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Vladimir_Nesov comments on Open Thread: February 2010, part 2 - Less Wrong
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The next few posts on my blog are going to be basically about approaching this problem (and given the occasion, I may as well commit to writing the first post today).
You should read [*] to get a better idea of why I see "preference over all mathematical structures" as a bad call. We can't say what "all mathematical structures" is, any given foundation only covers a portion of what we could invent. As the real world, mathematics that we might someday encounter can only be completely defined by the process of discovery (but if you capture this process, you may need nothing else).
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[*] S. Awodey (2004). `An Answer to Hellman's Question: 'Does Category Theory Provide a Framework for Mathematical Structuralism?". Philosophia Mathematica 12(1):54-64.
Hope to finish it today... Though I won't talk about philosophy of mathematics in this sub-series, I'm just going to reduce the ontological confusion about preference and laws of physics to a (still somewhat philosophical, but taking place in a comfortably formal setting) question of static analysis of computer programs.
Great to hear. Looking forward to reading it.
Yes, talking about "preference over all mathematical structures" does gloss over some problems in the philosophy of mathematics, and I am sympathetic to anti-foundationalist views like Awodey's.
Also, in general I agree with Roko on the need for an AI that can do philosophy better than any human, so in this thread I was mostly picking a nit with a specific argument that he had.
(I was going to remind you about the missing post, but I see Roko already did. :)