TonesInDeepFreeze

No, that's not correct. If there is no assignment in which all the premises are true, then the argument is valid. That is very different from what you...

"An argument is deductively valid if and only if it is not possible for the premises to be true and the conclusion false." (The Logic Book - Bergmann,...

"A sentence Phi is a consequence of a set of sentences Gamma if and only if threre are no interpretations in which all the sentences in Gamma are true...

(1) I did not say it is "trivial". That was another poster. I already pointed out to you that I did not say it is "trivial". So this is the fourth tim...

There is no question. He does not presuppose it. (1) The consequence relation is this: {<X Y> | X is a set of sentences & Y is a sentence & there is n...

Grabbed on the fly: Three equivalent variations: "Valid: an argument is valid if and only if it is necessary that if all of the premises are true, the...

Not just consistent, but equivalent with.

Quite not idiosyncratic. And the argument is valid by Gensler, Enderton, SEP and Wikipedia. Gensler: "An argument is valid if it would be contradictor...

You're wrong. The definition of 'valid argument' there is standard. And with the argument mentioned in the original post, it is the case that there is...

Indeed. Equivalent to the definition I've been stating. Indeed. Yet another way of saying the definition. Indeed. It is a point I've made many times. ...

That is the third time in this thread that you've put words in my mouth.

Just to note: tautology is semantic and contradiction is syntactic.

No, it's not. Yes. So? A rigorous definition: An argument is an ordered pair such that the first coordinate is a set of statements* and the second coo...

So would it be fair to say that 'why' is more amenable to being answered when causality is involved? That goes to the point that in mathematics it is ...

Of course, I understand the basis of the sarcasm. The original post challenges the validity of A -> ~A A therefore ~A I don't see your substitution ca...

Very good. Thank you.

I don't claim to have academic definitions of 'univocal' and 'equivocal', but at a naive level, as I'm merely winging it here, it seems to me that: 't...

It occured to me, when I thought of the irony operator, that we have the problem that we can't substitute salva veritae within a belief operator. That...

You mean substitute "George will open the store" with "If George will open the store then George will not open the store"? Why make that substitution?...

I edited my post to mention that, if I understand your main point, I agree with it. And, if I understand, I agree with your disjunction: Either make t...

If I understand your point, I agree with it, and I think it is incisive and apropos. Let Rx mean x runs (where 'runs' includes both 'moving quickly on...

No absurdity is a validity.

What is the conditional? / Maybe there could be an intensional logic with a defined irony operator 'i'. s is a speaker P is a statement B(s P) iff s b...

I said it over and over and over for you. All you had to do is read the replies given you. And that's hardly the only point I explained for you.

No, with a false antecedent the conditional is true, sometimes described as 'vacuously true'. It's the conditional that is deemed true when the antece...

What is the definition of 'flows'? I didn't say they are the same. They are very different. This the second time, in this thread alone, that you've pu...

As I said, in this particular regard, I'm merely applying the definitions of ordinary formal logic. As I said, I don't claim that those definitions ha...

You can retire to the blazes.

I very much appreciate that it may be quite counter-intuitive to many people.

You can't be serious. For the umpteenth time: An argument is valid if and only if there is no interpretation in which all the premises are true and th...

1. A -> ~A ... premise 2. A ... premise 3. A & ~A {1 2} 4. ~A {1} 5. ~A v A {} That is correct. Each inference is valid. No invalidity has been shown.

It would be nice to have a specification of your logic so that other people could determine for themselves what obtains and does not obtain in it, wit...

I can better comment on that if you provide the specific arguments you have in mind. The way to prove the invalidity of an argument is to show that th...

No, I am not doing that. The original argument is one thing. I don't substitute anything in it. But you claimed that the premises are consistent. So I...

That argument has been addressed extensively in another thread. In ordinary formal logic, the argument forms mentioned are valid. "ignoring premises" ...

You can't be serious. I've given the definition probably at least fifteen times already. An argument is valid if and only if there are no interpretati...

The key word there is "at first glance". Upon consideration, it is seen that the first premise is not contradictory.

I said nothing about identity. Certain posters are disputing the validity of an argument. I am only remarking about what happens to be the case in ord...

1 A -> ~A ... premise 2 A ... premise 3 ~A ... {1 2} 4 A & ~A {2 3} So the premises are not consistent. A -> ~A A therefore ~A Let A be false. That is...

There are no interpretations in which both premises are true.

I'm interested in what that definition is. Meanwhile, the context here is examination of a particular formal argument. In that context, you fallacious...

It's hardly an insult to say that I don't understand why you are not minding the definitions and explanations. I've patiently given you information an...

I'm restating in my own manner some of the points you've made. I agree that a pedantically correct application of notions in formal logic could be abu...

PS. 'vacuous' is more informative for the conditional than 'trivial', since 'vacuous' is specfic while 'trivial' is not. That is, vacuousness is a cer...

A -> ~A A therefore ~A There is no interpretation in which both the premises are true. I don't know why you continue to ignore the definitions and exp...

The argument: A -> ~A A therefore ~A valid Another argument: A -> ~A A therefore A valid The fact that the premises are inconsistent doesn't vitiate t...

You think incorrectly. I well know how logicians and mathematicians use the verbiage 'trivially true' and 'follows trivially' for statements and argum...

A -> ~A says If A then it is not the case that A That is equivalent with it is not the case that A In an interpretation in which A is false, "it is no...

That is wrong. You are plainly misusing the terminology. Considering different interpretations doesn't change formulas. And I'm not making "one A" fal...

Do you intend for this to be a Socratic interview?