements, and A and ~A are statements we have:

A -> ~A
A
therefore ~A

is an instance of modus ponens.

I don't usually say, "Please, let's move on" but I'm saying it this time.

The absurdity is that you think this a question of logic and not definition. No meaningful logical conclusion can follow from a contradictory conditional that assets the proposition and its negation can occur simultaneously.

Modus ponens "is the rule of logic stating that if a conditional statement (“if p then q ”) is accepted, and the antecedent ( p ) holds, then the consequent ( q ) may be inferred."

That is, it is the logical basis one asserts in support of the conclusion. If your conclusion is not true, you can't offer MP as the basis of it being true because it's not.

The absurdity is that you think this a question of logic and not definition. — Hanover

No, it's the DEFINITION of 'modus ponens'.

No meaningful logical conclusion can follow from a contradictory conditional that assets the proposition and its negation can occur simultaneously. — Hanover

Modus ponens doesn't require that a conditional is not contradictory, nor that the "major" premise (which must be a conditional) is not contradictory, nor that the "minor" premise (which might or might not itself be a conditional) is not contradictory, nor that the premises together are not contradictory.

Modus ponens "is the rule of logic stating that if a conditional statement (“if p then q ”) is accepted, and the antecedent ( p ) holds, then the consequent ( q ) may be inferred." — Hanover

What is your source of that quote?

If your conclusion is not true, you can't offer MP as the basis of it being true because it's not. — Hanover

You don't understand basic ordinary academic logic. You need the first chapter of a good textbook in print or online.

Meanwhile, you need to not litter a philosophy forum with confused, misinformational, and malformed bot garbage.

No, it's the DEFINITION of 'modus ponens'. — TonesInDeepFreeze

I already cited you the definition, which isn't as you're arguing.

Modus ponens doesn't require that a conditional is not contradictory, nor that the "major" premise (which must be a conditional) is not contradictory, nor that the "minor" premise (which might or might not itself be a conditional) is not contradictory, nor that the premises together are not contradictory — TonesInDeepFreeze

What is your cite for this definition?

Mine is from Google, which comes from Oxford Languages.

https://www.google.com/search?q=definition+of+modus+ponens&oq=definition+of+modus+po&gs_lcrp=EgZjaHJvbWUqDQgBEAAYkQIYgAQYigUyBggAEEUYOTINCAEQABiRAhiABBiKBTIICAIQABgWGB4yCggDEAAYDxgWGB4yCAgEEAAYFhgeMggIBRAAGBYYHjIKCAYQABgPGBYYHjIKCAcQABgPGBYYHjIICAgQABgWGB4yCAgJEAAYFhgeMggIChAAGBYYHjIKCAsQABgPGBYYHjIKCAwQABgPGBYYHjIHCA0QIRiPAjIHCA4QIRiPAtIBCTExODQ0ajBqOagCAbACAQ&client=ms-android-tmus-us-revc&sourceid=chrome-mobile&ie=UTF-8#ebo=0

And it is intellectually shameful... And risible...

Get outta here with that bot garbage! — TonesInDeepFreeze

How pathetic... — TonesInDeepFreeze

Meanwhile, you need to not litter a philosophy forum with confused, misinformational, and malformed bot garbage. — TonesInDeepFreeze

Calm down, please. You're making this emotive.

is clearly mistaken. As is ChatGPT.

I have no comment on that. Thank you for keeping things polite on your end anyhow.