Jean-marc pizano So why not give up saying that concepts are definitions and start saying instead that concepts are prototypes? That is, in fact, the course that much ofcognitive science has taken in the last decade or so. But it is not a good idea. Concepts can’t be prototypes, pace all theevidence that everybody who has a concept is highly likely to have its prototype as well. I want to spend some timerubbing this point in because, though it’s sometimes acknowledged in the cognitive science literature, it has been verymuch less influential than I think that it deserves to be. Indeed, it’s mostly because it’s clear that concepts can’t beprototypes that I think that concepts have to be atoms.51
For a dissenting opinion, see Barsalou 1985 and references therein. I find his arguments for the instability of typicality effects by and large unconvincing; but if you don’t, so much the better for my main line of argument. Unstable prototypes ipso facto aren’t public (see Chapter 2), so they are ipso facto unfitted to be concepts.
Some of the extremist extremists in cognitive science hold not only that concepts are prototypes, but also that thinking is the ‘transformation of prototype vectors’; this is the doctrine that Paul Churchland calls the “assimilation of ‘theoretical insight’ to ‘prototype activation’ ” (1995, 117; for a review, see Fodor 1995a). But that’s a minorityopinion prompted, primarily, by a desire to assimilate a prototype-centred theory of concepts to a Connectionist view about cognitive architecture. In fact, the identificationof concepts with prototypes is entirely compatible with the “Classical” version of RTM according to which concepts are the constituents of thoughts and mental processesare defined on the constituent structure of mental representations.But though prototypes are neutral with respect to the difference between classical and connectionistarchitectures, it doesn’t follow that the difference between the architectures is neutral with respect to prototypes. For example, in so far as Connectionism is committed tostatistical learning as its model of concept acquisition, it may well require that concepts have statistical structure on pain of their being unlearnable. If, as I shall argue, thestructure of concepts isn’t statistical, then Connectionists have yet another woe to add to their collection.
In a nutshell, the trouble with prototypes is this. Concepts are productive and systematic. Since compositionality is what explains systematicity and productivity, it must be that concepts are compositional. But it’s as certain as anythingever gets in cognitive science that prototypes don’t compose. So it’s as certain as anything ever gets in cognitive sciencethat concepts can’t be prototypes and that the glue that holds concepts together can’t be statistical.
Since the issues about compositionality are, in my view, absolutely central to the theory of concepts, I propose to go through the relevant considerations with some deliberation. We’ll discuss first the status of the arguments for thecompositionality of concepts and then the status of the arguments against the compositionality of prototypes.
The Arguments for Compositionality
Intuitively, the claim that concepts compose is the claim that the syntax and the content of a complex concept is normally determined by the syntax and the content of its constituents. (‘Normally5 means something like: with not morethan finitely many exceptions. ‘Idiomatic’ concepts are allowed, but they mustn’t be productive.) A number of people (see e.g. Block 1993; Zadrozny 1994) have recently pointed out that this informal characterization of compositionality can betrivialized, and there’s a hunt on for ways to make the notion rigorous. But we can bypass this problem for our presentpurposes. Since the argument that concepts compose is primarily that they are productive and systematic, we cansimply stipulate that the claim that concepts compose is true only if the syntax and content of complex concepts isderived from the syntax and content of their constituents in a way that explains their productivity and systematicity. I do sostipulate.
The Productivity Argument for Compositionality
The traditional argument for compositionality goes something like this. There are infinitely many concepts that a person can entertain. (Mutatis
mutandis in the case of natural languages: there are infinitely many expressions of L that an L-speaker can understand.) Since people’s representational capacities are surely finite, this infinity of concepts must itself be finitely representable.In the present case, the demand for finite representation is met if (and, as far as anyone knows, only if) all concepts areindividuated by their syntax and their contents, and the syntax and contents of each complex concept is finitelyreducible to the syntax and contents of its (primitive) constituents.