harnad@elbereth.rutgers.edu (Stevan Harnad) (03/15/89)
Based on Newell, "Physical Symbol Systems," Cog. Sci. 4, 1980,
Pylyshyn, Computation and Cognition 1984, and Fodor, passim, a symbol
system is (1) a set of PHYSICAL TOKENS (scratches on paper, holes on a
tape, events in a digital computer, etc.) that are (2) manipulated on
the basis of EXPLICIT RULES that are (3) likewise physical tokens and
STRINGS of tokens. The rule-governed symbol-token manipulation is based
(4) purely on the SHAPE of the symbol tokens (not their "meaning"),
i.e., it is purely SYNTACTIC, and consists of (5) rulefully COMBINING
and recombining symbol-tokens. There are (6) primitive ATOMIC
symbol-tokens and (7) COMPOSITE symbol-token strings. The atomic
tokens, the composite tokens, the syntactic manipulations and the rules
are all (8) SEMANTICALLY INTERPRETABLE: The syntax can be assigned a
systematic semantic interpretation (e.g., as standing for objects, as
describing states of affairs).
This definition may or may not capture a natural kind worth talking
about, but symbolic functionalists such as Fodor and Pylyshyn certainly
believe it does. They think it captures the level at which the real
action is in cognition. (For them, cognition IS symbol-manipulation.)
They also think symbol-strings of this sort capture what mental
phenomena such as thoughts and beliefs are. They particularly emphasize
that the symbolic level (for them, the mental level) is a natural level
of its own, that it has ruleful regularities that are independent of
their specific physical realization (which makes them different from
ordinary physical phenomena [and their explanations] in what F & P
believe is the "right" way) AND, perhaps most important, this
definition of the symbolic level seems to correctly describe all of the
work being done in symbolic AI, the branch of science that has so far
been the most successful at generating (hence explaining) intelligent
performance. It also conforms to general foundational principles in the
theory of computation.
There are a few tricky points associated with the concept of a symbol
system that people keep misunderstanding. All eight of the properties I
mentioned above are critical to this definition of symbolic. Many
phenomena have some of the properties, but that does not entail that
they are symbolic in this formal, explicit, technical sense.
For example, there is the celebrated Wittgensteinian problem about
explicit versus implicit rules: Wittegenstein asked what the difference
was between "following" a rule (i.e., explicitly) and behaving "in
accordance with" a rule (implicitly). Similar distinctions occur with
Chomsky's concept of "psychological reality" (concerning whether
Chomskian rules are really physically represented in the brain or,
instead, merely "fit" our performance regularities, without being what
actually governs them). Ed Stabler brought up his own variant of this
in BBS: explicitly represented rules versus hard-wired physical
constraints. In each case, an explicit representation would be symbolic
whereas an implicit physical constraint would not, although BOTH would
be semantically "intepretable" as a "rule." The critical difference is
in the compositeness and systematicity criterion. The explictly
represented symbolic rule is part of a system, it is decomposable
(unless primitive), its application and manipulation is purely formal
(syntactic, shape-dependent), and the entire system is semantically
interpretable, not just this chunk. An isolated ("modular") chunk
cannot be symbolic, which is a systematic property.
So if performance is "interpretable" as ruleful this does not entail
that it is really governed by a symbolic rule. Semantic
interpretability must be coupled with explicit representation,
syntactic manipulability, and systematicity in order to be symbolic.
None of these criteria is arbitrary, and, as far as I can tell, if you
weaken them, you lose the grip on what looks like a natural category
and you sever the links with the formal theory of computation, leaving
a sense of "symbolic" that is merely unexplicated metaphor.
[On the other hand, I do not myself happen to believe, as the symbolic
functionalists do, that this natural category -- symbol systems --
captures cognition (because of what I've dubbed the "symbol grounding
problem"); in the Categorical Perception book I instead propose a
hybrid symbolic/nonsymbolic system in which the primitive symbols are
grounded in iconic and categorical (feature-filtered) representations
of object categories. (For example, instead of seeing connectionism as
a rival to symbolic functionalism in the attempt to capture "mental"
processes, I see it as a candidate process that may be contributing to
the feature-filtering that must be done in order to form the
categorical representations. This bottom-up hybrid system -- not
connectionism on its own -- would be a rival to pure top-down symbolic
functionalism.) The robotic functionalism for which I argue purely
logically in "Minds, Machines and Searle" is explicated more fully as
an empirical theory in the last chapter of the Categorical Perception
book.]
Refs: Searle, J. (1980) Minds, Brains and Programs. Behavioral and Brain
Sciences 3: 417-457
Harnad, S. (1989) Minds, Machines and Searle. Journal of Experimental
and Theoretical Artificial Intelligence 1: 5 - 25.
Harnad, S. (1987) (Ed.) Cetgorical Perception: The Groundwork
of Cognition (Cambridge University Press)
--
Stevan Harnad INTERNET: harnad@confidence.princeton.edu harnad@princeton.edu
srh@flash.bellcore.com harnad@elbereth.rutgers.edu harnad@princeton.uucp
BITNET: harnad@pucc.bitnet CSNET: harnad%princeton.edu@relay.cs.net
(609)-921-7771lee@uhccux.uhcc.hawaii.edu (Greg Lee) (03/15/89)
From article <Mar.14.23.54.02.1989.21033@elbereth.rutgers.edu>, by harnad@elbereth.rutgers.edu (Stevan Harnad): # ... # the basis of EXPLICIT RULES that are (3) likewise physical tokens and # ... i.e., it is purely SYNTACTIC, and consists of (5) rulefully COMBINING # and recombining symbol-tokens. There are (6) primitive ATOMIC ... This characterization of 'symbol' is not appropriate for either the ordinary use of the word or the way it is used in logic. In the case of the latter, a logical semantics (e.g. the truth table characterization of sentence logic) cannot have symbols, by this account. But that's ok -- we can take the proposed definition as giving a special technical usage for purposes of discussion, though we'll have to remember that if later the conclusion is drawn that human thought is non-symbolic because it is based at least in part on denotations, this follows trivially from the artificial usage introduced earlier. Mustn't allow proof by definition. Does this definition help clarify whether brain-events evoked by or associated with perception, or evoked in other ways, can properly be called symbols? I don't see that it does. Of course if speculation is not to be permitted, we could point out that no one has given explicit rules which completely characterize the way these brain-events interact, based their physical form. Then the controversy is settled: human thought is not symbolic. No explicit syntactic rules. But this whole discussion is speculative. If we can imagine that the entire verbal behavioral repertoire of a human Chinese speaker has been captured in rules, it's either a small further step or no further step to imagine the syntax of brain-events has been discovered, also. In for a pound, in for a penny. Greg, lee@uhccux.uhcc.hawaii.edu
staff_bob@gsbacd.uchicago.edu (03/16/89)
>From article <Mar.14.23.54.02.1989.21033@elbereth.rutgers.edu>, by harnad@elbereth.rutgers.edu (Stevan Harnad): ># ... ># the basis of EXPLICIT RULES that are (3) likewise physical tokens and ># ... i.e., it is purely SYNTACTIC, and consists of (5) rulefully COMBINING ># and recombining symbol-tokens. There are (6) primitive ATOMIC ... > >This characterization of 'symbol' is not appropriate for either >the ordinary use of the word or the way it is used in logic. >In the case of the latter, a logical semantics (e.g. the truth >table characterization of sentence logic) cannot have symbols, >by this account. > As usual, you've gotten me a little confused. I thought that Harnad gave a list of criteria for any logical formalism, in an effort to explain that by 'symbolic' we mean 'capable of being processed within the context of a formal system'. I thought that this was exactly the way the word 'symbol' is used in logic. Granted, transforming a simple system such as ordinary arithmetic into a purely symbolic system that meets these contraints is difficult, but it can be done. The intention here is that iff a system meets these constraints, then we know that it can be processed by a Turing Machine. Furthermore, after having stared at your point about "a logical semantics..." for more than a few minutes, I must confess that I simply don't understand it. If you're saying that the truth table characterization of sentence logic is not a symbolic system according to these rules, I might be prone to agree, but if you're saying that sentence logic "cannot have symbols", I disagree. For the most part, we don't work with purely symbolic systems, but, for logical purposes, it has generally been shown that it is in fact possible to characterize them by the rules Harnad has supplied. A truth table representation of a Boolean statement is easy for us to grasp conceptually, and it is certainly possible to represent a Boolean statement in a way to meet Harnad's criteria, so, where's the beef? (as an aside, in re-reading Simon's "Science of the Artificial", I noticed that he claims that by "symbol processing" he means the same thing that others mean by "information processing". It's not at all clear to me that the two are the same if we take the above mentioned definition of symbolic system.) >But that's ok -- we can take the proposed definition as giving >a special technical usage for purposes of discussion, though >we'll have to remember that if later the conclusion is drawn >that human thought is non-symbolic because it is based at least >in part on denotations, this follows trivially from the artificial >usage introduced earlier. Mustn't allow proof by definition. > >Does this definition help clarify whether brain-events evoked >by or associated with perception, or evoked in other ways, >can properly be called symbols? I don't see that it does. >Of course if speculation is not to be permitted, we could >point out that no one has given explicit rules which completely >characterize the way these brain-events interact, based >their physical form. Then the controversy is settled: human >thought is not symbolic. No explicit syntactic rules. > I don't think that's the point. The question is whether or not human thought can be characterized by a symbolic system, not whether or not it is one. The implication is that if it can, then we can model human thought on a digital computing device of some sort (i.e. a Turing Machine). R.Kohout
rapaport@sunybcs.uucp (William J. Rapaport) (03/16/89)
In article <Mar.14.23.54.02.1989.21033@elbereth.rutgers.edu> harnad@elbereth.rutgers.edu (Stevan Harnad) writes: > >Based on Newell, "Physical Symbol Systems," Cog. Sci. 4, 1980, >Pylyshyn, Computation and Cognition 1984, and Fodor, passim, a symbol >system is [etc.] Some philosophers have argued that this notion is misleading or incorrect. See, e.g., Fetzer, James H. (1988), "Signs and Minds: An Introduction to the Theory of Semiotic Systems," in J. H. Fetzer (ed.), _Aspects of Artificial Intelligence_ (Dordrecht: Kluwer): 133-161.
lee@uhccux.uhcc.hawaii.edu (Greg Lee) (03/16/89)
From article <2308@tank.uchicago.edu>, by staff_bob@gsbacd.uchicago.edu: # >In the case of the latter, a logical semantics (e.g. the truth # >table characterization of sentence logic) cannot have symbols, # >by this account. # > # As usual, you've gotten me a little confused. I thought that Harnad # gave a list of criteria for any logical formalism, in an effort to explain # that by 'symbolic' we mean 'capable of being processed within the context # of a formal system'. 'Formal' doesn't mean non-semantic. There's something wrong with a "list of criteria for any logical formalism" that excludes formal logical semantics, don't you think? Consider the demonstration of a theorem of sentence logic that uses truth-table analysis. It's formal, since it begins from the form of expression of the theorem. It's semantic because it considers the possible denotations of the sentence variables. # >Does this definition help clarify whether brain-events evoked # >by or associated with perception, or evoked in other ways, # >can properly be called symbols? I don't see that it does. # ... # I don't think that's the point. The question is whether or not human # thought can be characterized by a symbolic system, not whether or # not it is one. ... Well, if it is one, it can be characterized by one. So maybe there some relevance to the Searle experiment. At any rate, I thought this other point was also under discussion. Greg, lee@uhccux.uhcc.hawaii.edu
andrew@nsc.nsc.com (andrew) (03/25/89)
I posted the message enclosed below on comp.ai.neural-nets some days ago,
but have had zero response. Having read this net, maybe I've found a home.
You are discussing ideas (Chinese Room -related) which are exactly in the
field of my inquiry; i.e. symbols and their attributes. Here's your context:
1. Steven Harnad:
"(there exist) ..iconic and categorical (feature-filtered) representations
of object categories".
"connectionism contributes to feature-filtering.. forms the categorical
representations"
2. Karl Kluge:
"Denotation seems to be `an arbitrary property of symbols in an
instantiated executing formal system, unlike the syntax and
operational semantics of the symbols.' "
3. Ray Allis:
"..but, at bottom, symbols are associated with non-symbols. The
non-symbols are what we compare to detect similarity and difference,
to discover analogy, to think."
All these refer to symbols, attributes, features and the central role
of the recognition of isomorphism. My note is prompted by recent
developments in neural-net research. There are now known to exist
architectures capable of extracting features from input datasets (in a
non-supervised fashion) whose properties are mathematically, physically
and biologically attractive and/or plausible. These features are either
Gabor functions or the eigenvectors of the input autocorrelation. These
features are nice because:
mathematically - known formal statistics of data
physically - eigenvectors/states are often used to describe fundamental
features of physical systems
biologically - learning rules are purely local
- learning is proven to converge, and to converge correctly
- random noise input produces feature representations similar
to those found in the early vision processing receptive fields
of certain mammals.
(They are not nice because convergence is not realtime - yet).
The note is:
1) Proposing a relationship between isomorphism and feature extraction
2) Questioning what is the best way to think about attributes.
==========================================================================
Could somebody out there in philosophy land please enlighten me as to
the "currently favoured" way to describe "the attribute of a thing" ?
(a little like Plato and "the whiteness of cream", except that's not my name).
Why I am asking this (hopefully not too idiotic) question:
1) Many people agree that the understanding of isomorphism is critical to
the understanding of cognition and intelligence.
2) The existence of isomorphisms seems only possible if attributes exist, else,
without predicates (attributes), we have only the crassness (sorry, holism)
of Zen "direct-pointing" whereby things just are, and all share none or the
same attribute! (kick the pot, Bunto). East/West diverges here...
3) The existence of attributes seems only possible when a feature extraction
process is performed, by which attributes are *created* as a direct
result of the interaction of the perceiver with the environment
(_vide_ the old saw about the Eskimo's <n> words for snow), or with his/
her own structure (the predisposition of infants to eye/nose/mouth forms).
The isomorphism issue thus seems decomposable to that of the qualities
of predicates, and therefore to the mechanisms of feature extraction.
(?comments?).
Note - I'm not suggesting that this pins down what an isomorphism *is*,
but maybe gives some leverage/ connection.
As to the qualities of predicates, there seem to me to be two ways to go:
1) a simple, "non-relational" predicate, like "whiteness" or "how many"
2) a set membership predicate, like "is a member of" or "has .. members".
These 2 ways seem to be related in that 1) appears to be subsumable under 2)
in a recursive fashion (i.e. "is a member of the set of white things");
nevertheless, it seems that maybe property inheritance and suchlike are
excess baggage for a general definition of what an attribute "is".
Is 2) an inclusive definition?
=========================================================================
I realise that "attribute" opens a whole can of worms, and I would like
to keep this definition as down-to-earth as possible, in line with the
bottom-up approach of nets. For example, attributes like "understanding"
are so high-level (emergent) that they are not relevant here.
One note on symbols, however: from the abovementioned reductionist
perspective,
symbols evaporate!
<Das Ding an Sich> becomes <the percept> becomes <a feature set>. The
feature set is all that is, all the way from just inside the
"transducer surface" to just inside the "effector surface".
Analytic deduction of "symbols" from patterns of activation equivocates to
just one more level of <significant feature extraction>, based on
<recognition of isomorphisms between feature sets in the current
context of feature sets>. Reasonable?
Analytic deduction of "understanding" from patterns of activation equivocates
to (cf. the fire/chemistry or the clock/physics analogies) the ability to
associate up to a prescribed "level" in the feature set of known
physical laws. One can replace the word "associate" by "recognise an
isomorphism" here, of course.
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