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Article 4645 of comp.ai.philosophy:
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>From: orourke@unix1.cs.umass.edu (Joseph O'Rourke)
Newsgroups: comp.ai.philosophy
Subject: Re: A rock implements every FSA
Keywords: Putnam, quantum mechanics
Message-ID: <45247@dime.cs.umass.edu>
Date: 21 Mar 92 20:10:49 GMT
Article-I.D.: dime.45247
References: <44855@dime.cs.umass.edu> <1992Mar21.164356.13660@uwm.edu>
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Reply-To: orourke@sophia.smith.edu (Joseph O'Rourke)
Organization: Smith College, Northampton, MA, US
Lines: 32

In article <1992Mar21.164356.13660@uwm.edu> 
	markh@csd4.csd.uwm.edu (Mark William Hopkins) writes:

 >In article <44855@dime.cs.umass.edu> 
	orourke@sophia.smith.edu (Joseph O'Rourke) writes:

   >>Assumption 1 (Continuity): 
   >>	S is a continuous function S(t) of time t.
   >>Assumption 2 (Noncyclical): 
   >>	For t1 != t2, S(t1) != S(t2)

 >Well, where are you ever going to find such an object?  Especially when the
 >very concept of continuum breaks down at small scales in the entire Universe.
 >Space and time are not continuous, and they're not infinitely divisible.  So
 >because of this finiteness, there MUST be FSA's so large that they cannot
 >be represented even by the whole universe -- except by a method of coding
 >that itself is too big to fit in the universe.

I agree.  I mentioned that one could criticize the physics of Putnam's proof,
and this is similar to what I had in mind.  Another way to say this is
that Putnam's assumptions require at the least a size restriction: on
the size of the FSA with respect to the size of the physical system.
For example, if the physical system is a single hydrogen atom, then his
assumptions are clearly false.
	Putnam has written at least two (if not more) papers on quantum
mechanics, so it is not as if he is unaware of the physics.  He does
use the phrase "ordinary macroscopic open system,"  which implies that
a hydrogen atom would not suffice.  Unfortunately, he uses this phrase
as if it had a precise technical definition known to the reader.
	I don't feel, however, that it would be a serious flaw if his 
theorem *only* fails for FSA's so large that they cannot fit in this 
universe.


