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>From: cbo@cs.toronto.edu (Calvin Bruce Ostrum)
Subject: Re: A rock implements every FSA
Message-ID: <92Mar18.182726est.14357@neat.cs.toronto.edu>
Organization: Department of Computer Science, University of Toronto
References: <1992Mar17.224156.9177@bronze.ucs.indiana.edu> <1992Mar17.231452.9979@husc3.harvard.edu> <1992Mar18.045939.3084@bronze.ucs.indiana.edu> <1992Mar18.095140.9984@husc3.harvard.edu>
Date: 18 Mar 92 23:27:58 GMT
Lines: 136



Joseph O'Rourke observes: 
jor|	That's it.  You can see that the mathematical content of
jor| his "theorem" is nearly trivial.  All the subtlety and complexity
jor| resides in the I/O to and from the math:  whether his assumptions
jor| which form the input to the mathematics are justified, and whether
jor| his interpretation of the output of the mathematics is sound.

Indeed. Someone else in this thread has suggested that Putnam may be
attempting to bamboozle us with a show of technical special effects.
His muched touted "cats and cherries" proof is of the same nature.
It reminds me of the proof of the existence of God with with Euler is said
to have bamboozled Diderot. According to de Morgan, the proof went as
follows, and effectively humiliated Diderot: "Monsieur, (a+b^n)/n = x,
donc Dieu existe; re'pondez!".

But unlike this proof, when the jargon is scraped off of Putnam's
proof, something of interest remains to be considered. To date, I don't
believe anyone has either defended Putnam's proof correctly; nor has
anyone criticised it with complete effectivness.

Dave Chalmers starts off with this consolation: 
dc| Well, if we're doomed to endure Nietzsche's eternal recurrence on
dc| this newsgroup, at least Putnam's rocks haven't cycled around as many
dc| times as the Chinese room.

A detail, with respect to the Chinese room: to recur, a thing must first
disappear...

And expresses his wishes that 
dc|(I'd hate to see it become folk wisdom that a rock
dc| implements any FSA, just through the claim being repeated enough
dc| times):

To that end, he gives us 
dc| My problems with Putnam's "proof" are roughly
dc| 
dc| 1. He sets it up so that the rock does indeed go through some actual
dc| sequence of states ABABAB... during a given time interval.  But an
dc| FSA must also satisfy counterfactuals e.g. of the form "if it had
dc| been in state C, then it would have transited into state D".  Given
dc| that the physical states corresponding to most states C (i.e., all
dc| those that aren't in the actual desired sequence between 12:00 and
dc| 12:07) aren't even defined, this would seem to be a problem.

One does not even have to go to states C and D, but can stick with states
A and B. Consider the counterfactual that if the rock had been started
in state B, as defined by Putnam, that it would then continue in the 
appropriate manner. This is false, since the integrity of the definition
of its states may very well rely upon its particular situation (for what is
outside the machine at a given time was constitutive of the definition of
these states).

So this seems to ruin Putnam's argument as it stands. But the essense of it
remains. Although substantially weaker, we can still state this result:

   | Any sufficiently causally isolated rock with an internal clock 
   | implements any FSA without input. 

This still seems unpleasant. And, mutatis mutandis, it will satisfy the
counterfactuals formed using the state names that occur in its actual
trace. Thus, we can say that it implements a particular subautomaton of
the original automaton. Dave's point remains that this is not enough,
and it is here that Mikhail Zeleny jumps in with an attempted rejoinder:

mz| Nonsense.  As I've demonstrated in the previous posting, Putnam considers
mz| every possible state of the automaton, not just a particular trace thereof.

Far from "the single trace objection" being nonsense, Mikhail finds it 
necessary to retreat upon being confronted with Putnam's actual text:

mz| I call for charity: to me, Putnam's text is suggesting a sequence
mz| exhaustive of all states that characterize the FSA.

As can be expected, Mikhail uses a great deal of charity when the result
is to his liking.  I don't know what Putnam intended here, but if he did
intend what Mikhail suggests he did, then his result does not apply to all
FSA without inputs, as he claims. For there are numerous such FSA which
do not have single execution sequences which actually enter every state.
Choosing FSA's at random, in fact, one would have to say that most lack such
sequences, I think. Mikhail has used charity toward Putnam in order to
have him believing a falsehood! Let's try a different tack.

Consider the C and D states mentioned by Dave. The problem is that these 
states aren't provided with a definition. We can provide them with a 
definition, however, by picking for each one of them some particular state 
of the rock which is not entered into during its actual trace. (This is 
not done by Putnam: here we are attempting to exercise charity in 
correcting/extending his result. cf. Ayn Rand, below).

Now we are starting to see some actual constraints come out upon this
multipurpose Rock. Not just any rock will do! First of all, its actual
trace must not exhaust all of its states. There must be left an adequate
number of physical rock states to represent the possible automaton states 
which are not realised in the trace. This doesn't seem like much of a 
restriction, but it does eliminate the example I usually use myself 
(where the rock's physical state at time N is simply the integer N).

Further, the rock states representing C and D must be such that they are
consistent with the states already defined. Suppse the FSA started in C 
leads to D,E,F, etc, but never to A. In such a case, we must be sure that
the definitions for D,E,F do not ever actually overlap those for A. (Of
course, if a rock started in C is supposed to lead to A, we must disjoin
the new physical states it reaches in with the previous definition of A,
but this is no real problem). This is an actual constraint upon the rocks
which is nowhere mentioned by Putnam. A programming analogy here might
result when someone placed some memory on the free list and then reallocated
it, although the memory was still in use elsewhere. Yechh!

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.

For one, I am certainly not comfortable with this result. Fortunately, 
I believe there are other ways to block it. Pace most of the commentators
to date, however, I don't think these are directly related to Putnam's
treatment of inputs and outputs, which, modulo the above considerations,
seems unproblematic. But I'll leave that for now, pleading in the words
of Jerry Fodor from Psychosemantics: "Don't ask me about the inputs and 
outputs right now. I'm very busy".  

Well, perhaps substitute "lazy" for "busy".

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Calvin Ostrum                                            cbo@cs.toronto.edu
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One further suggestion: if you undertake the task of philosophical
detection, drop the dangerous little catch phrase which advise you to
keep an "open mind".   -- Ayn Rand
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