Fair enough! Yeah what I've been really struggling with is the "philosophy" of it. LLMs *love* to say "this has been mathematically proven," while secretly using unformalized or unformalizable statements. Some weird combo of appeal to authority, prose reward hacking, a strong "intro to proofs" attractor, and worst of all sometimes that's just how logicians actually talk 😆
@terrible_archer@gravcapital Noted! Harper ch 1-3 seems GOATed, this is where I'm spending most of my time at the moment. And the metamath book, hanging on every word.
Or that Metamath applies Hilbert-style rules [always] but whether its database described Hilbert-style logic is different...
Is there a good web forum for this? Lean Zulip, and Metamath mailing list and github... I'm trying to have more human conversations, and though I'm checking references deeply I'm still bound to end up with wildly weird viewpoints and terminology *somewhere* when indep. studying.
You know how the closer you get in expertise to someone the more vehement your disagreements can become?
This is how I feel about 95% of what I've read in logic and formal languages. And 100% of things of the form "technically an X is a Y-system not a Z." Like wth those are entirely new English words used informally, I thought we were being formal, aren't you just adding to the pile of things we have to formalize?
"Actually in my notation ⊢ is a statement about the existence of a proof not merely [...]" oh really, I must be going crazy, I could have sworn it was a symbol written on a piece of paper.
Obviously the way out is just to build things but omg the way the theory is communicated is annoying.
👀Heck yeah ty. Yeah my selection of books is quite weird. When I tried to study Lean and Rocq I kept saying "no what is a type? No you're explaining it to me in English, I want to know what is a type?" so writing a Metamath interpreter and bootstrapping through type theory theorems to Lean is the only way for me to go.
I'm not even trying to insist on a philosophical position, I just have given up every time I tried to learn that stuff (incl. logic books, model theory, computability) for a decade+, out of confusion, and this is the first time I'm seeing things concretely.
@DevinWatson89 Nice!
Yeah as a indep. learner it's so difficult to get the terminology right, I keep having to cite like 5 different books.
I'm debating whether to just tell everyone "oh I'm a radical finitist" or whatever just to scare away anyone not making their statements concrete.
Why play Counter Strike when you could compute critical exponents with the conformal bootstrap? Had the silicon gods code SDPviBe, a port of the great SDPB solver, optimized to run on gamer GPUs. On one second hand RTX 3090, it is up to 40 times faster than a 64 core EPYC node.
I'll have you know the other day I told someone, "oh yeah kirancodes did something with formally verified shaders, let me look it up" and immediately ate crow 😆
No less cool as hell of course. I see now bloom filters are not Bloom filters. Bloom filters are one thing while Bloom filters are another, in other words.
Re: formalization. When I was learning classical mechanics I saw one of Tadashi Tokeida's talks in person. I came away doubting that the cm I was learning about -- which couldn't describe the phenomena in his talk -- was the cm physicists should care about at all.