Hanover

Nice. Much appreciated.

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

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, no...

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...

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...

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: ...

Nothing more regrettable than a life without regret I always say.

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 d...

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 nega...

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

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...

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 becau...

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...

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

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 ...

No, I get the distinction between a deductive conditional premise, and a linguustic counterfactual. I'm just engaging in the pedantry of determining w...

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. Validity does not require ...

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...

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

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 propositi...

We're not debating what can be substituted and what the logical implications are of such substitutions. Were debating whether to call certain formulat...

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

What I said long ago. https://thephilosophyforum.com/discussion/comment/943645

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 ...

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=Philos...

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 s...

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

I already cited you the definition, which isn't as you're arguing. What is your cite for this definition? Mine is from Google, which comes from Oxford...

The absurdity is that you think this a question of logic and not definition. No meaningful logical conclusion can follow from a contradictory conditio...

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...

Well, one of us does.

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 onc...

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 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.

This is where we disgree. A --> ~A <> A --> ~ B because A-->~A = ~A, yet A-->~B <> ~A.

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 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 co...

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 antec...

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

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 o...

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 t...

#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...

/uploads/resized/files/7g/luyufudbei70sr0w.jpg Fellow Chefs, I have for you today a whole wheat bagel infused with American cheese product delicately ...

/uploads/files/xb/thq95yp5ae0loz0h.jpg I just wanted to see if the picture feature now worked since the upgrade. I can confirm that it does, using a s...

I can confirm that is your understanding, but I can't confirm your understanding is correct. You're welcome.

Better to love and lose than to never have loved at all.