andriy_koval

8 ms·

61.
by andriy_koval 1mo ago
> Either way, it seems AI was involved. I think the important question which AI made breakthrough, Claude or Codex..
62.
by andriy_koval 1mo ago
> when someone refers to “ZFC” when they are filling a slot that needs a (axioms + rules of inference), the obvious interpretation is that they are referring to the usual system of ZFC. its bro-math. In formal math you need to be specifi
63.
by andriy_koval 1mo ago
zfc is a bunch of axioms and not inference system. It is commonly assumed that it is built on top of some unspecified first order logic which commonly assumed to include bunch of inference rules. There is no ground truth in my understanding
64.
by andriy_koval 1mo ago
> Formally, a function f is a relation discussion was if zfc has functions at all, not sure why you put relation here.
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by andriy_koval 1mo ago
Obviously citation from wikipedia can't be considered as replacement of math proof. > If you're going against the general consensus you should present something more than nebulous assertions that it's wrong. burden of proo
66.
by andriy_koval 1mo ago
and what is that system?
67.
by andriy_koval 1mo ago
we need to find real solvable problems. Those you listed are mostly not solvable in society with current governance process. AI got lots of abilities suddenly emerged, and can be applied on solving problems and not silly toys.
68.
by andriy_koval 1mo ago
No, once you start formalize this, it becomes complicated. There is a reason why looks like there is no "peano can be derived from zfc" theorem which would close dispute, and my opponents need to throw links on bro math from stack
69.
by andriy_koval 1mo ago
I referred to specific definition in wikipedia. Your "first course notes" are irrelevant here, they can't be reviewed, they not proofread and unlikely can be considered as any reasonable quality if we are talking about real
70.
by andriy_koval 1mo ago
Your third year notes from Cambridge has very low authority to me
71.
by andriy_koval 1mo ago
> you just build some sets to represent numbers and make operations that act the same way as arithmetic which is already "just" some non trivial problem(there is no "operations" in set theory), and we are discussing
72.
by andriy_koval 1mo ago
> According to ZFC, a function is a set whose members are pairs, such that no two different pairs have the same first element. Can you cite where did you get this?
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by andriy_koval 1mo ago
> Honestly I’m not sure how you simultaneously claim to be a PhD in formalisation and also not be aware of the existence of Isabelle/ZF, for example. I am aware, also I am not sure why you wrote all of this. Your unknown to me &quot
74.
by andriy_koval 1mo ago
Maybe there is truth in it? I asked Astra to make some changes, it built crazy overengineered code, switched back to Sol, said code is too complicated, rewrite it, and it made lot cleaner code. I feel some models could chaise complicated be
75.
by andriy_koval 1mo ago
ok, you now added some unknown inference system in addition to zfc
76.
by andriy_koval 1mo ago
zfc doesn't have functions, so you are building something new on top of it. Also, I am not sure successor function is enough for PA.
77.
by andriy_koval 1mo ago
imo, those two links are example of rather low quality weird math discussions, but you can keep your opinion
78.
by andriy_koval 1mo ago
coming back to your argument about peano being obtained from zfc, you obviously can't prove that it happened using purely zfc, and not some logical framework embedded into those proof assistants. I said I am not expert, I am indeed not
79.
by andriy_koval 1mo ago
you are entitled to have your opinion :-)
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by andriy_koval 1mo ago
looks like we are in disagreement
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by andriy_koval 1mo ago
> interpreted its hard to me to tell what this means formally(as I said I am not expert). There is no "interpret" operator in zfc. I believe what it says if you add some robinson axioms + some logical rules on top of zfc, you c
82.
by andriy_koval 1mo ago
> expressive enough to produce you understand that "expressive enough to produce" are not obvious elements of zfc, that's some average consumer napkin math and not strict formalization.
83.
by andriy_koval 1mo ago
support your point with explanation or be ignored :-)
84.
by andriy_koval 1mo ago
> Goedel Incompleteness -- the proof that the the axiomatic itself cannot be proven, like using ZFC to prove ZFC, but that's another topic. Godel theorems are for systems with basic arithmetic, zfc doesn't include arithmetic, t
85.
by andriy_koval 1mo ago
do we know if claude's formalization is built on top of zfc and not zfc+extra? zfc itself is not sufficient, you need some layers of extra concepts formalization to fit specific problem domain(e.g. zfc doesn't define even basic ar
86.
by andriy_koval 1mo ago
> I am sure a lot of this development was formalising the prerequisites How can you be so sure its not result of inefficiency?
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by andriy_koval 1mo ago
Not just lean, but math foundation itself, I am not strong expert, but my understanding is that there is no fully recognized axiomatic foundation for modern math, all proposals could lead to some weird results.
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by andriy_koval 1mo ago
especially compared to existing 129 pages proof by human
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by andriy_koval 1mo ago
it matters because they are irrelevant to ai and software, hence this discussion
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by andriy_koval 1mo ago
for every small GenAI model there will be larger model or cluster of models which are smarter than small model

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