[Wittrs] Syntax and Semantics in Mathematics

  • From: Joseph Polanik <jpolanik@xxxxxxxxx>
  • To: wittrsamr@xxxxxxxxxxxxx
  • Date: Sat, 27 Mar 2010 07:10:25 -0400

SWM wrote:

>Joseph Polanik wrote:

>>SWM wrote:

>>>... my view is that Searle's position on consciousness implies
>>>dualism of the Cartesian variety (but not that he is a subscriber to
>>>Descarte's complete philosophical doctrine[s]).

>>what, specifically, is the position that Searle explicitly takes that
>>tells you that Searle is implicitly (not explicitly) a Cartesian
>>dualist?

>The dualist implication is in the claim that the CR demonstrates that
>computational processes running on computers can't cause consciousness
>BECAUSE there is no understanding to be found in the CR, despite its
>"behavior". (Searle's third premise in the iteration of the CRA we have
>been considering on this list.)

according to an earlier post of yours, Searle's third premise is "Syntax
does not constitute and is not sufficient for semantics" and this
certainly qualifies as a position that Searle has explicitly taken.

>The only reason that THAT would be the case is if we presume that
>understanding must be a bottom line property, i.e., it must be found in
>the constituents themselves and not as a function of some of them in
>some possible combination (which the CR just may not be specked to
>provide). The dualism is grounded in the idea that understanding is
>irreducible to anything not like itself, that it's an irreducible
>property of certain things.

it sounds like you are saying:

dualism implies that understanding is a bottom line property which
implies that Searle's third premise is true.

Searle believes that his third premise is true.

(therefore) Searle is a dualist.

this is a slightly more complicated version of the fallacy of affirming
the consequent. you must really like that fallacy, Stuart!


* * *

in any case, there are grounds unrelated to the CRA Presumption for
believing that syntax does not constitute and is not sufficient for
semantics.

in the early 20th century the mathematician, David Hilbert, advocated
programmatic formalism. its aim was to reduce mathematics to a set of
axioms that could be manipulated syntactically and thereby prove its own
consistency.

from the wikipedia article:

"In foundations of mathematics, philosophy of mathematics, and
philosophy of logic, formalism is a theory that holds that statements of
mathematics and logic can be thought of as statements about the
consequences of certain string manipulation rules."

"For example, Euclidean geometry can be seen as a "game" whose play
consists in moving around certain strings of symbols called axioms
according to a set of rules called "rules of inference" to generate new
strings. In playing this game one can "prove" that the Pythagorean
theorem is valid because the string representing the Pythagorean theorem
can be constructed using only the stated rules."

"According to formalism, the truths expressed in logic and mathematics
are not about numbers, sets, or triangles or any other contensive
subject matter — in fact, they aren't "about" anything at all. They are
syntactic forms whose shapes and locations have no meaning unless they
are given an interpretation (or semantics)."

[http://en.wikipedia.org/wiki/Formalism_(mathematics)]

the mathematicians of the world woke up from Hilbert's dream when Godel
showed that a non trivial formal (axiomatic) system would not be
complete and could not prove its own consistency.

now, as it happens, Godel is part of the Plato/Penrose axis of platonic
dualism; but, his mathematical results stand on their own.

Joe


--

Nothing Unreal is Self-Aware

@^@~~~~~~~~~~~~~~~~~~~~~~~~~~@^@
      http://what-am-i.net
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