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Article 4539 of comp.ai.philosophy:
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>From: chalmers@bronze.ucs.indiana.edu (David Chalmers)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech
Subject: Re: A rock implements every FSA
Message-ID: <1992Mar18.045939.3084@bronze.ucs.indiana.edu>
Date: 18 Mar 92 04:59:39 GMT
References: <44993@dime.cs.umass.edu> <1992Mar17.224156.9177@bronze.ucs.indiana.edu> <1992Mar17.231452.9979@husc3.harvard.edu>
Organization: Indiana University
Lines: 40

In article <1992Mar17.231452.9979@husc3.harvard.edu> zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:

>To quote the source, p.122: "A finite automaton is characterized by a table
>which specifies the states and the required state-transitions.  Without
>loss of generality, let us suppose the table calls for the automaton..."

Curiously you omit the immediately following: "to go through the
following sequence of states in the interval...that we wish to simulate
in real time."  The trouble, of course, is that one can't infer from

(1) The table calls for the automaton to go through sequence ABABAB...
in real time;

to

(2) Anything which goes through sequence ABABAB... in real time implements
the FSA.

The reason being, of course, that the table imposes lots of *other*
constraints on the system, not just about its actual behaviour, but
about its counterfactual behaviour.  e.g. "if the system were in
state C, it would transit into state D", where state C is a state
that never occurs in the particular sequence in question.

>In other words, the "Theorem" talks about the very *identity* of the FSA in
>question, whence your states C and D will ipso facto be found in the same
>table.

Of course C and D will be found in the table.  That's my point.  They
won't be found in the rock, though.  Putnam's construction doesn't
even *define* any physical states corresponding to C and D, let alone
ensure that the right transition relation holds between them.
Therefore the claim that the system in question implements the FSA is
groundless.  At best, it implements a "trace" of a particular run
of the FSA, as Joseph O'Rourke nicely put it.

-- 
Dave Chalmers                            (dave@cogsci.indiana.edu)      
Center for Research on Concepts and Cognition, Indiana University.
"It is not the least charm of a theory that it is refutable."


