TonesInDeepFreeze

That is a bad misconception. It's not how it works. Proof is from a set of premises. A natural deduction proof lists premises. A reductio premise howe...

Logicians and philosophers of mathematics examine logics with intense scrutiny and may be interested in all kinds of formal and philosophical alternat...

It would be rare that any one poster can answer all questions. I have given corrections, explanations about the logic that is being critiqued, answers...

We need to be careful to recognize that "A is false" is not simpliciter. Rather, "A is false in model M" (with sentential logic, a model may be repres...

That's not what I said. If I recall correctly, you said that "A -> (B & ~B)"* may be translated as "A implies a contradiction". (*Or it might have bee...

This caveat will cover my posts in general: People may have different contexts with different meanings of terms, different fundamental conceptions, di...

I don't think that way, except possibly as elliptic. Especially if the context demands analysis of the logical connections, I would says something lik...

Does "apply" there refer to proofs of "(A -> (B & ~B)) -> ~A" or "~(B & ~B)"? LEM is not needed to prove those.

I asked because I wanted to know whether you think they are equivalent, and if not, then knowing in what ways they are different would shed light on t...

I am still looking at references to get a grasp of those terminologies. I think I have at least a picture of the notion of analogical equivocal and an...

That might be because, for ease of clarity, the sentence needs parentheses. "¬(A?(B?¬B)) entails A" In order not to conflate with 'entails' to stand f...

What in the world?! The poster takes issue with the fact that it happens sometimes that one needs to delete! I deleted some posts that were only start...

The hypocrisy there is astounding. The poster has written a whole lot of posts in this thread. Possibly a lot more characters I have written in this t...

And actually we don't need the 'F'. (Z\I)+~I is bi-interpretable with PA.

I said the quote is incorrect. You agreed. So I asked why you posted it. Now you've reversed yourself. I don't offer this as a philosophy, not somethi...

So why do you quote something that is seriously incorrect?

I find mathematics to be the opposite of boring.

Usually we have to have LEM to have truth tables. For example, intutionistic sentential logic cannot be evaluated with truth tables with any finite nu...

I explained why "if a statement is true, then that statement is implied by any statement whatever" is a misleading characterization.

I think the context of the paper is classical logic, or a logic that has material implication.

To be clear, that is not my own claim. Not untrue to me. You skipped what I said about that. I didn't intend to enlighten you. You asked me for a tran...

I understand the proviso "in same time in all respects". But that proviso may be given more generally, upfront about all the statements under consider...

Yes. Well put.

So when you say you claim the opposite, do you mean you claim the denial of: "It is not the case that both water can be green and water can be not-gre...

At least for my sake, you don't need to link me to a generator for such simple matters. In the case that ~(A -> (B & ~B)) is true, A is true. I asked ...

I meant 'non-contradiction', not 'contradiction'. I meant: Do you take "It is not the case that both water can be green and water can be not-green." a...

Whatever the relative merits, do you see my point that the quote is incorrect, since there are approaches to formalism that don't view mathematics as ...

If I understand, you take It is not the case that both water can be green and water can be not-green. as an instance of the law of contradiction. (?) ...

You may hold that the view has merits. I'm only pointing out that formalism is not confined to that view.

Would allow simplifying that to: For any statement A, it is not the case that both A and not-A.

That is one extreme view. That is extreme formalism. It does not speak for all formalists.

What is your statement of the principle?

I haven't followed your posts, so there may be context I need. That said, (1) What is your context? Classical logic? Some other formal logic? Notions ...

I haven't followed your posts, so there may be context I need. But at least at face value: "the presence of water implies the presences of oxygen" is ...

Yes, I can see a distinction between metaphysics/ontology and foundations. Perhaps though the distinctions can be quite less than sharp.

Why not? Maybe if 'logical truth' was regarded as a property of formal semantics? I mean, can't we regard 'logical axiom' as merely a logical notion w...

Right. I wonder about the categories. The schools could be something like: realist logicist formalist structuralist constructivist

Right, I caught that a moment later, and edited mine.

So you are asking "couldn't a formalist not be a nominalist?" I'll try to check it out.

An interpretation, aka 'a model'. For sentential logic, an interpretation assigns to each sentence letter a value True of value False. Most commonly t...

No, not tout court. There's an 'however'. They correctly say it is invalid but they also incorrectly say that, however, symbolic logic disagrees. It's...

Whatever you think was meant to be highlighted, or plausible, or your interpretation, the plain fact is that the paper says that symbolic logic regard...

It correctly says it is invalid, but incorrectly says that symbolic logic "disagrees". It's right there in the paper. It is amazing that you ignore th...

Again, look at the exact words in the paper: "Its premises do not prove its conclusion." 'it' refers to the Lassie argument. "modern symbolic logic di...

https://thephilosophyforum.com/discussion/comment/916812 Since there were so many typos in my reply, here it is corrected: Symbolic logic definitely d...

No, the paper says the argument is invalid, but that symbolic logic says it's valid. The paper is a polemic against symbolic logic, and it argues (egr...

Is Hilbertian formalism incompatible with platonism? I'd like to see an argument that it is.

That is what the paper says. The paper is incorrect. Not just incorrect, but incorrect due to egregious sophistry, ignorance or blatant lack of reason...

It's not ambiguous. It's as plain as day, with a plain reading: "Its premises do not prove its conclusion." 'it' refers to the Lassie argument. "moder...