Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!tut.cis.ohio-state.edu!rutgers!elbereth.rutgers.edu!harnad From: harnad@elbereth.rutgers.edu (Stevan Harnad) Newsgroups: comp.ai Subject: A Definition of "Symbol," "Symbolic," and "Symbol-Manipulation" Keywords: syntax, semantics, formality, systematicity, interpretability Message-ID: Date: 15 Mar 89 04:54:03 GMT Organization: Rutgers Univ., New Brunswick, N.J. Lines: 95 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)-921-7771