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Article 4773 of comp.ai.philosophy:
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>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: sci.philosophy.tech,comp.ai.philosophy
Subject: Re: A rock implements every FSA
Message-ID: <1992Mar28.092723.10365@husc3.harvard.edu>
Date: 28 Mar 92 14:27:21 GMT
References: <45390@dime.cs.umass.edu> <1992Mar24.231518.10230@husc3.harvard.edu> <45426@dime.cs.umass.edu>
Organization: Dept. of Math, Harvard Univ.
Lines: 120
Nntp-Posting-Host: zariski.harvard.edu

In article <45426@dime.cs.umass.edu> 
orourke@sophia.smith.edu (Joseph O'Rourke) writes:

>In article <1992Mar24.231518.10230@husc3.harvard.edu> 
>zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:

>>In article <45390@dime.cs.umass.edu> 
>>orourke@sophia.smith.edu (Joseph O'Rourke) writes:

>>>In article <1992Mar24.112548.10215@husc3.harvard.edu> 
>>>zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:

MZ:
>>> >...as I've said earlier, all
>>> >that remains to be done is to 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.  [...]  Just string all possible traces
>>> >together in a sequential order.  

JO'R:
>>>Let's face it:  your rock doesn't realize or
>>>implement the FSA in an interesting sense.  It just sits there, whereas
>>>the FSA is active: it responds to the input.

MZ:
>>I don't believe you are saying this seriously, but I'll bite.  Please give
>>me a precise definition of the essential difference between "just sitting
>>there", and "actively responding to the input".

JO'R:
>It may be that I misinterpreted your proposal.  David Chalmer's rebuttal
>seems to interpret it differently.  So perhaps you could clarify
>with the following simple example.  I'll lay out what I thought you had
>in mind, and you correct where necessary.
>	Here is a two-state FSA, call it FSA1, with two possible input 
>symbols:
>
>        FSA state   Input   ==>   FSA state
>	---------   -----         ---------
>	    A         0               A
>            A         1               B
>	    B         0               B
>            B         1               A

JO'R
>You make an new FSA, call it FSA2, that has no inputs, and whose states
>are <A,0>, <A,1>, <B,0>, <B,1>.  The transition table for this automaton
>is not clear to me.  What did you intend?  Let me plow on nevertheless.

No, what you want to do is as follows.  Say the maximum input length bound
is 2; then your FSA2 gets the following states: <A, 00>, <A, 01>, <A, 10>,
<A, 11>, <B, 00>, <B, 01>, <B, 10>, <B, 11>.  By the way, FSA2 is not an
FSA, but we'll let it slide.

JO'R:
>Now you fix a limit to the length of possible inputs; let's use n=2,
>so the possible input streams are 00,01,10,11.  For each possible
>input stream, you make a trace of the states of FSA2 (let's assume
>A is the start state):
>
>        00:  <A,0>, <A,0>, <A,x>
>        01:  <A,0>, <A,1>, <B,x>
>        10:  <A,1>, <B,0>, <B,x>
>        11:  <A,1>, <B,1>, <A,x>

Again, what you get is as follows:

        00:  <A,00>, <A,00>, <A,00>
        01:  <A,01>, <A,01>, <B,01>
        10:  <A,10>, <B,10>, <B,10>
        11:  <A,11>, <B,11>, <A,11>
    
JO'R
>I don't know what to put for the last state, so I just used x.
>You list all these traces one after the other:
>
>        <A,0>, <A,0>, <A,x>; <A,0>, <A,1>, <B,x>; 
>        <A,1>, <B,0>, <B,x>; <A,1>, <B,1>, <A,x>

Mutatis mutandis.

JO'R
>Now we take a rock, and identify 12 time consecutive intervals,
>and call these rock states S1, S2, ..., S12.  And we map the states
>of the traces to these physical states:
>
>	<A,0> -> S1
>	<A,0> -> S2
>	...
>	<A,x> -> S12
>
>Now the rock "realizes" FSA1.

Yes, that's it.  Note that your basic understanding of my proposal is quite
sound; it's Dave who got it all bass-ackwards.  Note also that the outputs
can be coded in a similar way.  My original point had to do with the
well-known, demonstrable lack of a sound theoretical distinction between a
material object "responding" to input by "producing" output, and another
medium-sized piece of dry goods "just sitting there".  This, to me, is the
crucial turning point of Putnam's argument.  Again, once we get this
straight, I'll try to elicit the author's own opinion on this subject.
Unfortunately, Harvard Philosophy Department is not on the net; however,
given that his appointment until very recently was joint with the
"well-connected" Math Department, perhaps I could persuade him to make some
electronic comments.


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: Mikhail Zeleny                                                     :
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