TonesInDeepFreeze

"provide support for" is vague in supposedly explaining the vague "has no foundation" The main branches of classical mathematics are formalizable in s...

Thanks. What I wrote eventually:

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....

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 ...

Prime real estate was offered for free from the beginning. Or put another way, the horse was offered the freshest, coolest, cleanest mountain spring w...

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 con...

The rule DOES imply we can since the rule quantifies over ALL formulas. For that matter the rule doesn't explicitly mention any particular substitutio...

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

Calm down! You're making this emotive!

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...

(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 t...

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 ignor...

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

(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 c...

No, it's the DEFINITION of 'modus ponens'. Modus ponens doesn't require that a conditional is not contradictory, nor that the "major" premise (which m...

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 no...

That bit from the bot is atrocious confusion and misinformation. And it is intellectually shameful for a poster to post a confused and misinformationa...

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 amazi...

I'm not inclined to compose a post about it.

Of course LNC and LEM are different. I can't find the post about the liar paradox; my own point was merely the technical one that the contradiction of...

My statements are in context of ordinary symbolic logic. Things may be different depending on alterative logics: No. A tautology is a formula that is ...

Yes, that is the truth table.

You need to reevaluate your mistaken notion about substitutions. Let P and Q be meta-variables (read as 'phi' and 'psi' if you like) ranging over sent...

You can instantiate P and Q to whatever formulas you want. You somehow got in your head a wrong notion. I said nothing about logical equivalence. Read...

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...

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 ...

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 -...

It's where you disagree with the definition 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.

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 con...

That is incorrect. If A is false then "If A is true then A is false" is true. That is correct.

Then you'd argue incorrectly 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 incl...

It's a valid argument, so the conclusion is true in any interpretation in which all the premises are true. There are no interpretations in which all t...

An argument is valid if and only if there is no interpretation in which all the premises are true and the conclusion is false. An argument is not "inc...

There is no interpretation in which both premises are true. If the interpretation has A as true, then A -> ~A is false. If the interpretation has A ->...

A -> ~A is true when A is false and it is false when A is true.

That's correct. So is: A -> B A therefore B

You missed my point. Of course, there are different ways to show the validity of the argument. But my point is that one of the ways doesn't require ap...

In classical logic (but not intuitionistic logic), ~G -> ~(P -> A) ~P therefore G is valid. That's wrong. Or, you're welcome to state your alternative...

My view was characterized by posters recently. I take the problem to be to explain the puzzle: How did we infer a seemingly false conclusion from seem...

There is. An argument is an ordered pair where the first coordinate is a set of formulas (the set of premises) and the second coordinate is a formula ...

As given, 3 is a conclusion. 3 follows from 1 and 2 by modus ponens.

In this case we don't need to appeal to the fact that the premises are inconsistent. If the logic includes modus ponens, then the example is valid, ev...

That is correct, but it is not necessary to appeal to explosion, since the argument is valid as it is an instance of modus ponens.

I can't parse that.

Define "follows from". In ordinary logic, a conclusion follows from a set of premises if and only if there is no interpretation in which all the premi...

Cauchy sequences themselves are infinite sets.

Followup to myself: Yes, each of the above is correct.

It depends on what the purpose of the translation is. If the purpose is to directly emulate the sentence as literally said, then: ~G -> ~(P -> A) If t...

I wouldn't assume that the everyday sense of "if then" in the problem has a truth table interpretation. And, the premise is "If there is no God, then ...