From: Sparks Simon (snjs197@ecs.soton.ac.uk)
Date: Thu Mar 01 2001 - 13:15:40 GMT
Simon Sparks (snjs197)
Subject: Harnad: Cognition isn’t Computation
http://www.cogsci.soton.ac.uk/~harnad/Papers/Harnad/harnad94.computation.cognition.html
> HARNAD:
> I do accept the Church Turing thesis, in both its formal and physical
> versions (CTT and CTTP), yet I too will be arguing against C˙
Sparks:
I will argue in favour of the postulate of Computationalism, but I will
conjecture that cognition is not the implementation of a nontrivial
symbol system in itself but a constituent of a systematically
interpretable symbolic system which encompasses both the physical world
around us and the mental world within us.
When discussing Intelligence, in the absence of a solid definition it is
common to assume the Human mind as a benchmark. I suggest that it may be
wrong to isolate the Human from the world in which it exists when
considering ourselves an implementation of a symbol system.
> HARNAD:
> Formal computation is clearly Symbol Manipulation, with the operations
> on symbols (read, write, move, halt) being based on the shapes of the
> symbols.
Sparks:
Considering our known Universe as an instance of formal computation, as
opposed to considering only our cognition, it may be easier to regard
both our thoughts and the physical world around us as the manipulation
of symbols.
A physical entity is, by definition, an object of the physical universe
or, for the purposes of this argument, a symbol or manipulation of
symbols in the universal system.
> HARNAD:
> Meaning does not enter into the definition of formal computation.
Sparks:
What does meaning mean? The linguist Ferdinand de Saussure’s work on
this question provides us with three important ideas:
1. The relation between signifier and signified (a physical entity and
it’s mental manifestation) is virtually discarded leaving the meaning
of a sign (the inference of an object) resting on the structure of
values constituted by the language as a whole. The meaning of an
expression relies solely on discourse (verbal communication) and its
relation to other expressions.
2. It is difficult to see how two adult humans could communicate if
their vocabularies didn’t coincide precicely. It would be impossible to
determine whether a difference of opinion was due to one person being
incorrect or that the two people were at cross purposes to each other
because they would effectively be speaking different languages.
3. Saussure’s Theory recognizes that meaning must be studied in the
context of a three-term relation: the mind, the world and the language,
the later being conceived from social phenomenon; “Language never
exists apart from social fact”
So, with emphasis on describing a formal system, meaning is the whole
structure of our network of ‘ungrounded’ mental symbols, which requires
similarity among all humans and is defined by social consensus.
Meaning, as interpreted here, does not enter into the definition of
formal computation (discarded relations between signifier and
signified), yet maintains a semantic interpretation.
> HARNAD:
> Although it is usually left unstated, it is still a critical, if not a
> definitional property of computation that the symbol manipulations
> must be semantically interpretable…All the interpretations of the
> symbols and manipulations must square systematically with one another,
> as they do in arithmatic, at the level of the individual symbols, the
> formulas, and the strings of formulas. It must make systematic sense,
> in whole and in part (semantic interpretability).
Sparks:
Regarding my conjecture that cognition isn’t the entire implementation
of a symbol system, I extend the ideas of meaning above to suggest that
the meaning of physical symbols lies in their discourse (or interaction
using an implementation of the Universal Language) with other physical
symbols, including humans, providing the complete system (Universe) as
a systematically interpretable implementation of symbol manipulation.
> HARNAD:
> The set of semantically interpretable formal symbol systems is surely
> much smaller than the set of formal symbol systems simpliciter…the kind
> of computation we are concerned with (whether we are mathematicians
> or psychologists), is nontrivial computation: The kind that can be made
> systematic sense of…Nontrivial symbol systems do not in general have
> coherently interpretable duals…It is this rigidity and uniqueness of
> the system with respect to the standard, “intended” interpretation
> that will, I think, distinguish nontrivial symbol systems from trivial
> ones…So we are interested only in…symbols, manipulated on the basis of
> their shapes only, but nevertheless amenable to a systematic
> interpretation. Symbol systems that are meaningful, in other words.
Sparks:
I have implied that there is a single symbol system that defines
everything we conceive as existing in our world. Indeed, it is the
realm of Theoretical and Meta-Physicists to discover this ever elusive
“Universal Equation” (does Goedel’s Theorem expose a futility in this
persuit?) from empirical knowledge of our implementation of the symbol
system.
Our Universal System, if it is a symbol system, would appear to be a
nontrivial one: gravity, for example, could not be swapped for heat
without systematically changing every symbol’s interpretation in order
to maintain coherence.
These alternate implementations would still be valid meaningful symbol
systems and could be realized in other Universes, if there are such
things.
> HARNAD:
> A computer, then, will be the physical implementation of a symbol
> system – a dynamical system whose states and state-sequences are the
> interpretable objects.
Sparks:
Without assuming that the computer needs be physical itself, but instead
supra physical or meta-physical, our Universe complies with the above
definition of a computer.
> HARNAD:
> The shapes of the symbol tokens must be arbitrary. Arbitrary in
> relation to what? In relation to what the symbols can be interpreted
> to mean.
Sparks:
This statement implies the implementation-independence requisite for a
non-trivial, semantically interpretable implementation of a symbol
system to support the strong version of the Church-Turing Thesis for
Physical Systems (CTTP). This is disgused below.
> HARNAD:
> All formal languages (like arithmatic, predicate calculus and LISP)
> are subsets of natural language.
Sparks:
Perhaps not. Human cognition is not necessarily the benchmark for
intelligence , but mabey a subset of it. There may be this proposed
Universal Language from which which natural language and all its formal
subsets are themselves subsets.
> HARNAD:
> We may need a successful human interpretation to prove that a given
> system is indeed doing nontrivial computation, but that is just an
> epistemic matter. If, in the eye of God, a potential systematic
> interpretation exists, then the system is computing, whether or not
> any Man ever finds that interpretation.
Sparks:
Can one disagree that there is a formal specification for our Universe,
regardless of whether man can distinguish it or not? As mentioned
earlier, Goedel’s Theorem may suggest that we cannot in fact distinguish
the formal specification of our Universe.
It is not a requisite of a formal system that its symbols and symbol
manipulations can individually deduce its specification (1 + 1 ň does
not give us the complete specification of arithmatic).
> HARNAD:
> It would be trivial to say that every object, event and state of
> affairs is computational because it can be systematically interpreted
> as its own symbolic description…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.
Sparks:
A physical symbol’s shape would be precicesly what it is interpretable
as meaning if we were considering cognition as the implementation of a
symbolic system and the physical entities as separate from that system,
but we are not. We are considering everything as being manipulated on
the basis of one universal set of syntactic rules and the meaning is
manefested in relation between every thing within that implementation.
> HARNAD:
> “Implementation Independent”: 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 bases of
> the same syntactic rules.
Sparks:
In another implementation of the Universal Symbol System, i.e. another
Universe, the “shape” or implementation of all symbols and symbol
manipulations (higher order symbols) in the system could be different
while maintaining the semantic interpretabillity of the Universal Symbol
System. For example a cat sat on a mat in our system implementation
could bear the same semantic interpretabillity as paint dripping up a
wall in another.
The Universe as a whole is the implementation of the symbol system when
we regard physical entities as being symbols of that system, as opposed
to external entities that need grounding in a human Cognitive Symbol
System. The Universal Symbol System could be implemented in any number
of ways as any number of interpretable Universes, i.e. the Universal
Symbol System would be implementation independent.
> HARNAD:
> All physicalist attempts to solve the “mind/body problem”, which is a
> problem we all have in seeing how mental states could be physical
> states, run aground on one point: Any causal or functional explanation
> of a physical system is always equally compatible with a mental and a
> nonmental interpretation…the causality/functionality always look
> perfectly capable of managing equally well, in fact indistinguishably
> (causaly/functionally speaking), with or without the mentality.
Sparks:
In my argument, the mind/body problem should be viewed as the body/mind
problem. I have taken the step of assuming an intelligence or
computation that encompasses the existance of both the mind and the
body as symbols, and that considers physical states as being a superset
of mental states (given the definition of a physical state to be a
symbolic implementation of the Universal System). I use this definition
to justify the use of intelligence and computation interchangeably as
they must be equivalent in an abstraction of computation that reaches
beyond cognition.
> HARNAD:
> If cognition is just a form of computation, it’s no wonder we have
> trouble equating the mental with the physical: We’d have trouble
> equating the computational with the physical too, because computation
> is independent of physical realization (Pylyshyn 1984).
Sparks:
I suggest that Universal Computation provides for physical realization.
The Universe as an implementation af a symbol system is the embodyment
of physical realisation.
> HARNAD:
> Since computation is implementation independent, [Searle’s Chinese
> Room Argument] is evidence against any understanding on the part of
> the computer when it is implementing that same symbol system.
Sparks:
What’s to say that cause and effect isn’t the means by which things
progress. It is arguable that every action is a reaction of previous
actions, that we are who we are as a result of who we have been and
what we have done and experienced, that the Universal symbol system is
just being implemented.
> HARNAD:
> Symbol systems have the remarkable property of being able to compute
> whatever is computable (that’s CTT). In this respect, what they can do
> and what people can do seems to run along the same channels. But there
> is one critical respect in which they diverge: A string of symbols
> such as…“the cat is on the mat”, generated by a symbol system, is an
> instance of nontrivial computation if it is systematically
> interpretable as meaning what…“the cat is on the mat” mean[s].But
that
> meaning, as stated earlier, is not contained in the symbol system.
Sparks:
In my interpretation, the symbols “the cat is on the mat” actually is
the physical entities whereby the physical cat is physically on the
physical mat in an instance of the nontrivial Universal Computation.
> HARNAD:
> [My thoughts] are about something, they are meaningful, and they are
> not about what thay are about merely because they are systematically
> interpretable by you as being what they are about. They are about
> them autonomously and directly, without any mediation. The symbol
> grounding problem is accordingly that of connecting symbols to what
> they are about within the mediation of an external interpretation…But
> there is a price to be paid for grounding a symbol system: It is no
> longer just computational!
Sparks:
I propose the Sparks test to present a thought or cognition that is
Sparks distinguishable. By that I mean something that could be thought
about that couldn’t conceivably be realised by the constituents of our
Universal Symbol System (I say conceivably because we haven’t
interpreted the system, we only have empirical suggestions. We are part
of the implementation after all).
Under this system, I would say that it is impossible to present such a
thought because one which could not conceivably be realised by an
interpretation of the symbol system, could actually be realized by the
very fact that it was thought, and the interpretation would have been
incorrect. Any thought in this sense has meaning by definition of its
existance (i.e. being a symbol whose meaning is given by its relation to
all other physical symbols).
So what does it mean to ground symbols in this system? Actually nothing.
The symbol grounding problem arises from relating cognitive symbols
(i.e. those in the mind) to infer meaning from physical entities. Under
this system, all cognitive symbols are physical entities and all
physical entities are symbols as implemented by the Universal Symbol
System, the language (meaning) of which being defined by all constituent
symbols structured as a network of relations. As all symbols are related
in this structure, there is nothing left within this Universal System to
ground any further meaning to.
Unfortunately, this implies that the meaning of the system is only
apparent from without the system. If this were to be true, the meaning
of life or the meaning of the universe would never be within our grasp.
With cognitive symbols perceived as a subset of all physical symbols,
thus eliminating the requirement for cognitive symbol grounding, and all
physical symbols an implementation of the Universal Specification, we
can visualise an heirarchy of “intelligence”. Within this hierarchy,
knowledge (albeit incomplete) can be seen by us to be passed down from
the Universal Language to the level of physical symbols through the
medium of science and inherited from the level of physical symbols to
the subset of cognitive symbols through the ungrounded relational
structure of all symbols. It is verifyable under the Universal Symbol
System that our cognitive symbol structure could possibly attain some
knowledge of the language of the Universal Symbol System without the the
intermediary physical superset (this could account for autonomous
individual thought, dreams, revalations that appear to have no direct
consequence of the physical world around us).
> HARNAD:
> There is no problem with the weak CTTP, because it merely claims that
> every phisical system is formally equivalent to a Turing Machine…But
> no one would ever mistake the simulation for the real thing.
Sparks:
By “Virtual World”, do we mean a Formal Symbolic System of sub –
cognitive “reality”? And by “the real thing”, i.e. the real
“interpreter-independent” world as we know it, do we mean this
implementation of the rules of this nontrivial symbol system in which we
exist?
In such a system, both implementations are symbolic and are equally real
in the sense that we define reality. Furthermore, both implementations
can be considered a simulation as the Universal Symbol System is
potentially systematically interpretable, or is systematically
interpretable in the eye of God.
> HARNAD:
> The truth of the weak CTTP…would strongly imply that computational
> modelling was an excellent way of arriving at an understanding of
> physical systems…but it would not support C˙(“Strong AI”). Why?
> Because even if the simulated T3 robot captured (i.e. simulated)
> every relevant property of cognition, it would still be just an
> ungrounded symbol system.
Sparks:
Here, the analogy one level of abstraction up would be the the persuit
of science as being an excellent way of developing an understanding of
our Universal System but being impossible to prove because it isn’t
grounded to the “external” specification of the system or the
meta-physical reality.
> HARNAD:
> If every physical process is in fact computation, then the cognitive
> scientist might as well have ignored the computationist’s message and
> just kept on hunting for what the right physical process(es) might
> turn out to be…I actually think the Strong CTTP is wrong…because it
> fails to take into account the all-important
> implementation-independence that does distinguish computation as a
> natural kind.
Sparks:
The Strong CTTP (that all physical systems are just computers, or
implementations of systematically interpretable symbol manipulation)
holds for the Universal Symbol System and inplementation-independence
of this nontrivial symbol system is permissible in the manifestation
of alternate universes.
> HARNAD:
> The pertinent invarient shared by all things that fly is that they
> obey the same sets of differential equations, not that they implement
> the same symbol systems. The test, if you think otherwise, is to try
> to…get to Seattle with the one that implements the right symbol system
> but obeys the wrong set of equations.
Sparks:
Flying to Seattle following the rules of differential equations is
merely in implementation of the Universal Symbol System. Using the
wrong differential equations is not an alternative implementation of the
system, it is an attempted corruption of the nontrivial computation
using a dual that doesn’t exist in the Universal Symbol System.
In an arbitrary alternative implementation of the system, (i.e. an
alternative universe), where the interpretation of every physical symbol
is different, our interpretation of displacement may be implemented as
our interpretation of a change in colour. Under this interpretation,
you might be able to “fly” to “Seattle” using only a lightbulb.
> HARNAD:
> Strong computationalism, according to which every implementation of
> the right symbol system would cognize, is either wrong in exactly the
> same way the Strong CTTP is wrong (or vacuous), or, if it posits the
> Strong C˙while rejecting the Strong CTTP then it is merely
> equivocating on the unobservability of cognition (a property that sets
> cognition apart from flight, heating, movement, and even gravity).
Sparks:
As mentioned earlier, it is not a requisite for us, as physical symbols
of the Universal Symbol System (apparently implementing the system’s
interpretation of cognition), to have the ability to observe our own
meaning or to cognize cognition, in the same way that flight cannot
itself fly, heat has no temperature and equality doesn’t equal anything.
> HARNAD:
> A first step might be to try to deinterpret the symbol system into the
> arbitrary squiggles and squoggles it realy is (but, like unlearning a
> language one has learnt, this is not easy to do!).
Sparks:
This excersise can be left to Steven Hawking et. al. to try and work out,
but I would suggest that it is a futile exercise, if indeed this was the
case. Of course I can’t say that my idea of the Universal Symbol System
as a candidate for computationalism is a correct one, I can only play
the “Devil’s advocate” for a proposal of “God”.
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