# Re: Computation

Date: Sun Feb 04 1996 - 13:15:43 GMT

> From: "Harrison, Richard" <RJH93PY@psy.soton.ac.uk>
> Date: Wed, 24 Jan 1996 16:45:13 GMT
>
> Computation is the implementation of a symbol system. A symbol system
> involves the manipulation of a set of arbitrary symbols and
> symbol-strings by an explicit set of rules (also arbitrary symbols and
> strings) on the bases of their shape alone (i.e. by syntax not
> semantics). Although the manipulation is based merely on the shape of
> the symbols, the system and its symbols must be systematically
> interpretable as having meaning.

Kid brother ready to bolt unless you quickly follow up this series of
incomprehensible abstractions with CLEAR examples. Give arithmetic as
an example. Show how the symbols ("0" "1" "+" "=" and even "true"
"false") are combined into axioms (x + y = y + x), then the true
theorems can be "derived" by applying the symbol manipulation rules
mechanically, never even knowing what numbers are and what addition is
-- yet the theorems really will be true. Same is true of logic, computer
programming, and even of natural language (though, being grounded in
thought, that's a more complicated case).

You also have to explain what implementation, as well as
implementation-independence are, and how they are relevant to the
question of whether cognition really is just computation: A computer
programme has to actually be executed or run or implemented or
physically realised in order to deliver any results, but the details of
the physical mechanism that implements it, and how it does so, are
irrelevant to the success in delivering the results: That success comes
from the computational or software level, not the hardware. It could
have been run on completely different hardware and given the same
results.

You also have to explain in what sense the shapes of symbols are
arbitrary: They are arbitrary in relation to what they can be
interpreted as MEANING. "+" in arithmetic stands for addition, and
"4" for the quantity four, but their shapes do not resemble addition or
fourness, any more than the shape of the English word "red" resembles
redness.

for extracting roots from quadratic equations of the form:
aX2 + bX + c = 0 namely X = -b =/- squareroot of (b**2 - 4ac)/2a
That can be correctly solved by manipulating these symbols based on
their SHAPE alone (syntax) without having any idea about what they mean
(semantics).

> For a number of reasons cognition has been thought by many to be
> computation (e.g. Fodor, 1980; Pylyshyn, 1973, 1984); computation is
> all powerful, it is implementation-independent and its use led to some
> successes in modeling human behavioural capacity. However, it was its
> main strength that became its down fall.
>
> Computation is all powerful, both formally and physically (The
> Church/Turing Thesis). Any attempt to define computation will always be
> and has to be the same. This also goes for any particular aspects of it
> (e.g. 1+1=2). In a physical sense it is all powerful as any physical
> system can be simulated using computation (from the movement of atoms
> to the movement of galaxies).

This too went by too fast! What is the power of mathematics, hence the
power of computation. Give examples to show how general this is.

Now the fact that every attempt to capture what computation really is
(like the symbol-manipulation account above) has turned out to be
equivalent suggests that the notion of computation captures something
special. The fact that -- not exactly, but to as close an approximation
as you like -- computation describes not only just about everything
that mathematicians do, but just about everything physics can do --
makes the notion a very general and powerful one indeed.

> If cognition captures everything you can
> do formally and physically then why can't it capture what it is that
> minds are? The argument is extremely persuasive, especially as the way
> computation works seems to be the way certain aspects of our abilities
> work at an introspective level, for example, our logical reasoning
> capacities.

Too fast again: Give examples of how the language of thought seems to be
like a symbol system. Kid brother won't take such declarations on
faith.

> The aim of psychology (although not everyone would agree) is to explain
> how humans do what they do. In a hundred years of the subject there had
> not really been any progress until computational systems were made that
> could generate behaviour that was like ours. Computationalism, under
> the heading of Artificial Intelligence (AI), provided systems that
> could replicate our behavioural capacities. Particular successes
> included linguistic skills such as answering questions on text, chess
> playing, and reasoning skills.

Fine, though a bit dry.

> Perhaps the strongest evidence that cognition was computation was the
> fact that computation is implementation-independent. This means that
> the output of a symbol system is not dependent on the physical system
> it is being run on.

Kid brother would pounce on you for this: "You mean the output of my
calculator doesn't depend on the calculator? Then what on earth DOES it
depend on?"

What you really mean is that if someone wants to know how the calculator
reaches the results it reaches, there is no point in talking about its
hardware; you must explain what programme it is running. And that
programme could have been done on radically different hardware yet still
produced the same output.

Implementation-independence is not the "strongest" evidence that
cognition might be computation. (Is it stronger than the power of
computation? the success of computation in generating -- and hence
explaining -- intelligent behaviour? the computation-like properties of
language and reasoning?) It does, however, appear to cast some light on
the mind/body problem: i.e., the "hardware-independence" of the mind
would explain why we don't succeed in seeing the mental as physical),
and if it were indeed true that cognition was computation, it would
separate the study of cognition from the study of other physical systems,
making it unnecessary to worry about the hardware details.

> In computers, the symbol system is the software and
> the physical system is the hardware. The same software could be run on
> different hardware and the processing and output would be unchanged.
> The attraction of this aspect of computation to mind theorists was that
> it seemed to give some answer to the mind-body problem which had
> escaped philosophers and psychologists since at least Descartes' time.
> That is, how is it that a causal body explanation could be reached for
> the seemingly irreducible property of the mind - consciousness?
> Symbolists said this was not a problem as there is no connection
> between the brain (the hardware) and the mind (the software) as in any
> computational system the software is independent of the hardware.

NO connection is putting it too strongly: Symbol systems still have to
be implemented physically in order to generate cognition. It's just that
the physical details of the implementation are irrelevant -- as long as
the hardware does indeed run the software.

> This
> also led to the proposal that if the 'mind program' could be
> implemented that produced behaviour indistinguishable from ours on
> another hardware system (i.e. a computer) it too would be conscious.
>
> Paradoxically, this main benefit of computation became its downfall
> enabling it to be shown that a purely symbolic system could not have a
> mind. Searle (1980) used the fact that computational systems are by
> definition implementation-independent to demonstrate this shortfall by
> becoming the implementation himself of a hypothetical symbol system
> that produced behaviour indistinguishable from ours . His thought
> experiment involved a symbol system that could fool a Chinese penpal
> into thinking it could understand Chinese (i.e. pass the Turing Test
> (Turing,1964) in Chinese).

To say "fool" is to prejudge the outcome: We don't know whether the
computer does or does not really understand Chinese. If it does, it's
not fooling! The Turing Test is meant to actually give the system the
capacity to do anything a penpal can do in response to your letters, for

> He said that the computer would not
> understand Chinese (and thus have a mind) as Searle himself could
> implement the symbol system that provided the Chinese text output
> without understanding Chinese. If the computer could understand Chinese
> then it would be due to the hardware and not the software as proponents
> of the symbolic view of mind had claimed.

The last sentence should be in parentheses, as it is just a long-shot
hold-out for someone who still wants to believe the computer penpal
understands. The point is that Searle himself is proof that
implementing meaningless symbol manipulations is not the same as
implementing understanding.

> There is a version of the Turing Test that is immune to the Chinese
> Room Argument (the Total Turing Test; Harnad, 1989) in which the
> symbols are grounded in the world and do not depend on the
> understanding of the observer for their meaning. Cognitive Psychology
> is left to attempt to discover how such a system might work while still
> retaining the benefits symbolic systems have in modeling human
> behaviour.

That was a bit too fast for the Chinese Room and the Robotic Test. But
this question itself was rather short on the positive case for
computation overall. Apart from the counterarguments, is this the
strongest case that could be made for the thesis that cognition IS just
computation? You have most of the raw ingredients, but you still have to
make it into a (kid-brother-proof) argument FOR cognition as
computation.

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