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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: <1992Mar19.000544.22634@bronze.ucs.indiana.edu>
Date: 19 Mar 92 00:05:44 GMT
References: <1992Mar18.045939.3084@bronze.ucs.indiana.edu> <1992Mar18.095140.9984@husc3.harvard.edu> <92Mar18.182726est.14357@neat.cs.toronto.edu>
Organization: Indiana University
Lines: 48

In article <92Mar18.182726est.14357@neat.cs.toronto.edu> cbo@cs.toronto.edu (Calvin Bruce Ostrum) writes:

>It does seem likely that we should be able to choose physical states 
>corresponding to C,D, etc, such that the argument will still go through,
>but it is not obvious how to prove this. Moreover, Putnam does not
>consider it at all. Nevertheless, I am willing to assume that it can 
>be proven easily, for only a slightly less limited class of rocks (Can
>someone please do this for us?) This result still seems far too liberal 
>(in Ned Block's terminology) for functionalists to remain comfortable
>with.

It's pretty straightforward to do this.  We need only assume that the
system has (a) an internal clock, and (b) an independent internal
"dial", which can be set to one of an arbitrary number of settings,
and which remains in that setting over time.  So think of states of
the system as ordered pairs (k,n), where k (the dial) stays fixed
with time and n (the clock) varies with time.

Then mapping an arbitrary FSA without input onto this system is
easy.  We can divide the states of such an FSA into a number of
parallel "streams", by following its evolution from a given state.
Of course streams may eventually converge, and may eventually
go into loops.  Each stream will have an initial state, which cannot
be reached from any other state.  Map each of these states to the
physical state (k,1) for various values of k.  Map the nth state
in each stream to (k,n) for the appropriate k.  If a given state
appears in different streams (as will happen if streams converge),
or numerous times within a stream (as will happen if the stream
goes into a loop), then map the state to the appropriate
disjunction.

That's all we need to do.  It's actually a very weak constraint
on the system (I'm sure that most rocks satisfy it).

The moral, I take it, is that inputless FSAs are an inherently
trivial formalism.  As an earlier poster said, FSAs have to be
sensitive to inputs for the formalism to have any bite.  (Of
course, there are nontrivial FSAs that may *happen* not to
receive any input, but that's a different matter, as long as
they're potentially capable of dealing with it.  There may seem
to be a potential problem with blind-deaf-and-everything paralytics,
but I think those can be handled by placing the input boundary
correctly.)

-- 
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."


