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Article 4599 of comp.ai.philosophy:
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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: <1992Mar19.011133.10015@husc3.harvard.edu>
Date: 19 Mar 92 06:11:31 GMT
Article-I.D.: husc3.1992Mar19.011133.10015
References: <1992Mar18.045939.3084@bronze.ucs.indiana.edu> <1992Mar18.095140.9984@husc3.harvard.edu> <45094@dime.cs.umass.edu>
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In article <45094@dime.cs.umass.edu> 
orourke@sophia.smith.edu (Joseph O'Rourke) writes: 

>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: 

DC:
>    >>At best, it [Putnam's rock] implements a "trace" of a particular run
>    >>of the FSA, as Joseph O'Rourke nicely put it.

JO'R:
>Thanks :-).

MZ:
> >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.

JO'R:
>There was an objection to your [MZ's] extension of Putnam's rock theorem
>to handle I/O by Anthony Francis based on the need for inputs of unbounded
>length.  But it is clear from Putnam's description (p.124) that he is
>imagining that the I/O is not actually present, but rather talks of
>an automaton that behaves "as if" they were.  So I don't see that Francis's
>point kills your idea.

Furthermore, as I've observed elsewhere, contextual constraints allow us to
put a finite limit on the length, and hence the number of inputs.  Refer to
the lookup table argument for more.  I should note that I don't accept
Philip Santas' "discrete and bounded world of ideas" argument, but admit
some of its premisses merely because they seem to be presupposing by the
sort of functionalism Putnam is addressing.

JO'R:
>	To rephrase Mikhail Zeleny's idea (which goes beyond what is
>present in Putnam's book):  if we list out all possible traces that
>the FSA could make on any input, string them end-to-end, and map
>those lists of traces to the rock's physical states, then all possibile
>state transitions of the FSA are "realized" in the rock.  It seems to
>me that this is right.  (It also may not be precisely what MZ had in
>mind.)

In fact, you've anticipated me: I was thinking along the same lines,
hedging on the posting simply because I wanted to present something a bit
fancier, e.g. a concurrent coding of all possible traces of the state-input
transitions, indexed to the inputs using some standard recursion-theoretic
technique.  Still, it would seem that the sequential stringing would do
just as well.

JO'R:
>	But it is only right by a significant weakening of what it
>means to "realize" or "implement" an FSA.  Since Putnam doesn't seem
>to define the key notion of "realization" (at least I couldn't find
>it in the Appendix or book proper), it is not easy to claim this 
>is a departure from what he had in mind.  But according to this new,
>implied definition of realization, a rock not only realizes every
>FSA, it also realizes every sonnet written by Shakespeare.  For
>one could string out the symbols in a sonnet end-to-end and map them
>onto physical states of the rock.  In other words, a rock realizes
>every FSA only in a very uninteresting sense of realization.

Indeed, Putnam doesn't seem to define realization; for that matter, neither
does anyone else.  In the past, I've expressed some reasons for being
dissatisfied with Dave Chalmers' attempt at tightening the related notion
of implementation; at this point I don't believe it wort arguing until and
unless some participant in this discussion commits himself to the extent of
having something of this sort actually appear in print. 

JOR:
>	Incidentally, I think it is possible to quibble with Putnam
>on other grounds, in particular, his physical assumptions.  But since
>his theorem is rather weak when all the important terms are explicated,
>it is not worth attacking his physics.

I agree on both counts.  As an aside, I find this "Theorem" rather badly
presented, especially when compared to Putnam's other writings (sometimes I
really wish he had stuck to higher recursion theory instead of bothering
with all his "internal realist" nonsense...); still, I believe that the
basic intuition is sound, and can be easily salvaged, *unless* a strong,
non-circular notion of realization or implementation is developed in order
to counter it.


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: Mikhail Zeleny                                                     :
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