> But, again, phonetics doesn't help when twelve words have identical phonetics! You keep missing the point, so I'll try one last time. Look at a picture of the Rosetta stone. I can read Greek but I find the Greek part…
> Japanese is only spoken language like others basically only for small children and idiots. Literate, grown-up Japanese is a written language first. I seriously doubt that. Literacy levels rose in Japan during the…
I don't deny that reading Japanese written in kana alone is currently more painful than with kanji. However, it seems to me that the current writing system is a local optimum and not a global one. If people started…
> There are uncountably many correct mathematical theorems. Almost all of them can't even be written in symbols. What are you talking about? A theorem is a statement that has been proved from some axioms. A statement…
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 proving not-P by assuming P and reaching a…
> 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 accordingly, rather than try for a…
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 [] are not. On a QWERTY keyboard, this…
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 properties that are not described by it,…
> 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 context? Yes, that's what I mean. (For me,…
> 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 can do complete, consistent and…
> 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 the context of set theory. What is the…
> 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 to the claim that "most mathematicians…
> 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 what actually determines truth [...]…
> 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 rigorous. But we do use the word "true" alone.…
> 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 valid in set theory". The point being that…
> 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; [...] Sure. But I feel we are deviating from…
> 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 notion. Honestly, "true but unprovable"…
> 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 of "true but unprovable" which is wrong…
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 axioms, typically ZFC. Then "every model"…
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 and only if it is provable. So, another…
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 at 4MHz. So a modern 2 GHz processor…
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 was "What is the most important thing…
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 always the compiler, then I agree, but…
> 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 allocation (through graph coloring). Register…
> But, again, phonetics doesn't help when twelve words have identical phonetics! You keep missing the point, so I'll try one last time. Look at a picture of the Rosetta stone. I can read Greek but I find the Greek part…
> Japanese is only spoken language like others basically only for small children and idiots. Literate, grown-up Japanese is a written language first. I seriously doubt that. Literacy levels rose in Japan during the…
I don't deny that reading Japanese written in kana alone is currently more painful than with kanji. However, it seems to me that the current writing system is a local optimum and not a global one. If people started…
> There are uncountably many correct mathematical theorems. Almost all of them can't even be written in symbols. What are you talking about? A theorem is a statement that has been proved from some axioms. A statement…
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 proving not-P by assuming P and reaching a…
> 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 accordingly, rather than try for a…
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 [] are not. On a QWERTY keyboard, this…
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 properties that are not described by it,…
> 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 context? Yes, that's what I mean. (For me,…
> 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 can do complete, consistent and…
> 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 the context of set theory. What is the…
> 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 to the claim that "most mathematicians…
> 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 what actually determines truth [...]…
> 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 rigorous. But we do use the word "true" alone.…
> 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 valid in set theory". The point being that…
> 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; [...] Sure. But I feel we are deviating from…
> 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 notion. Honestly, "true but unprovable"…
> 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 of "true but unprovable" which is wrong…
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 axioms, typically ZFC. Then "every model"…
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 and only if it is provable. So, another…
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 at 4MHz. So a modern 2 GHz processor…
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 was "What is the most important thing…
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 always the compiler, then I agree, but…
> 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 allocation (through graph coloring). Register…