Semiotics of connectionism and classical cognitivism from
a Peircean standpoint
Breno Serson
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).
References
Dennett, Daniel
1990 La stratégie de l’interprète. Paris: Gallimard.
Fetzer, James H.
1993 Philosophy and cognitive science. New York: Paragon House.
Fodor, Jerry and Brian P. McLaughlin
1990 "Connectionism and the problem of systematicity: Why
Smolensky’s solution doesn’t work", Cognition 35:
183-204.
Peirce, Charles S.
1931-1966 The collected papers of C. S. Peirce. 8
vols. C. Hartshorne, P. Weiss, and A. W. Burks (eds.). Cambridge, MA:
The Belknap Press.
Serson, Breno
(forthcoming) "On Peirce’s Pure Grammar as a
general theory of cognition.
Semiotica.
Smolensky, Paul
1988 "On proper treatment of connectionism", Behavioral
and Brain Sciences 11(1): 3-31.
Thagard, Paul
1988 Computational philosophy of science. Cambridge, MA: MIT
Press.
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