Semiotics of connectionism and classical cognitivism from a Peircean standpoint
One of the central theoretical problems of contemporary Cognitive Science is to find a comprehensive theory of "representations" (proposition-like, image-like, concept-like) and "inferences" (deduction, but also induction and abduction). How to integrate, within the same basic framework, low-level and high-level cognitive processes, such as pattern recognition, image/word matching, proposition generation, and human-like reasoning? In this paper I present a minimal overview of the semiotics of classical cognitivism (hereafter CC) and connectionism (hereafter CX), and I suggest that Peirce’s Logic (or Semiotic) may help us to understand any cognitive process within the same descriptive, normative, and prescriptive semiotical framework, throwing new light on the contemporary debate on mental representations and inferences, beyond CC and CX views.
C. S. Peirce is an old-time forgotten logician having very little direct influence on the theory or practice of contemporary cognitive scientists. One might say that this has been changing in the last few years (e.g., Thagard 1988; Fetzer 1993: 62-75); nevertheless, within the "cognitive galaxy" of researchers, the main semiotical backgrounds are still drawn from modern symbolic logic, generative grammar principles, computer programming tools, and, sometimes, Roschian prototype theory. The semiotic underlying mainstream Cognitive Science is basically still related to Fregean, Russerlian, Turingian, and Chomskyan views, and/or to an ad hoc account of sign systems (such as block or letters "worlds" or other restricted semantic domains of CC and CX current examples). What is worse, influential authors, such as Fodor or Pylyshyn, behave as if a simple Semiotic (or no semiotic concern) were more than enough. If thought is made of English-like phrases indeed, phrases that are made of physical signs which refer to outside single objects and situations such as "cats" or "be on something", why bother? (e.g., Fodor & McLaughlin 1990: 185-186). In all, it would be no exaggeration to say that an insufficient dyadic/direct reference semiotic, if not a "folk semiotic" underlies contemporary Cognitive Science. Even if a comprehensive "non-folk" alternative theory is not at hand, its features may be envisageable for a Peircean semioticist, who may analyse the semiotics of CC and CX without appealing to complex jargon and theories: he or she needs not much more than evoking some conceptual 1-2-3-type distinctions, such as icon/index/symbol, vague/definite and determinate/general and abduction/deduction/induction.
1. Semiotics of CC and CX: minimal overview
Recall that Peirce distinguishes indices from other signs because of a physical connection or the temporo-spatial contiguity these latter entertain with their objects. Classical cognitivism, similarly to the theory of formal systems, is held together by a sign theory within which discrete index-like atomic signs — having no vagueness or generality — are manipulated only through modus ponens and its variations (sophistication by meta-rules, or by probabilistic/heuristic procedures, does not invalidate the preceding claim). CC, in its Fodorian orthodox version, semiotically reduces itself to a view that cognition is a complex concatenation of syllogistic formulae, built of meaningless "physical symbols" that stand for our human meaningful Peircean symbols. Atomic elementary signs (such as mentalese for "cat") dyadically refer to both a sequence of physical events that may be coded by numbers (such as 01011010) and to a completely determined and singularized "object" (even if, a posteriori, this object corresponds to an individual, a concept or a general class). These "double face" atomic elementary signs act as indices put in one-to-one correspondence with tokens of Peircean types, manipulated through the rules of some formal language (e.g., first order logic), once they are properly organized - syntactically and truth preserving — into proposition-like structures.
Daniel Dennett is one of the sharpest critics of cognitive scientists having a linguistic, logic or computer science background that "have a tendency to suppose that the mind’s 'internal representations' resemble well formed phrases of a grammatical language — a language of thought". In fact, stresses Dennett (1990: xv), "some of the theoretician’s hardest problems are by-products of this simplistic hypothesis". It is at once simplistic and tempting to explain the plasticity and the self-engenderment that characterize our intelligence by Turingian manipulation of formal languages. Contrary to the irreducible triadicity through which Peirce describes any intelligent process, sign transformation processes postulated (and simulated) by CC are strictly dyadic. Recall Biology’s main coding process DNA/RNA/aminoacids: however different from each other, coding processes conform to a one-to-one correspondence of signs acting as indices of one another. However simple their main principle may be, coding processes may have rich informative alphabets and/or imaginative combinatorial syntax. For instance, prefixes, roots, and suffixes may indicate grammatical positions within (computer language) well-formed phrases or lists. Metalinguistic "words" may code things such as first/last, doubt/belief, and possible/actual/general. DNA/RNA/aminoacids coding, for instance, has at least one simple metalinguistic level. None of these fascinating facts about "coding" renders my main claim invalid: within the universe of dyadic deductive manipulation of marks there is no place for iconicity or generality. In consequence, there is no place for real abduction or inductive learning of general laws, only for analytical reasoning obtained by index/rule manipulation.
For connectionism, the basic semiotical operation consists in the classification and the pairing of icons to more general icons through a semiotic habit, related to a matrix of synaptic weights. CX deals with a rudimentary kind of statistic guided inductive matching of iconical inputs with output signs that code for or represent, a posteriori, concepts, classes or ad hoc signs that are meaningful to us. CX attractors correspond to general classes to which input icons are recognized as belonging. Note that in contrast to a certain "semiotical univocivity" that permeates CC, connectionism is still in quest of the theoretical status of the various "representations" and "inferences" with which it deals in empirical and technical arenas (e.g., localized vs. distributed representations; supervised vs. non-supervised learning; emergence vs. instantiation/reductibility of CX to CC symbol processing; see Smolensky 1988). However heterogeneous, neural networks (hereafter NN) exhibit many interrelated features — robustness, graceful degradation, parallel processing, auto-organization — which have a global biological and psychological appeal of verisimilitude. Moreover, specific semiotic features — icon generalisation/categorialization, self-corrected learning, prototype-extraction — are compatible not only with living cognitive systems’ style, but also with many Peircean theories (e.g., the habit/final interpretant theory, the general theory of evolution). In constrast, CC seems to be hardly compatible to anything other than a strange rationalist and non-evolutive world, filled with Frege’s signs created ex nihilo and powered by symbolic logic.
In order to study the semiotic of CX, it is important to distinguish (i) operation , (ii) learning, and (iii) interpretation of the output of an NN. Operation (i): any likeness between two objects is always made in relation to one or more characters or qualities. For Peirce, a given form is an icon of another form through the mediation of a ground (the law related to the common quality establishing the iconic similarity). Accordingly, the operation of a given NN is based upon the satisfaction of the best "iconicity" between input and output, through the mediation of a ground that corresponds to the habit instantiated by the synaptic weights. Learning (ii): the synaptic weights may or must change in the operation of an NN (Peirce’s habit and habit change). The memory of a CX system — the stocked representations within "invisible" synaptic weights and attractors — is really general and potential, being able to subsume a multitude of forms. Moreover, it is plastic: once in contact with an environment of input forms (the "perceptive window" of a given NN), the capacities of generalization of some NN may become self-corrective and they may function as rules not learned as rules proper. Interpretation of the output (iii): the semiotic status of the so-called local representations — where one active unity in the output layer corresponds to a definite predication for a human interpreter — resembles the semiotical status of "physical symbols". Therefore NNs working with local representations may be directly coupled to a CC system (at least in theory). Distributed representations are much more interesting, insofar as they can play the role of icons that might, potentially, be put in correspondence with more general icons (or even, a posteriori, with prototypes or concepts), in a cascade manner. Contrary to CC, other kinds of "representation" are possible within CX, without any a priori exclusion.
2. Peirce’s Semiotic=Logic and Cognitive Science
Classical cognitivism is tempting because of easy computability, generativity and compositionality, methodological solipsism, and syntax/semantic strict parallelism, but its "coding" character (one-to-one correspondence of signs acting as indices of one another) blocks the road to the understanding of image representation, real abduction and induction. Moreover, CC, being committed to "classical" Cartesian background and to "classical" logical axiomatisation, is therefore obliged to face demiurgically created primitive atoms and/or innate languages (grammars, parsing mechanisms, etc.). Connectionism is fascinating because of its biological and psychological "realism" in respect to learning and adaptation, but its semiotical characteristics, however interesting, taken in isolation, are insufficient to build any language-like sign system exhibiting compositionality, and thus human-like intelligence. I will now briefly suggest that, from a Peircean point of view, both CC and CX may be viewed as only single clusters of puzzle parts within the "cognition" puzzle, respectively of the indexical and iconical "components" of Peirce’s triadic symbol. Due to the limits of a very short article, the arguments to support my last claims will be left implicit in what follows.
For Peirce, Logic equals Semiotic because the three kinds of symbols — inferences, propositions and logical terms — all share the same semiotical syntax and are all built out from the same simpler indexical and iconic signs. A term is "generalized" far beyond Frege’s propositional function to become an "unsaturated" rhematic symbol, the predicate of the broadly conceived "saturated" proposition or dicent symbol (which can be even a portrait with a name underneath). Accordingly, an inference or argument symbol is considered as a conditional (if... then) proposition, where the consequent is a predicate (a sign) of the antecedent. I attempted to show elsewhere (Serson, forthcoming) that these claims may be formalized with the aid of lattices which exhibit the relations between the ten classes of signs described in 1902 (Peirce 1931-1966, 2: 138-150, i.e., CP 2.233-65). All this may help us to understand how almost every perceptual and cognitive human activity articulates (i) iconic representation with (ii) propositional representation and (iii) inference making (either abduction, deduction, or induction).
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