If, in an interpretation, the antecedent is false, then, in that interpretation, the conditional is true. In more lax formulation: If the antecedent i...
Which argument? A conditional sometimes called a 'hypothetical'. Sometimes the antecedent is called 'the hypothesis'. To avoid confusion between 'hypo...
It's not a matter of frustration. Rather, since you want to know about this, my sincere helpful suggestion is for you to get a book that explains this...
You're mixing up 'premise' and 'antecedent'. If the antecedent is false then the conditional is true. As to premises, let's not mixup two things, and ...
I didn't change any premises. And I didn't make anything true or false. And there is no "first A" and "second A". There is only one A. I merely pointe...
I'm not swapping any premises, and I'm not making a reinterpretation. Let G stand for "grass is green". Let C stand for "cows bark". G ~G therefore C ...
You need to remedy your misunderstandings of this. I suggest starting with the first chapter of a good textbook in formal logic. Yes, a conditional is...
That's okay for me, as long as I take 'degenerate' in a non-pejorative sense as often in mathematics. Of course, formal logic, or at least a particula...
No, not right. The first premise is not necessarily false. It's been correctly pointed out over and over and over, by different posters in this thread...
I see, the earlier argument. See my edit that I composed while you were posting. A -> ~A is not contradictory. A formula is contradictory if and only ...
~A is a negation but it is not a contradiction. But wait, which argument are we talking about? (1) ~A A therefore A & ~A (2) ~A A therefore ~(A & ~A) ...
(1) The first premise in that argument is not necessarily false. (2) I don't know what 'conclusion is false for validity' means. (3) The conclusion is...
We are not restricted to looking only at the interpretations in which all of the premises are true. If there is no interpretation in which all of the ...
'valid' has three senses: (1) an argument is valid if and only if there are no interpretations in which all of the premises are true and the conclusio...
I appreciate that you say that now. Yet: I was the one who remarked that the argument whose conclusion is ~A is modus ponens. I'll take your word for ...
An argument is valid if and only if there is no interpretation in which all the premises are true and the conclusion is false. That is not a valid arg...
I have never believed that logic is arbitrary symbol manipulation. I have never posted that logic is arbitrary symbol manipulation. I have never poste...
I've said before, and hopefully won't need to say again: When questions about formal logic come up, it is appropriate to check that the claims about f...
All purely symbolic. Get outta here with this "Oh but the poor boy was just trying to get in a bit of common sense everyday logic; not about formal lo...
Actually, I have personally gained a lot from study of mathematical logic, in use outside of mathematics, in practical applications, in organizing ide...
There the poster is (in horrible confusion) discussing truth values per formulas in a context of formal logic (a response to my own mention of modus p...
In his first post: That misconception is not explained merely as a contrast with everyday reasoning. I have never heard everyday reasoning say ""~ A o...
That cuts a crucial part of the sentence: Of course I understand that many people refer to everyday senses. My point though is that after it is made c...
The first states modus ponens as a principle not an argument form. But as an argument form it is such that the premises are a conditional and its ante...
It's interesting that the proof of "if set theory is consistent then set theory does not prove that set theory is consistent" is not so much analogous...
Yes, A -> ~A with A is contradictory. I don't know anyone who has said otherwise. But I can't say what is the source of the mental block in people who...
Meaning that it wouldn't be the case that all tautologies are theorems. If you are interested in the basics of ordinary formal logic, then it would be...
No, you need to know the difference between truth and validity. That difference has been explained in this forum at least a hundred times. It is funda...
I don't know what question you are raising. In ordinary formal logic: (A -> ~A) <-> ~A (A -> ~A) <-> ~A v ~A (~A v ~A) <-> ~A etc. A -> ~A A therefore...
Right. But there is a person here who claims that A -> ~A is necessarily false. That is what is being addressed. Also, the person claims that if the p...
No. Because the premise "If the OP uses propositional logic, it doesn't use propositional logic" is false. At least read the first chapter of a book o...
So what? Modus ponens is well understood and defined in thousands of books and articles and your remarks about it are not consistent with the common d...
(1) Here is that definition in full: "Modus ponendo ponens is the principle that, if a conditional holds and also its antecedent, then its consequent ...
Of course, anyone can stipulate their own definition. But your definition is not the one used in ordinary formal logic, or, as far as I know, in any t...
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