From: Salcedo Afonso (firstname.lastname@example.org)
Date: Fri May 25 2001 - 02:00:31 BST
> So although it is usually left unstated, it is still a criterial, if
> not a definitional property of computation that the symbol
> manipulations must be semantically interpretable -- and not just
> locally, but globally: All the interpretations of the symbols and
> manipulations must square systematically with one another, as they do
> in arithmetic, at the level of the individual symbols, the formulas,
> and the strings of formulas. It must all make systematic sense, in
> whole and in part (Fodor & Pylyshyn 1988).
For a more complete definition of what computation is one has to note
that even if all the symbol manipulations occur on arbitrarily chosen
symbols that don't have any form of meaning by themselves, it must still
make systematic sense when looking at the symbol system.
But what is exactly meant by a symbol being systematically
interpretable? Well, a '+' is only a plus sign because we were taught
that it represents addition. It might have several different meanings,
but it still makes sense to whoever sees it.
> We usually invoke this image to contemplate the likelihood of [monkeys]
> their typing a passage from Shakespeare by chance.
There is also now the theory that we already have millions of monkeys
typing away on computers and Usenet is not yet a Shakespeare work of
> A computer, then, will be the physical implementation of a symbol
> system -- a dynamical system whose states and state-sequences are the
> interpretable objects (whereas in a static formal symbol system the
> objects are, say, just scratches on paper). A Universal Turing Machine
> is an abstract idealization of the class of implementations of symbol
> systems; a digital computer is a concrete physical realization. I think
> a wall, for example, is only the implementation of a trivial
> computation, and hence if the nontrivial/trivial distinction can be
> formally worked out, a wall can be excluded from the class of computers
> (or included only as a trivial computer).
Harnad says that trivial systems are those where you can swap the
interpretations of the symbols and still come out with a meaningful
I cannot understand how a wall can be considered the implementation of a
trivial computation. A wall is not performing anything at all. What
arbitrary set of symbols can you change on the "wall" symbol system?
What semantics? Does it even have semantics? I don't think this example
is important for the discussion being fought here: the difference
between trivial and non-trivial computation and that we are actually
only interested in non-trivial computation (is this an example of strong
> A cat on a mat can be interpreted as meaning a cat on the mat, with the
> cat being the symbol for cat, the mat for mat, and the spatial
> juxtaposition of them the symbol for being on. Why is this not
> computation? Because the shapes of the symbols are not arbitrary in
> relation to what they are interpretable as meaning, indeed they are
> precisely what they are interpretable as meaning.
> Completely different symbol-shapes could be substituted for the ones
> used, yet if the system was indeed performing a computation, it would
> continue to be performing the same computation if the new shapes were
> manipulated on the basis of the same syntactic rules.
I still have some trouble understanding this. Considering that the
symbols "cat", "being on" and "mat" only exist in english and are only
associated with their real-world meanings if one knows english. Now
considering three completely symbol-shapes in some other language, that
somehow if the symbols in "cat being on mat" were substituted by these
new symbols in order to mean exactly the same thing, would this now be
Anyway, a "cat" is only a cat because the evolution of the language said
it to be so, so it is intrinsic to us. If for a Martian a "cat" means
"1", "being on" means "+" and "mat" meant "2", then would this be
computation for him but not for us? Surely, "true" computation is
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