Where pray tell do you find a definition of MP that takes into consideration a self referential contradictory conditional and asserts it satisfies the definition of MP?

All definitions I have located say otherwise, as do all Google and AI engines.

Provide to me your cite to close out this incredibly irrelevant question.

They don't say otherwise. But they do not specifically rule out any substitution, including ~A for B.

Find one that does so, and you will have support for your claim.

Otherwise, the rule is that any formula can be substituted for A and B, including ~A.

And this is quite basic stuff. So from Open Logic:

A rule of inference is a conditional statement that gives a sufficient condi-
tion for a sentence in a derivation to be justified. Modus ponens is one very common such rule: it says that if φ and φ →ψ are already justified, then ψ is justified. This means that a line in a derivation containing the sentence ψ is justified, provided that both φ and φ →ψ (for some sentence φ) appear in the derivation before ψ. — Open Logic p.120

Nothing says that we may not substitute A for φ and ~A for ψ. Hence, we may. Indeed, that's kinda the point.

But this is trivial stuff! Why don't you already know this?

(1) That definition does not contradict that

A -> ~A
A
therefore ~A
is an instance of modus ponens

(2) Here are definitions of 'modus ponens':

"if a conditional holds and also its antecedent, then the consequent holds." (Beginning Logic - Lemmon)

"C is a direct consequence of B and B -> C." (Introduction To Mathematical Logic - Mendelson)

"From the formulas Alpha and Alpha -> Beta, we may infer Beta" (A Mathematical Introduction To Logic - Enderton)

"from P and P -> Q we may infer Q" (as the rule corresponding to the tautology (P & (P -> Q)) -> Q) (Introduction To Logic - Suppes)

"Psi is obtained from Phi and Phi -> Psi" (Mathematical Logic - Monk)

"A, A -> B |= B" (A Concise Introduction To Mathematical Logic - Rautenberg)

"the inference from A and A -> B to B" (Computability And Logic - Boolos, Burgess and Jeffrey)

"Gamma, Phi -> Psi and Gamma, Phi; therefore Gamma, Psi" (Mathematical Logic - Ebbinghaus, Flum and Thomas)

"passing from two formulas Alpha and Alpha -> Beta to the formula Beta" (A course in Mathematical Logic - Bell and Machover)

"Phi -> Psi, Phi; therefore Psi" (Logic: Techniques Of Formal Reasoning - Kalish, Montague and Mar)

"If P and P -> Q are proved, then one is entitled to infer that Q is proved" (Logic For Mathematicians - Rosser)

"A, A -> B |- B" (Introduction To Metamathematics - Kleene)

"p, p -> q |- q" (Foundations Of Mathematical Logic - Curry)

"from the premisses Phi -> Psi and Phi to Psi" (Mathematical Logic - Quine)

"From A -> B and A, to infer B" (Introduction To Mathematical Logic - Church)

"Psi may be entered on a line if Phi and Phi -> Psi appear on earlier lines" (Elementary Logic - Mates)

"From Psi and Psi -> Phi infer Phi" (Model Theory - Chang and Keisler)

"If p then q, p, conclude q" (Symbolic Logic - Copi)

And on and on in as many books on basic formal logic that you may look at.

All those definitions have in common that there is NO requirement that we may not instantiate the variables to A and ~A.

All those definitions have in common that there is NO requirement that the premises are not contradictory

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? — Hanover

It's not a definition! It's a comment about definitions. It is not itself a definition.

Meanwhile, you will find NO cite of a definition that requires that P can't be instantiated to A while Q is instantiated to ~A. And you will find NO cite of a definition that requires that the premises are not contradictory.

Justifiably.

I thought this forum was going to warn against citing bot misinformation.

It's not a matter of opinion that

A -> ~A
A
therefore ~A

is an instance of modus ponens.

It is a plain fact.

It is quite impolite to continue to ignorantly insist on bad misinformation and to cite wildly erroneous and incoherent bot messages as if they are information.

Waiting for someone to bring up quantum theory. :roll:

Where pray tell do you find a definition of MP that takes into consideration a self referential contradictory conditional and asserts it satisfies the definition of MP?

All definitions I have located say otherwise, as do all Google and AI engines.

Provide to me your cite — Hanover

(1) There is no "self-reference".

(2) The conditional A -> ~A is not contradictory.

(3) Nowhere in the definition of 'modus ponens' is it disallowed to instantiate to P to A and Q to ~A.

(4) Where "pray tell" do you find a definition that says "except Q cannot be instantiated to the negation of what P is instantiated to"? Hint: You don't.

There is no cite, no source, no reference that says such a thing.

You just somehow got it stuck in your head that such a thing is implied by the definition. But it's not.

AGAIN you need to read and comprehend.

P and Q range over formulas.

From P and P -> Q, infer Q by the rule modus ponens

Since A and ~A are formulas, we have:

From A and A -> ~A infer ~A by the rule modus ponens

You cannot show any definition, explanation or argument in any logic book or reliable article that says, implies or insinuates that the definition of 'modus ponens' disallows:

From A and A -> ~A infer ~A by the rule modus ponens

But you many look up arbitrarily many logic books that do imply that

From A and A -> ~A infer ~A by the rule modus ponens

from the plain definition of 'modus ponens' such as:

From formulas Phi and Phi -> Psi, infer Psi

where 'Phi' and 'Psi' are variables ranging over formulas.

Why don't you already know this? — Banno

Indeed, at a certain point in discussions where a poster is flat out wrong about a matter that is not even a matter of opinion, and persists to insist despite copious explanations given him, then the pertinent question turns from the simple fact of the matter about the subject to what is wrong in the head of the stubbornly clueless poster.

But this is trivial stuff! — Banno

Calm down! You're making this emotive!

Nothing says that we may not substitute A for φ and ~A for ψ. Hence, we may. Indeed, that's kinda the point.

But this is trivial stuff! Why don't you already know this? — Banno

Nothing says we can, which is kind of the point.

The absurd question of whether MP includes instances of A causing not A while A is the case doesn't seem to have gained much interest in the world outside the 3 or 4 of us debating it here. Thus the lack of an explicit statement supporting your position anywhere.

But yes, profoundly trivial and entirely irrelevant from a logic perspective. But, if you're asking me to read and define terms, your definition of MP is not logically entailed. It makes as much sense to define MP as excluding instances where A and not A coexist.

We haven't left @Hanover any space to back down without loosing face. Bit of a shame. It is astonishing that a third of those who could be bothered to vote got the answer wrong. I guess that tells us about the clientele.

After exhaustive explanations and citations, I'm waiting for someone to say to me, "You just argue with ad hominem".

Nothing says we can — Hanover

The rule DOES imply we can since the rule quantifies over ALL formulas.

For that matter the rule doesn't explicitly mention any particular substitutions. [EDIT: replace 'substitutions' with 'instantiations', which is more strictly correct.] For example, the rule doesn't explicitly mention that:

(A & B) -> C
A & B
therefore C

is an instance of modus ponens. But it is an instance of modus ponens.

And

A -> ~A
A
therefore ~A

is another instance of modus ponens though it too is not explicitly mentioned in particular in the rule.

It is part of the POINT of being a rule that it can be applied to ANY formulas.

your definition of MP is not logically entailed — Hanover

It's a DEFINITION. It's not supposed to be "entailed".

We haven't left Hanover any space to back down without loosing face. — Banno

It's not the job of the person who is giving correct information to provide a face saving escape hatch for the stubbornly irresponsible person who continues to spew misinformation no matter how many times he or she has been provided ample explanations and citations. If the person doesn't have the intellectual honesty to admit a glaring mistake then that's on the person entirely, especially after having been given copious explanation and citations. Also, one could be as conciliatory as pie to such a poster, and still he or she would not admit his or her error but rather on the contrary, he or she would persist even longer. That is the nature of Internet forums.

No, but it might make for shorter threads. As it stands the acrimony will only build. Good for thread length, of course. Hanover has not understood substitution, as you have succinctly explained, and hasn't understood validity. We might allow some space for them to learn.

Logic is generally handled very badly here - as if it were a question of opinion as to what is valid and what is not, rather than of structure. That a third of folk think the argument in the OP is invalid... that's cause for concern.

We might allow some space for them to learn. — Banno

Prime real estate was offered for free from the beginning.

Or put another way, the horse was offered the freshest, coolest, cleanest mountain spring water. He won't drink is his choice.

Logic is generally handled very badly here — Banno

It is deplorable the number of people who come into a philosophy forum without having read even page one of a book in logic or mathematics while spewing hyper-opinionated misinformation and nonsense on those subjects. It is utterly reasonable that one would become exasperated by that. Meanwhile, a moderator comes into scold the expression of exasperation while not a word that it is at least seriously frowned upon to cite bot misinformation and confusion, despite that (at least last I happened to read) the forum has said in general that that is not acceptable.

It makes as much sense to define MP as excluding instances where A and not A coexist. — Hanover

As Tones explained, it's not MP you have misunderstood, but substitution. MP is a rule of inference, saying that if you have φ and φ →ψ, then you also have ψ, where φ and ψ are whatever formulae or propositions or sentences you are discussing. That includes substituting the same formula for both, and the negation of φ for ψ.

You are mistaken. Sorry.

A thread of mine attempted amongst other things to discuss plausible cases in which modus ponens might not apply. It was lost in misunderstanding, which is a shame but perhaps not a surprise.

I've used ChatGPT occasionally to check things, usually nomenclature, sources, who first proposed an idea, or such. This case is a reminder to be aware of confirmation bias. ChatGPT gave @Hanover too great a confidence in his error.

A thread of mine attempted amongst other things to discuss plausible cases in which modus ponens might not apply. It was lost in misunderstanding, which is a shame but perhaps not a surprise. — Banno

An example of Modus Ponen failure is presented in the Wiki article as the Vann Mcgee case:

https://en.m.wikipedia.org/wiki/Modus_ponens#:~:text=Philosophers%20and%20linguists%20have%20identified,The%20following%20is%20an%20example:

Something I came across in tonight's research.

The antecedent directly contradicting the consequent isn't an example given of MP failure, as far as I can tell, anywhere except here.

So, you're either you're the first to notice it, or it's not really an example of MP failure because it's not MP.

Meanwhile, a moderator comes into scold the expression of exasperation while not a word that it is at least seriously frowned upon to cite bot misinformation and confusion, despite that (at least last I happened to read) the forum has said in general that that is not acceptable. — TonesInDeepFreeze

I'm making efforts to clarify the sourcing issue in the guidelines and the mod forum. I'd ask for some patience with us and with other posters on this issue while we sort it out.

Of course, fair enough that it a tough and complicated matter for moderators.

But, in the meantime, I think it is appropriate for a poster to express exasperation when a poster plasters bot misinformation. Indeed, more appropriate to express it than to be quiet about it.

My own view is to not enforce censorship but on, the other hand, to be clear that it is not welcome.

So, while you ask for patience with the moderation, I suggest that the moderation have patience with justified exasperation in reaction to poster abuse of bot quoting, especially not to scold the poster who at least is providing correct info.

Not the sort of thing I had in mind. Nor, frankly, am I inclined to go into details here, where simple substitution is apparently contentious. More agreement is needed before we might proceed to such other disagreements.

An example of Modus Ponen failure is presented in the Wiki article as the Vann Mcgee case — Hanover

If I recall, the Van McGee paper was the subject of a thread. And, if I recall, his argument hinged on adopting a different notion of the conditional.

Anyway, just to be clear, dissent from modus ponens doesn't change what the definition of 'modus ponens' is.

https://thephilosophyforum.com/discussion/11395/a-counterexample-to-modus-ponens/p1

Thanks.

What I wrote eventually:

It turns out that his argument does not suppose that the conditionals mentioned are taken in the sense of the material conditional. He says that if the conditionals mentioned are taken in the sense of the material conditional then modus ponens is not impeached by his argument. — TonesInDeepFreeze

It violates the LNC, which is foundational and introduced by Aristotle before modus ponens so he certainly didn't intend that the inference can work.

If contradiction, then anything.
contradiction.
therefore anything.

Not the sort of thing I had in mind. Nor, frankly, am I inclined to go into details here, where simple substitution is apparently contentious. More agreement is needed before we might proceed to such other disagreements. — Banno

The horse has been beaten to death here, but do at least understand I don't struggle with understanding your position, but I simply include within my definition of MP a requirement that it not self contradict.

As I've noted, this is a definitional debate, and we might as well be arguing if a cup with a hole in it entirely incapable of use is still a cup.

That is to say:

If I don't agree with you, I agree with you, and since I don't agree with you, I do. mp.

So says Alice when she's ten feet tall.

How I avoid this logical absurdity is to deny mp permits it, but you may insist that it is as it is. Sometimes cups just don't hold water you say.

I submit p can't be q for a valid mp, except among the speakers in Wonderland.

But at any rate, as always, I do appreciate the passion for such a crazy conversation though. An odd lot we are.

A → B means ¬A ∨ B. So A → ¬A means ¬A ∨ ¬A.

The argument in the OP is:

¬A ∨ ¬A
A
∴ ¬A

It's valid, but of course the premises cannot both be true. Necessarily one is false and so the argument is necessarily unsound.

What I said long ago.

https://thephilosophyforum.com/discussion/comment/943645