From: "Noam Chomsky" To: "Jeffrey E." <[email protected]> Subject: RE: Date: Tue, 09 Jun 2015 01:41:58 +0000 I have a VERY thick skin, and love to hear criticism. One of the best ways to learn. And I've often given up closely held beliefs on the basis of persuasive argumentation. But in this case, I just don't see the arguments. It's true that the mathematics lacks rigor, but that's for the same reason that publications in professional math journals lack rigor. The steps that are not spelled out are straightforward enough so that they can be easily filled in. I don't know of any problems about set theory, apart from the classic ones. Some version of set theory is presupposed in every branch of math, including category theory. As for the brain as a computer, I'm not sure what you see as the problem. The papers I sent you do assume that I-language is a computational system, with the properties mentioned, easily formalized. I don't know of any coherent alternative. Actually, very good professional mathematicians and physicists, one working primarily on quantum computers, have attended my regular seminars for years, but I've never heard a suggestion as to how mathematical ideas used in quantum theory would be relevant to systems of the kind we're considering. The "displacement conjecture" is, in fact, an immediate consequence of what would be the best possible theory if it's true: SMT, in particular, the assumption that the basic combinatorial operation is the simplest one possible. Merge is simply set-formation, presupposed in all of mathematics. I agree that it's naïve, if by that you mean very simple, arguably optimally so. But hasn't that been the pretty explicit goal of science, at least since Galileo, quantum theory included? I'd like to hear the objections, and hope to learn from them. Noam From: jeffrey E. [mailto:[email protected]] Sent: Monday, June 08, 2015 3:07 PM To: Noam Chomsky Subject: I will take your word that you share