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>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech
Subject: Re: A rock implements every FSA
Message-ID: <1992Mar18.095140.9984@husc3.harvard.edu>
Date: 18 Mar 92 14:51:37 GMT
References: <1992Mar17.224156.9177@bronze.ucs.indiana.edu> 
 <1992Mar17.231452.9979@husc3.harvard.edu> <1992Mar18.045939.3084@bronze.ucs.indiana.edu>
Organization: Dept. of Math, Harvard Univ.
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In article <1992Mar18.045939.3084@bronze.ucs.indiana.edu>
chalmers@bronze.ucs.indiana.edu (David Chalmers) writes: 

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

MZ:
>>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..."

DC:
>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."

I omit it because it in no way vitiates the all-inclusive meaning of the
first clause.  In any case, it's good to see you engage the actual text.

DC:
>	         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.

I call for charity: to me, Putnam's text is suggesting a sequence
exhaustive of all states that characterize the FSA.

MZ:
>>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.

DC:
>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.

This is easy: first, you interpret the states of Putnam's automaton as
ordered pairs <state, input> of a FSA (cf. the relevant comments on p.124);
follow this by running through enough input/state combinations to exhaust
the finite combinatorial possibilities afforded by the machine's table.
Finally, you do the mapping.  In this way, there will be no counterfactual
possibilities left unaccounted for.

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: Mikhail Zeleny                                                     :
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