The fact that the premises are inconsistent doesn't vitiate that the argument is valid. Actually the fact that the premises are inconsistent entails that the argument is valid.

(2) A conclusion itself is valid if and only if it is true in all interpretations. An argument is valid if and only if there are no interpretations in which the premises are all true and the conclusion is false. — TonesInDeepFreeze

The premises are consistent and the conclusions are not.

The conclusion is not true under all interpretations. Sometimes it's A and sometimes it's not A.

Yes, so — TonesInDeepFreeze

Per the definition of "valid":

An Argument is valid if and only if it would be contradictory for the conclusion to be false if all of the premises are true.[ — Hanover

Assuming all premises in the OP true, the conclusion of not A is shown to be false because a valid conclusion of A was shown.

How are you getting A as a conclusion? — frank

I might have mistyped at some point.

The OP:

1. A->~A
2. A
3. Therefore ~A (1,2 mp)

A cab also be concluded from the second premise.

A (2)

I can also continue from the conclusion:

4 ~A v A (3, disjunctive introduction)
5. ~ (~A) (2, double negation)
6. Therfore A.

All grass is green
All grass is not green
Cows can bark.

think you're treating A -> ~A as if it's hypothetically true. They're just declaring it to be necessarily false. — frank

No, I get the distinction between a deductive conditional premise, and a linguustic counterfactual. I'm just engaging in the pedantry of determining whether the OP satisfies a hyper analyzed definition of "valid."

As @Banno notes, validity is determined by asking if the conclusion flows from the premises, and so he argues under mp, it does, so it is valid.

The wiki cite adds criteria, namely (1) that the negation of the conclusion cannot also flow from the premises for validity and (2) the premises under any formulation must also reach the same conclusion.

The OP falls under those criteria because: (1) both A and ~A can be derived from the premises, and (2) when Premise 1 is changed from a conditional format to a disjunctive one, it reduces simply to ~A, clearly contradicting the second premise A, and further violating criterion 1 that prohibits the negation and assertion to consistently flow from the same premises.

This is to say, if I were reviewing a contract, and it said "you get $1,000,000 if the OP is a valid syllogism," I'm saying no if I'm the guy who has to pay. Does the other side have a colorable argument? Maybe, but it must argue validity despite contradiction and accept the absudity that follows.

I do think @Benkei's comment regarding the necessity of acknowledging the LNC as foundational is correct.

Your OP (original post) and subsequent posts provide almost no specific information. They include a vague and undetailed description of the elements of your ECMT and it's supporting information. You claim it is testable and makes specific predictions but you don't describe any specific hypotheses or how they might be tested. — T Clark

Yeah. No accusations, but sounds AI-ish, like a corporate memo.

"Argument is valid if and only if it would be contradictory for the conclusion to be false if all of the premises are true.[3] Validity does not require the truth of the premises, instead it merely necessitates that conclusion follows from the premises without violating the correctness of the logical form. If also the premises of a valid argument are proven true, this is said to be sound.[3]

https://en.m.wikipedia.org/wiki/Validity_(logic)#:~:text=An%20argument%20is%20valid%20if%20and%20only%20if%20it%20would,correctness%20of%20the%20logical%20form.

From the same wiki article:

"A Formula of a formal language is a valid formula if and only if it is true under every possible interpretation of the language. In propositional logic, they are tautologies."

So:

1.

A -> ~A
~ A
Therefore A (1,2 mp)

But

2.

A->~A
~A
Therefore ~ A (2)

Test 1 for validity: It is valid if it would "be contradictory for the conclusion to be false if all of the premises are true."

So, #1, could A be false if the premises true? Yes, see #2. Same premises, yet in #1 A is true, but in #2 A is false.

Test #2 for validity (which is really just a clearer restatement of #1): "A formula of a formal language is a valid formula if and only if it is true under every possible interpretation of the language."

Note "every possible interpretation of langauge."

Premise #1 is logically equivalent to ~A. That is, a possible interpretation of this syllogism:

~A
A
Therefore A.

Therefore ~A is also true.

This is not a valid argument.

1. If Hanover is correct, Hanover is not correct
2. Hanover is correct
3. Hanover is not correct (1,2 mp)

4. Hanover is not correct or 3 is an invalid conclusion derived from mp.(3, introduction)
5. 3 is an invalid conclusion derived from mp (3,4)

Right. The contradiction is 1. ~A, 2. A.

The OP uses propositional logic. In propositional logic, the argument is valid. — Banno

Let me test it.

If the OP uses propositional logic, it doesn't use propositional logic.
It uses propositional logic
Therefore it doesn't use propositional logic.

MP has spoken. It doesn't use propositional logic

We're not debating what can be substituted and what the logical implications are of such substitutions.

Were debating whether to call certain formulations "modus ponens."

There is no governing body in what to call it. My basis for excluding self contradictory versions has been stated.

As noted, there are exactly zero citations so far found where someone other than us has analyzed whether the OP case belongs in mp. Where we have found debate over invalid mp formulations on the web, exactly zero deal with the OP case.

The point being, should we guage term usage for meaning, I see no evidence supporting your usage.

As I've also repeatedly said, this is a definitions question, not a logic one. We both agree upon what entails what and what can be substituted in for what.

The OP is not a problematic example of mp. It's not mp at all.

Again here:

https://thephilosophyforum.com/discussion/comment/943647

What I said long ago.

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

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 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.

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.

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.

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

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.

Or someone else's.

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."

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

Well, one of us does.

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.

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.

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.

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.

Then you'd argue incorrectly — TonesInDeepFreeze

This is where we disgree.

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

That's wrong.

If A is false then "If A is true then A is false" is true. — TonesInDeepFreeze

If my dog does not have have fleas, then "if my dog has fleas, then my dog does not have fleas" is false.

It's a valid argument with a necessarily false premise and so is necessarily unsound. — Michael

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

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.

But my point is that one of the ways doesn't require appealing to explosion or even contradiction since the argument is in the form of modus ponens. — TonesInDeepFreeze

I'd argue A --> ~ A is not of the form A --> B as required as a first premise of modus ponens.

The generic modus ponens syntax requires that the antecedent and consequent be different, meaning that A --> A is not logically equivalent to A -->B because the latter is not reducible to a contradiction.

A --> B = ~ A v B.
A --> ~A = ~A v ~A
~A v ~ A = ~A

If so, can you say which premise is false and why? — NotAristotle

1 is false. "If A is true, then A is false" is a necessarily false statement.
"If A is true, then A is false" is logically equivalent to "A is false or A is false." This means that A is false.

3 follows from 1 and 2 by modus ponens. — TonesInDeepFreeze

1 means "If A is true, A is false." This means A can never be true, despite it being true. It's a walking contradiction. This in itself can be taken to mean A is false because, as noted A -> ~A is logically equivalent to ~A or ~A as a disjunction of the conditional ( A --> B = ~A or B). 1 therefore means ~A.

This can be reduced to:

1. ~ A
2. A
Therefore ~A.

The conclusion is a restatement of #1. 2 is a contradiction of 1..

1. A -> not-A
2. A
Therefore,
3. not-A. — NotAristotle

#1 is a contradiction, reducible to ~ A or ~A. Since it concludes A cannot be true, the antecedent (if A) is always false.
#2 is false and contradicts #1 that establishes ~A.
#3 is not a conclusion, but is a restatement of #1.

I’m posting that video here because I think it challenges us to re-consider what constitutes language. To what extent is an immediate relationship with our non-human surroundings a language? — Joshs

This causes me to want to better clarify what non-essentialism entails. It does not entail an abandonment of definition entirely. It just means there is no one element required to define what langauge is, but it does not suggest that language can be whatever you want it to be. The person in the video was not engaged in any language that could be deciphered from watching her. She seemed to be interacting with her environment to be sure, but that is not langauge. I might skip around and hum and animals of all sorts might do things that explore and feel the things around them, but that's not langauge.

We needn't do a disservice to what it means to engage in langauge in order to show respect to those who think and interact differently than the most of us. That person might lead a life richer in experience and joy than the vast lot of us, but she doesn't engage in langauge, at least not in that video.

The problem is that English doesn't adequately distinguish the counterfactual or hypothetical conditional from the logical conditional of the syllogism and so we confuse ourselves with the ambiguity.

1. Consider the sentence "If God exists, he will answer our prayers."

2. Consider this sentence "If God exist, he will answer our prayers."

Now represent these both formally.

Note the 2nd is not in the indicative, but the obsolete subjunctive and I'd submit incapable of being reduced formally. It does not say what will be. It hypothesizes. #1 has an antecedent. #2 has a hypothesis.

Or, to better clarify:

If I was President, I'd lower taxes.

I was president

I lowered taxes

P -> T.

P

T. Monus ponens.

But not:

If I were President, I'd lower taxes

I were President. (???)

I lowered taxes.

"I was President" can be represented as P.
"I were President" cannot.

The "were" becomes misplaced because it was a hypothetical as written and now it's being modified into an actual.

This is just to say our langauge poorly captures the distinction and the OP ridicules it

There is no purpose. — Michael

This is an aside, but I disagree. It's no more or less logical to choose backward looking reasons (causes) for why things exist as they do than it is to choose forward looking reasons (purposes) for why things exist as they are. In either instance the first cause or the final purpose is unknowable, and both provide explanatory power. The resistence to looking for purpose is that it demands an altered world view where you accept that purpose exists instead of the typical view that accepts that just causes exist, but the acceptance of causation or the acceptance of purpose are both acts of faith.

So we accept that not only is a zygote's "right to life" not absolute but also that their lives are worth less than other things (even things other than something's life). We might disagree with how little/much a zygote's life is worth, but at the very least we must accept that "we ought not terminate a pregnancy because the zygote has an absolute/overriding right to life" is false. — Michael

If someone accepts that a zygote is a second class person, then I do think they'll have a problem not prioritizing the mother's life. A real pro-lifer could not accept that and would have to bite the bullet and do as Alabama did and say that zygotes in test tubes are people and their disposal is murder. If you're getting concessions from pro-lifers that zygotes are red headed stepchildren, then they aren't true believers.

Would you kill 3 barely conscious, immobile, unresponsive people who will never recover in any way in order to save a single child who is in all ways healthy? That is, do you believe that all people are of the same moral worth in terms of preserving their lives or do you value some more than others? That is, you have a trolly with 3 wonderful people barreling towards a cliff in which all will surely die, but if you veer right, you'll save them, but you'll kill a dozen prisoners, all in for violent felonies.

What about killing 1 person to save 50,000 dogs? Would you do that? And they're super cute dogs. They have floppy ears and their entire body wags when they see you. Fucking cute as shit. Are you going to kill those just for one snotty nosed kid?

This second trolly question is important because it might be that pro-choicers can be accused of picking which people they want in society, offering no inherent value to human life. It's just a human choice based upon human priorities at the time.

A lot of people I have encountered who pontificate about the 'sacredness of human life' are simple hypocrites. They're quite comfortable with capital punishment and don't seem to mind if the poor die in vast numbers through lack of affordable services. — Tom Storm

I'd also hold that the sanctity of human life encompasses the right to live to the ability to one's creation, so much so that I would be violating your human rights if I held you against your will in my basement, yet I don't think it hypocritical to incarcerate the guilty. What this means is we draw a distinction between justifiiable imprisonment and unjustifiable imprisonment.

We can do the same for killing. Examples would be war, self-defense, and punishment. I get that you disagree that capital punishment should go in that list perhaps for a variety of other reasons, but someone who is opposed to murder can consistently and non-hypocritically be in favor or capital punishment just as someone can object to an unjustifiable X but support a justifiable X.

The death due to lack of services I know occurs worldwide, but much less so in the West. I'm not suggesting all is well and that there isn't room for improvement, but I don't see where people don't mind unavoidable death occuring all around them or where that mindset is more pronounced among the religious. Are you saying the religious shrug their shoulders to worldwide hunger and withhold support where their non-religious counterparts are trying to assist?

That presents the opportunity to explain that the life of a zygote has less moral weight than the woman's bodily autonomy. — Michael

I don't see where this conclusion comes from. I agree the trolly problem can show that there are certain circumstances that justify the killing of an innocent person, but I don't see how that changes the weight a pro-lifer would afford an embryo.

I would assume that if the question is whether one should kill one person to save five, that question would be answered by the pro-lifer the same whether "person" is defined as an infant of an embryo.

The trolly argument (as typically presented) doesn't ask you evaluate the lives that would be killed versus those saved before you decide how to steer the trolly. Questions like "who do I throw off the sinking ship to save it, the nun or the thief?" are typically answered by the Kantian that you cannot morally decide to throw anyone off and both the nun and the thief have to die.

In any event, I don't see how we can make the trolly problem fully applicable to the abortion issue because the only true instance where a choice of life has to be made is when there's a question about saving the mother, which even the most pro-life folks usually defer to saving the mother. That is, most would argue the trolly should be steered to save mom and to run over the embryo. The bigger question is why some sick fuck would put an embryo and a mom on the railroad tracks in the first place

As a general matter, I advocate for sanctifying life, not just in a humanist way, but in a way that truly seperates life and humanity in a mystical way. It's not enough for me to simply say we're humans so therefore we afford ourselves priority, but it means something more to me, where I hold each person out in the universe as a child of God with special purpose.

That argument does hold sway with me, and I can understand why some want to avoid stripping that special assignment from the deserving. I don't think it helps though to assign it where it isn't deserving. To say that the value of my life and your life is infinite is true, but to then to say that also of the zygote doesn't just benignly elevate the zygote to special status, but it demeans my status. It suggests that the loss of the zygote is truly is as monumental as the loss of a child.

As in really? You read of a child drowning and that evokes the same thoughts as a zygote being disposed of at the fertility clinic?

And this is where I think the pro-choice get rightly offended, even if it's doubtfully based in anything I've said about the sacred and holy. It's not in the idea that zygotes are afforded great value. It's in the idea that living breathing people are reduced to the value of a zygote and the rights of each must be weighed as if my life is of no more woth than a zygote.

And I say all this because I am about as religious a poster as posts here, but I find this pro-life position hard to swallow. It just seems the result of some dogma that demands zygote = person without much thought into what that means and it obviously comes from a religious tradition foreign to my own that violates my views of the who we all are.