From: "Noam Chomsky"
To: "Jeffrey E." <jeevacation@grnail.com>
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:jeevacation@gmail.com]
Sent: Monday, June 08, 2015 3:07 PM
To: Noam Chomsky
Subject:
I will take your word that you share my thick skin for criticism and share a strange pleasure in learning, even if
it means having to accept that some formerly closely held beliefs might need strong correction. I have no
particular knowledge re politics or history, so I will never offer an opinion. however re mathematics and or
money , I feel on strong ground. That being said, thought puzzles in the paper are brilliant and insightful. the
mathematical descriptions lack rigor , and the metaphors suffer from the common science limitation of trying to
describe things using the engineering metaphors or the tools of the moment.ex. The human or its brain as a
computer ., set theory . It was popular in the early 20th as you know to describe the body as an electric
machine.. the mathematics used today in quantum show more promise , as it attempts to describe things that
appear counter intuitive. or difficult to comprehend , ( your displacement conjecture) your simple X and Y ,
Merge , is quite naive and unfortunately incorrect.
2. from the paper you sent. ; a much more elegant way of conveying what i had failed to do re sentences and
money
European structuralism commonly adopted the Saussurean conception of language ( MONEY) (in the relevant
sense) as a social entity; as Saussure put it, a storehouse of word images ( values ) in the brains of a collectivity
of individuals founded on a "sort of contract."
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