TonesInDeepFreeze

Got it. The last line of this post: Yes, explosion is similar, in the context of what I posted preceding, with ""any argument with an inconsistent set...

I was editing my post, dropping the comment about a link, while you posted yours above.

We have a definition of validity. Then we show that that definition entails the principle of explosion. It's not my concern to sort out what is in you...

I haven't said anything about 'presuppose'. Rather, I have shown that the definition of validity (semantic) entails the (semantic) principle of explos...

I have not applied the definition in any strange way. And the definition is not based on the principle of explosion. Rather, the definition implies th...

I already explained that the only time a rule yields a contradiction is when it is applied to an inconsistent set of formulas. So, if you want to defi...

Posters are citing me as if to represent what I've said. That calls for, in my words, not those of other people, representing what I've said. My comme...

What, according to you, is the difference? Yes, they are different formulas, but equivalent according to your own definition. Just waving "meta-logic"...

You've not shown any illogic I've committed. Meanwhile, you are slippery mess of informal illogic.

While you are slipshod.

Yes, my typo. Thank you.

A v B is a sentence, not a rule.

What is the difference between "followed" and "present"? And, according to you, how does it vitiate what I said about contradiction. The ordinary rule...

Is that your offering? So, the conditional is false when A is true and B is false (that is ordinary), when A is false and B is true, and when A is fal...

That's very incorrect. Why don't you just read one chapter in an intro textbook? Is there some reason you won't read even a few pages of a book or art...

You still have not stated any rules. The argument: A -> ~A therefore A makes use of the interpretative clauses for '->' and '~'. But I have not mentio...

What are the "full meanings" of "If P then Q" and "P does not imply Q", according to you? And what is the difference, according to you, between "the m...

I was disputed that the following definitions are equivalent versions of the ordinary textbook definition: (1) An argument is valid if and only if the...

The ordinary clause is: P v Q is true if and only if either P is true or Q is true. ('or' inclusive) P -> Q is true if and only if either P is false o...

According to you, what is the full meaning of P -> Q?

"P does not imply Q". Depends on what 'implies' means. It is not the case that if P then Q is formalized ~(P -> Q) that's in the object language It is...

A -> B A therefore, B is not the same argument as ~A v B A therefore, B That doesn't vitiate that A -> B and ~A v B are equivalent.

Where G is a set of sentences and Q is a sentence, "G entails Q" is symbolized: G |= Q I.e, there is no interpretation in which all the members of G a...

Hanover's confusions in this thread start in his very first post: All three of the above are incorrect. A -> ~A is not contradictory. A is true or fal...

To emphasize that, for example, nothing I've said is a barrier to you adding whatever else to the subject you might have to add other than what has al...

Very inviting.

That table of contents looks pretty good. But I wonder whether it is best as a very first book to read.

It is exactly responsive to your post. You said: So, I addressed that. And I didn't say that you said that formal logic lacks value. As to the differe...

Again, the distinction I adduced: P -> Q is true in a given interpretation if and only if either P is false in that interpretation or (inclusive 'or')...

* For argumentation, I suggest studying both informal and formal logic. Informal for practical guidance; formal for appreciation of rigor. I don't hav...

Meanwhile, I hope you're looking up the method of truth tables.

(1) How is your meaning of the conditional different from the ordinary meaning in formal logic? You use "must"; is that in addition to "is"? Example: ...

That is equivalent to saying: A rule is correctly used only if application of it never leads from true premises to a false conclusion. And "never lead...

Nope. You say that your notion of validity is based on proper use of rules, but your notion of proper use of rules goes through the notion of rules be...

Notice that you didn't say anything about the meanings of P and Q, even if they were translated to a natural language. Rather, you mentioned only the ...

(1) What is the meaning of the conditional? (2) A set of premises can prove more than one conclusion. So what is "the" conclusion that "should be"? (3...

You say a relevant rule is on such that if all the premises are true then the conclusion is true. That is the ordinary definition of 'valid' in formal...

What is an example of rule that if it weren't followed then the conclusion would be different? Different from what? The rules of formal systems in mat...

What relevant rules? What makes a rule relevant? Whose rules? What if people use different sets of rules from one another? What if the rules are uncle...

They don't imply a definition of validity. If you read chapter one, you'll understand that we have: (1) a definition of 'valid argument' (2) a definit...

Meanwhile, do you have any thoughts about offering your own unequivocal definition of 'valid argument'?

I was re-composing my post while you were posting your reply.

Your question is answered by looking at the method of truth tables. That is in chapter 1 of any book in 'Logic 1'.

Whatever "structurally consistent" means there, a clear and simple way to say it is: The argument is and instance of modus ponens. And no instance of ...

Having a false premise and a false conclusion does not in and of itself make an argument invalid. You have forgotten or did not understand the definit...

Of course. But the ordinary formal definition is itself not equivocal. It is definite. It gives an 'if and only if' with a definiens in which all the ...

Where can one read an account of ordinary modal logic, ordinary intuitionistic logic or basic Kripke semantics in which that is the case?

It makes sense in the sense of having a truth value. No, quite incorrect. Egregiously incorrect. That you say that shows that you haven't paid attenti...

(1) You say "in a consistent deductive system" but your remarks wouldn't apply to ordinary sentential or predicate systems, but rather, more specifica...

Yes: Df. ~P stands for P -> f where 'f' is primitive. But, just to note, that can be a definition in classical logic too.