Candidly, there can't be any sensible doubt that the argument in the OP is valid for formal propositional logic. So in order for those who claim it is invalid to be correct, there must be more than one form of validity, and hence logical pluralism follows. — Banno

That is true, but shouldn't there be a distinction not just between "valid but not sound" but also between "valid but incoherent"?

For example:

If P then not Q
P
not Q

This is valid. It is sound if P and ~ Q are true. Unsound if not.
If P and Q are the same thing such that:

If P then not P
P
Not P

This is valid and not sound, but also not coherent.

As in, "If I went to the store, I did not go to the store, and I went to the store, so I did not go to the store." That is valid, but meaningless. I have no idea what you did, whether you went to the store, didn't go to the store, and I can't understand how your going to the store made you not go to the store."

And that was the debate for 20 pages I suppose. The pluralism might not be over "validity" if you wish to protect that term to only reference formal structure, but perhaps over soundness if you want to speak of what synthetically is false versus what is analytically false.

This conversation is pedantic and legalistic if I'm understanding it correctly. We all can agree with what truth tables show and what logic dictates, but the battle might be over terms, but I might misunderstand because that was the extent of my disagreement.

The incoherently true statement is also distinct from the vacuously true statement. As in, "if Tokyo is in Spain, then the Eiffel Tower is in Bolivia." There the antecedent cannot ever be satisfied, so it can never be true, but it's impediment to truth is due to a synthetic falsehood, but that's unlike the OP where the antecedent is premised to be false.

I'll let you guys better explain it to me if I've misunderstood this, but the contradiction and the incoherence that follows is what trips this issue up to me at least.

Yeah but it probably won't beat places like China and India given how much more lax their regulations are. Those are the countries they need to compete with. — Mr Bee

I'm not supporting Trump here, but I'm just going through his policies. What you bring up here is why he wishes to impose tarriffs. He's using his bully power to limit trade with a nation that needs it, which will weaken them. If they locate other markets in Europe, I would expect tarriffs in Europe. And so what would then happen is that someone takes out a calculator and realizes the better way to make money is not to create their economic policies from moral theories, but instead to maximize profits.

Has he suggested decreasing defense spending before? It sounds like he will just continue the status quo of the US being the biggest spender on defense by far. I think it appeals to his tough guy persona. — Mr Bee

This is the whole thing about him wanting to force NATO nations to pay for their own defense. He's threatening Europe with insecurity by underfunding NATO unless European nations better foot the bill. This fits his "everything is a deal" persona.

There's only so much more drilling that can be done to reduce oil prices (contrary to what some on the right say the Biden administration is overseeing record production right now). Also contrary to what Trump says, there is little correlation between the price of other goods the price of oil and gas. — Mr Bee

I'm not getting into the weeds of what causes what because I don't know enough about it. I can say that fuel costs are an important part of everyone's budget and they've increased. Sam's Club sells gas at like 10 cents cheaper per gallon and cars are up and down the street to save the $2.00 on a tank. It's part of inflation control.

This is in Europe's interest, though. Relying on other countries for defense is nothing other than giving up one's sovereignty. This is exactly why I view Europe as little more than Uncle Sam's vassals. — Tzeentch

Sure, but the price one pays for a defense results in the loss of other things, like public healthcare, losses in revenues from business regulation and all sorts of things.

The EU should decouple from the US, and instead seek engagement with continental powers like China. — Tzeentch

Yeah, great idea. Work with China. Let me know how that works out. Know who loves Trump? The Vietnamese and Vietnamese Americans. Know why? They hate China, just like he does. That is, a nation that was devastated by the US has aligned itself with the US instead of China because it needs protection from China. Think that one through.

If you're in any way geopolitically conscious, you will keep the US very far from your door. — Tzeentch

If you're Iran that's probably true.

1. As the U.S. scales back on environmental regulations, the EU could solidify its global leadership in climate action. This moment could further the European Green Deal and enhance the EU's position as a hub for green technology innovation and investment. By strengthening partnerships with like-minded regions (e.g., Canada, Japan), the EU could lead a coalition to tackle climate change and attract global investors focused on sustainability.

2. The EU could also capitalize on a more protectionist U.S. approach by attracting foreign investors looking for stable markets.

3. The EU can leverage its more stable stance to exert greater influence in institutions like the UN, WHO, and WTO. By doing so, the EU could shape international policy in ways that align with its standards on trade, human rights, and environmental protection.

4. Given Trump's prior skepticism toward NATO and multilateral security, the EU could take a stronger stance on European defense and autonomy. This might involve further funding for the European Defence Fund and strengthening PESCO (Permanent Structured Cooperation).

5. Policies may lead to a U.S. shift away from renewable energy production, possibly leading to increased oil and gas prices. The EU may want to fast-track its transition to renewables to mitigate potential price shocks and reduce reliance on external energy sources, especially in a time of political instability. — Benkei

1. The US economy will boom under this plan, as global change regulations are expensive. The US will outproduce the EU and will attract places like Canada and Japan to engage in business with them. It is doubtful those nations will prioritize the ethics of global resource management over reduced prices.

2. The US isn't as much protectionist as it is narcissist. It doesn't think it can live by itself. It thinks it's the only one that matters because it's better than everyone else. Particularly under Trump, he's willing to do business with anyone under his terms. Whatever foreign investors the EU acquires are subject to US interests because a deal that disrupts US interests will have negative consequences as the US tries to eliminate the disruption. This isn't to say the US will prevail in any and all competitive efforts against it, but I don't think it's reasonable to think a competive response wouldn't be forthcoming.

3. Those organizations are paper tigers without US support. If you can't get US buy in, they become debate clubs.

4. This is exactly what Trump is trying to motivate. He's trying to save on defense costs by pushing it back on Europe.

5. A shift toward more drilling will reduce oil prices and forestall climate friendly alternatives like electric cars and the like, which many Americans have no interest in anyway. Any drop in cost of living, even if temporary, will make Trump very popular because inflation of basic needs (like fuel, housing, and food) have risen drastically recently.

The solution is for the EU and its many nations is to figure out how to work closely with the US in order to function together harmoniously. You guys are going to have to deal with the devil. I can deal with having to deal with the devil since its the devil my fellow Americans and I created, but for you, wow, that must really suck. You were just sitting there eating your sandwich and this lands on your plate.

The average American doesn't want to be ruled by a woman. I never expected their sexism to be that severe. — javi2541997

You can't say it's because she's black because Obama was in office two terms, so if you can't call the average American racist, you've still got misogyny to argue.

Who'd have thunk Trump's election theft routine was a successful reelection strategy? The man thinks outside the box.

Trump Wins!

Since you weren't going to call it, I got to do it.

This is the NYT election predictor based on the current info. https://www.nytimes.com/interactive/2024/11/05/us/elections/results-president-forecast-needle.html#

It shows 78% chance Trump wins.

Is a software licence in a natural language or in a formal language? — Banno

I speak from the Anglo legal perspective, particularly American. Ambiguity in contracts feeds an industry, and even should there be clarity, ambiguity will be argued because the value of one's claim or obligation will be greatly affected by what the word means.

But in the law, we have a whole system to decide what things mean. And they mean what the person or people authorized to say it means.

But Americans like risk, so we keep things vague and subject to argument. Trials and hearings have the element of surprise, so compromises become of great value. We over pay sometimes just for certainty.

What this has to do with logic is that any argument goes so long as it's colorable. And this sparks creativity if you enjoy such chaos.

So how do you know what's what? You rely upon past decisions, and the art of the analogy and the ability to distinguish comes into play. Such is the significance of precedent. That we've been wrong for 100 years might hold more sway than a rigorous reevaluation. If you can't have clarity from the past, you'd have it nowhere.

Persuasion is the skill of the lawyer. Sometimes that has to with other than being strictly right. But what is "right" anyway?

Nice. Much appreciated.

I don't know what you mean. Example? — TonesInDeepFreeze

https://en.wikipedia.org/wiki/Proof_by_contradiction

Why would I? Every argument is its own thing. If the conclusion deductively follows from the premises then the argument is valid — Michael

Checking the validity of one argument using another is done all the time.

You say that because you're not linking your first argument to your second. That is, I consider Argument 1 to be "an interpretation" of Argument 2, not as two seperate arguments. This is one argument with 2 conclusions, both Q and ~Q. The premises must be true because they are taken as givens. Given P1 and P2, both Q and not Q are implied. The conclusion can be shown to be false by analysis of the same premises.

This is just what the word "valid" means. I think you think it means something else. — Michael

This is what "valid" means: "An argument is valid if there is no interpretation in which all the premises are true and the conclusion is false."

It is raining
It is not raining
George Washington is made of rakes

Per our definition, this argument is not valid becasue all the premises are true and that conclusion is false because you also indicated:

It is raining
It is not raining
George Washington is not made of rakes

I fully understand that the conclusion is also true, so there's that, but that's the nonsense of contradictions. That is, these arguments both meet and do not meet the definition of "valid."

I don't quite understand what you're trying to say here. — Michael

I'm saying that if you can interpret the same argument and obtain contradictory conclusions, then the argument is not "valid" under this definition of "valid":

"An argument is valid if there is no interpretation in which all the premises are true and the conclusion is false."

If we interpret it under my first iteration, we receive the conclusion ~P.
If we interpret under my second iteration, we receive the conclusion P.

We therefore have an "interpretation" in which all the premises of #1 are true and the conclusion is shown to be false via interpretation #2.

2. An argument is valid if there is no interpretation in which all the premises are true and the conclusion is false. — Michael

It depends on the length to which we "interpret" an argument and how you interpret "interpret."

P1. P->~P
P2. P
Conclusion: ~P

can be interpreted as:

1. ~P (P1, which is equivalent to ~P v ~P)
2. P (P2)
3. ~P v P (1, 2, this is correct as either v or &)
4. P - > P (3)
Conclusion: P (2,4 )

These two arguments are interpretations of each other because they maintain truth throughout based upon the premises provided.

Interpreting the same argument, we arrive at contradictory conclusions, which violates the definition of "valid."

This is the explosion issue. Everything follows from a contradiction. The question of validity versus soundness doesn't typically contemplate the contradiction, but it instead contemplates synthetic falsity of contingent premises yet valid logical structure (e.g. All cats can fly, I have a cat, my cat flies, valid but unsound because cats don't fly versus If all cats can fly then all cats can't fly, I have a cat, my cat can't fly.).

I'll put this to rest if someone can find an article outside our blabbing that actually considers the issue of the "validity" of the OP.

In this case, there is no interpretation in which all the premises are true. — TonesInDeepFreeze

A premise is defined as an analytic truth. It cannot be false, regardless of its synthetic falsity. If C means "Cows bark," it is irrelevant if they don't for the purposes of formal logic.

My point is simply that if you have an analytically false premise (meaning it cannot be true in any world), it fails to meet the definition of "premise."

An argument without premises is not a syllogism.

That is to say, accepting what you've argued as true, the OP is not a valid argument because it's not an argument at all.

A premise is an assumed truth.

Alright, so you're substituting the conclusion of the OP from A to A &~A, which can simply be represented by an F, for false.

Back to my truth by negation maneuver then.

The opposite of (A & ~ A) is (A v ~ A), which is a tautology

So, if I can prove from the OP that (A v ~ A) flows, then the argument is invalid because I would have shown F is T.

P1. A -> ~ A
P2. A

1. A&~A (1,2)
2. ~A (1)
3. ~A v A ( 2 disjunctive introduction)

Still not valid, considering the contradiction allows me to prove anything I want, even that T is F.

Yes, I do see the issue of identity versus inference, but that is solved by superfluous logical machinations and becomes a pedantic exercise to maintain the distinction between "identity" and "inference."

For example:

P1. A -> ~A
P2. . A

1. ~A (1,2 m.p.)
2. ~ A v A ( 1 and disjunctive introduction)
Therefore:. A (P2, 2 negation of ~ A)

Note I've not just reasserted P2 in my conclusion, but I've logically deduced that since not A could not be true based upon A being a given premise, by elimination, A must be true.

I'm sure there are more convoluted ways to go about it, but does that satisfy your objection?

You can't deny that A is a conclusion because it is proven by the second premise, which is also A.

To deny A flows from the premises makes the curious argument that a premise has been eliminated by other premises.

In any event, premise 1 is reducible to ~A, so when you couple that with the second premise of A, you then can claim "A and ~A," allowing you to prove whatever you want.

Premise A & ~ A

Inferences:
:
A
~ A
A v C (cows bark)
~A
Therefore C

and so on and on

The argument:

1. A -> ~A
A
therefore ~A
valid

Another argument:

2. A -> ~A
A
therefore A
valid — TonesInDeepFreeze

If under #1, I assume A (the negation of the conclusion) and I prove A from that (as is shown under #2), then I've proven invalidity by negation because I've shown my negation is true.

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.