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Article 4818 of comp.ai.philosophy:
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>From: ske@pkmab.se (Kristoffer Eriksson)
Newsgroups: sci.philosophy.tech,comp.ai.philosophy
Subject: Re: A rock implements every FSA
Message-ID: <6726@pkmab.se>
Date: 28 Mar 92 09:24:18 GMT
References: <1992Mar24.042009.12510@organpipe.uug.arizona.edu> <1992Mar24.051654.18747@bronze.ucs.indiana.edu> <1992Mar24.112548.10215@husc3.harvard.edu>
Organization: Peridot Konsult i Mellansverige AB, Oerebro, Sweden
Lines: 114

In article <1992Mar24.112548.10215@husc3.harvard.edu> zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:
>The relevance of the difference remains to be shown through an adequate
>treatment of the logic of counterfactuals.  Such a treatment, if
>accomplished through the usual possible-worlds framework,

I don't see why one should have to involve possible-worlds in this
question. All you should have to do to bring out the important (here)
aspect of the FSA, is to look at the transition function for the physical
states of the object that is claimed to implement the FSA (the function
that maps physical state and current input into the next physical state),
and check that it corresponds to the FSA transition table (which maps FSA
states and input into the next FSA state) that defines the FSA for _all_
allowed inputs, and not just the input that happens to occur at any
particular moment.

>... interpret the states of Putnam's automaton as ordered pairs <state, input>
>of a FSA ...; 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.

Still, if you check the transition functions for the counterfactual inputs
(per above) at any one particular moment during the run, Putnam's automaton
will most often transit to the wrong state. His automaton only "works" for
the single factual input at every moment, and fails for the counterfactual
ones (except as for chance). Only by putting together <state, input> pairs
from many different moments during the run, can you put together a complete
transition function covering all allowed FSA inputs for every FSA state. But
each one still will only be valid for the moment where they occured, rather
than for the entire duration of the run, so it is wrong to base any claim
about counterfactual inputs at other moments on them. Clearly, the actual
result of counterfactual inputs would not be governed by this artificial
collection of <state, input> pairs.

Usually we don't have to bother about the point in time where a <state,
input> pair applies. Usually they are constant during the entire run of
the system, even during the entire operational life of the system. And
Putnam tries to use <state, input> pairs collected during the runs of
his system as if they where valid for the entire run, when, in fact, his
system is conceived in such a way that they are not. What he really has
is <state, time, input> triplets, since the <state, input> pair alone
does not uniquely determine the next state, if counterfactual inputs are
also taken into consideration.

Also note that "state" in the above pairs refers to the FSA states (FSA
states that have occured during some run), not physical states. Several
physical states are mapped to the same FSA state, in order to gather a
complete transition table with all the different allowed inputs for each
FSA state (with a mapping to physical states). But there is no complete
transition function for the _physical_ states obtainable from the
concatenated traces, where counterfactual inputs can be checked against
all possible physical states. Since there are gaps in the physical
transition function, clearly there can be no guarantee of the system's
behavior with when counterfactual inputs fall into those gaps. If you, on
the other hand, obtain the true physical transition function based on the
physical laws of the system, then, most likely, it will contradict the
artifical mapping to the FSA transition table that is based on the
concatenated traces.

(And perhaps I should point out that knowing the physical laws of the
system does not necessarily require omniscience, except if you have
chosen to use that impossible goal as your personal meaning of "knowing".)

In order to satisfy the counterfactuals requirement, there has to be a
complete mapping back from all possible combinations of physical states
and physical inputs (according to how the physical states are quantized
in this particular implementation), and the FSA states and inputs, and
not only a mapping of all FSA states and inputs to physical states and
inputs. I think this is an important conclusion about physical
implementations of FSAs, and even about implementations in general.
It is especially important when each FSA state is realized by discontinuous
physical states.

Or put it another, very simple, way: if you don't distinguish the
implementation and the abstract FSA, and their respective sets of states,
but in stead apply the theoretical definition of an FSA (recently stated
in article <1992Mar18.102043.20148@csustan.csustan.edu>) directly to a
physical object, where each FSA states consists of continuous or distinct
ranges of physical values and not just atomic symbols, then the transition
function that maps states and inputs into the next state, must be true for
the _entire_ range of each state and input. That should really be obvious,
since otherwise the function is simply stating falsehoods about the physical
system. When the function maps a <FSA state, input> pair to the next state,
it has to be true of any physical value that belongs to that state and input,
and any combination of the two, otherwise the system could sometimes choose
to go through other transitios than what the mapping function specifies. In
Putnam's case, he only provides a mapping for particular combinations of
point values in the ranges (only one state value for each input), leaving
large gaps in the mapping.

Also, it should be relevant to ask just what object it is that we claim
constitute a particular FSA. If you want to say that a particular _material_
object constitutes some FSA, then I think it is reasonable to expect the
mappings that provide the connection between the physical object and the
abstract FSA to be fixed for the whole lifetime of that object (or assembly).
If it is not fixed; if it has to change even though the object itself keeps
on working the same, then clearly something more than the object is involved,
and the case for attributing the "FSA-ness" to the object itself becomes much
weaker. In Putnam's case, the FSA-ness can be more attributed the the ever
changing mapping than to the material object that the mapping connects to.

In fact, if Putnam's mapping was implemented in another FSA (and a fixed one,
this time), then it could finally be turned into a normal device, with real,
physical inputs and outputs. On the other hand, the original object wouldn't
contribute much to the function of the compound system.

Maybe the reason that possible-worlds are brought into this, is an
attempt to somehow rescue Putnam's FSA by using a more complicated
theory where the holes aren't as visible.

-- 
Kristoffer Eriksson, Peridot Konsult AB, Hagagatan 6, S-703 40 Oerebro, Sweden
Phone: +46 19-13 03 60  !  e-mail: ske@pkmab.se
Fax:   +46 19-11 51 03  !  or ...!{uunet,mcsun}!mail.swip.net!kullmar!pkmab!ske


