Viewing profile — loicd

The distinction you make is correct in the sense there is indeed a fundamental difference between proving P by assuming not-P and reaching a contradiction and on the other hand pro…

> Even their inventor had trouble writing correct code in their presence I didn't know that. Could you provide a more specific reference?

In addition to $TERM, I wish there was a standard variable defined by terminal emulators that would contain the background color. This would let programs choose their colors accord…

The QWERTY layout has a funny difference with for instance the french AZERTY layout. On an AZERTY keyboard, the parentheses () are directly accessible whereas the square brackets […

In section II.D: > If one rejects the ERH, one could argue that our universe is somehow made of stuff perfectly described by a mathematical structure, but which also has other prop…

> On the other hand, I think you understand it to mean: "true in all models of some latent theory left implicit", where the theory may be ZF(C) or something else depending on conte…

> Systems of mathematics cannot be both complete and consistent No. They can't be at the same times complete, consistent, decidable and powerful enough to express arithmetic. You c…

> 3. The definition I suggested, where we say P is true iff it holds in some “standard model”; By the way, I wish you would answer my previous objection about that definition in th…

> This is very far away from my original point Yes, the discussion has deviated, and I don't think we will resolve the disagreement, but I wanted to make my position clearer w.r.t …

> I suspect that most mathematicians are Platonists (this may be my bias creeping in) and they believe the objects they work with are real > [...] I dispute that rigourous proof is…

> As per 1, my position is that there is no such thing as “true alone”, at least not in mathematical logic Yes I agree. There is always some context implied if we are being rigorou…

> That doesn’t mean “X is valid”; if something follows from the axioms of set theory then it holds in all models of set theory Yes, I was being elliptic. That should read "X is val…

> We both agree that there is a clear distinction between formulae that are true in some model (specified, or inferred from context) and formulae that are true in all models; [...]…

> I don’t think this is a standard definition. Well, I suppose it depends on your definition of standard. That's how I have been taught logic. I also believe it is the historical n…

> You can't claim that's it's even "widely accepted" that the axiom of choice is "true". I have never claimed anything like that. The original comment was a reaction to the notion …

If you don't have any axioms, the statements that are true in every model are exactly the tautologies (by definition). Usually though, one is interested in a particular set of axio…

Exactly. A statement is true by definition if and only if it is satisfied in every model. Also, Gödel also proved the completeness theorem that states that a statement is true if a…

I think it would make more sense to measure the longest computation in the number of cycles executed rather than in seconds. If I'm not mistaken, Voyager 2 had a processor running …

Nice! I got a bit enthusiastic about this: "Modern large language models are powerful but often slow to use and lack information about current events." One of my first questions wa…

OK, I suppose I have to dig deeper into Rust to determine whether I really disagree with that, or maybe this is too vague. The question is: who applies your workarounds? If this is…

> Compilers already solve multiple NP-complete problems in the course of compilation after all, for example register allocation. The NP-complete problem is optimal register allocat…

The nature of the elements of the set does not matter, since the existence of a choice function on the set A guarantees the existence of a choice function on the set B as soon as t…

There are weaker forms, those accepted in intuitionistic logic. The law of excluded middle usually appears in mathematical proofs in the form of reasoning by contradiction: To prov…

> The rejection of double-negation elimination is more or less the (rather intuitive) idea that knowing why something must be true doesn't automatically mean you know how it's true…