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Article 4731 of comp.ai.philosophy:
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>From: chalmers@bronze.ucs.indiana.edu (David Chalmers)
Newsgroups: sci.philosophy.tech,comp.ai.philosophy
Subject: Re: A rock implements every FSA
Message-ID: <1992Mar26.034816.29572@bronze.ucs.indiana.edu>
Date: 26 Mar 92 03:48:16 GMT
Article-I.D.: bronze.1992Mar26.034816.29572
References: <1992Mar24.112548.10215@husc3.harvard.edu> <1992Mar25.003556.6063@bronze.ucs.indiana.edu> <1992Mar25.094354.10243@husc3.harvard.edu>
Organization: Indiana University
Lines: 65

In article <1992Mar25.094354.10243@husc3.harvard.edu> zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:

>It is.  Your response never made it here; please repost.

Newsgroups: comp.ai.philosophy,sci.philosophy.tech
>From: chalmers@bronze.ucs.indiana.edu (David Chalmers)
Subject: Re: A rock implements every FSA
Message-ID: <1992Mar18.202206.10276@bronze.ucs.indiana.edu>
Organization: Indiana University
References: <1992Mar17.231452.9979@husc3.harvard.edu> <1992Mar18.045939.3084@bronze.ucs.indiana.edu> <1992Mar18.095140.9984@husc3.harvard.edu>
Date: Wed, 18 Mar 92 20:22:06 GMT

In article <1992Mar18.095140.9984@husc3.harvard.edu> zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:
>In article <1992Mar18.045939.3084@bronze.ucs.indiana.edu>
>chalmers@bronze.ucs.indiana.edu (David Chalmers) writes: 

>>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.

Ah, good old Charity.  In any case, this won't work, as there's
no reason to believe that such a sequence will exist.  Most FSA's
don't have the property of reversibility, i.e. that if there is
a path from state A to state B then there is a path from state B
to state A.  It would be particularly surprising if an FSA intended
to model human cognitive function had this property: as far as I
can tell, once I've exited my current state, no sequence of external
inputs is likely to take me back to an identical state.  Without
reversibility, no actual sequence can try on all state/input
combinations.  Any FSA that models cognitive function is also likely
to have the property of exclusivity, i.e. that there exist states
A and B such that there's no path either from A to B or from B to A.
so there won't even be a sequence that includes every state.

>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.

See above.  I should note that even if such a sequence were possible,
it still wouldn't provide an adequate correspondence of logical
states to physical states.  e.g. take a 2-state, 2-input machine, such
that we want the state/input pair (S1,I1) to lead to S1, and (S1,I2) to
lead to S2.  Following the above means of construction, logical state
S1 will correspond to the disjunctive physical state P1-or-P2.  The
construction here will ensure that the combination (P1,I1) will lead to
a state realizing S1, and that (P2,I2) will lead to a state realizing
S2.  However, it ensures nothing about the behaviour upon the
combinations (P1,I2) and (P2, I1) (which never come up in the actual
sequence), and so cannot guarantee the appropriate transitions, i.e. 
that (P1-or-P2,I1) leads to a state realizing S1, and that (P1-or-P2)
leads to a state realizing S2.  So counterfactual sensitivity is still
lacking.

-- 
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."


