From: daryl@oracorp.com (Daryl McCullough)
Subject: Re: A rock implements every FSA
Organization: ORA Corporation
Date: Sun, 12 Apr 1992 12:01:15 GMT

In article <1992Apr6.121330.21448@cs.ucf.edu>
clarke@acme.ucf.edu (Thomas Clarke) writes:

>In article <1992Apr2.202206.25306@bronze.ucs.indiana.edu>  
>chalmers@bronze.ucs.indiana.edu (David Chalmers) writes:
>> In article <1992Apr2.132116.26024@cs.ucf.edu> clarke@acme.ucf.edu (Thomas  
>>Clarke) writes:
>> 
>>> Thus with proper of identification of 
>>> {single state} X {physical states} the single-state machine implements
>>> the 5-colour-map-checker, computationally as well as behaviorally.

>> No it doesn't, for the usual reasons.  (I hate to say "strong conditionals"
>> again.)
>> 
>
>I still don't get your conter argument.  Referring to the more general  
>machine/rock with I/O case, the condition that the rock produce identical
>I/O behavior to the machine seems to me to establish sufficient
>boundary/initial conditions to insure that the rock reproduces the machine
>in all respects. In this respect it seems Putnam's argument is correct.

I agree with you. As a matter of fact, in the the theory of processes,
as developed by Robin Milner, quite a bit is done with a notion of
"functional equivalence", and it is a theorem that any two processes
that are (1) deterministic, and (2) behaviorally equivalent, are also
functionally equivalent. If this is what Putnam was getting at, then I
think that there is a core of truth to what he is saying.

Note, however, that the theorem that behavioral equivalence implies
functional equivalence only applies to deterministic systems. For
nondeterministic systems, functionally different systems can have the
same behaviors. For example, I could either decide today whether to
vote Republican or Democrat in this November's election, or I could
wait until the day of the election. If the time for making the
decision doesn't otherwise affect the behavior, then the two systems:
(1) a person who has already decided to vote Democratic today, and (2)
a person who decides in November to vote Democratic could be
behaviorally equivalent but could not be functionally equivalent,
since there is no way to map states of a person who has already made
up his mind to states of a person who has not. This only works for
nondeterministic systems, however, because if people are
deterministic, then the decision to vote Democratic is not an internal
decision, but is determined by the environment. For deterministic
systems, if two systems make decisions at different times, then that
implies that they are affected by the environment in different ways,
which implies that they are behaviorally different (in some possible
world).

As to David Chalmers' comment about "strong conditionals" the only
thing I can think of is that he must be demanding that two
functionally equivalent systems must have the same behavior even when
started in unreachable states. For example, if you start the 5 color
map program in the state that corresponds to having found a map that
requires 5 colors, then it will behave differently than the do-nothing
one-state machine. Even though it is impossible to reach such a state,
you could artificially put the 5-color map program into a "success"
state, by, for instance, setting the success boolean to "true". (Is
that what you mean, Dave?)

Daryl McCullough
ORA Corp.
Ithaca, NY
Newsgroups: comp.ai.philosophy