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Article 4644 of comp.ai.philosophy:
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>From: markh@csd4.csd.uwm.edu (Mark William Hopkins)
Subject: Re: A rock implements every FSA
Message-ID: <1992Mar21.164356.13660@uwm.edu>
Keywords: Putnam, implementation
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Organization: Computing Services Division, University of Wisconsin - Milwaukee
References: <44855@dime.cs.umass.edu>
Date: Sat, 21 Mar 1992 16:43:56 GMT
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In article <44855@dime.cs.umass.edu> orourke@sophia.smith.edu (Joseph O'Rourke) writes:
(Putnam's proof that every FSA is contained in a rock)

>[Hilary Putnam, "Representation and Reality" (1988), Appendix, 121-5]
>
>Let S represent the state of a physical system (the rock).
>
>Assumption 1 (Continuity): 
>	S is a continuous function S(t) of time t.
>Assumption 2 (Noncyclical): 
>	For t1 != t2, S(t1) != S(t2)  [where "!=" means "not equal"].

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.


