92 Prototypes and Compositionality

were
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supposed to exhibit severally necessary and jointly sufficient conditions
for a thing’s inclusion in a concept’s extension. On the present account, by
contrast, whether a feature is in the bundle for a given concept is primarily
a question of how likely it is that something in the concept’s extension has
the property that the feature expresses. Being able to fly isn’t a necessary
condition for being a bird (vide ostriches); but it is a property that birds are
quite reliably found to have. So, ceteris paribus, +flies belongs to the
feature bundle for BIRD. The effect, is to change from a kind of
metaphysics in which the concept-constitutive inferences are distinguished
by their modal properties to a kind of metaphysics in which they’re picked
out epistemically.4
Notice that the thesis that concepts are individuated by their inferential
roles (specifically by their inferential relations to their constituents)
survives this shift. It’s just that the individuating inferences are now
supposed to be statistical.5 A fortiori, we’re still working within a
cognitivist account of concept possession: to have a concept is, at least
inter alia, to believe certain things (e.g. in the case of BIRD, that generally
birds fly). Notice also that the new story about concepts has claims to
philosophical good repute that its definitional predecessor arguably
lacked. Maybe, as Quine says, conceptual entailment isn’t all that much
clearer than the psychological and semantic notions that it was
traditionally supposed to reconstruct. But if there’s something philosophically
wrong with statistical reliability, everybody is in trouble.
So, then, consider the thesis that concepts are bundles of statistically
reliable features, hence that having a concept is knowing which properties
the things it applies to reliably exhibit (together, perhaps, with enough of
the structure of the relevant conceptual hierarchy to at least determine
how basic the concept is).
A major problem with the definition story was the lack of convincing
examples; nobody has a bullet-proof definition of, as it might be, ‘cow’ or
‘table’ or ‘irrigation’ or ‘pronoun’ on offer; not linguists, not philosophers,
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4 Elanor Rosche, who invented this account of concepts more or less single-handed,
often speaks of herself as a Wittgensteinian; and there is, of course, a family resemblance.
But I doubt that it goes very deep. Rosche’s project was to get modality out of semantics
by substituting a probabilistic account of content-constituting inferences.Whereas I suppose
Wittgenstein’s project was to offer (or anyhow, make room for) an epistemic reconstruction
of conceptual necessity. Rosche is an eliminativist where Wittgenstein is a reductionist.
There is, in consequence, nothing in Rosche’s theory of concepts that underwrites
Wittgenstein’s criteriology, hence nothing that’s of use for bopping sceptics with.
5 Just as it’s possible to dissociate the idea that concepts are complex from the claim that
meaning-constitutive inferences are necessary, so too it’s possible to dissociate the idea that
concepts are constituted by their roles in inferences from the claim that they are complex.
See Appendix 5A.
least of all English-speakers as such. By contrast, the evidence that people
know (and agree about) concerning the prototype structure of words and
concepts is ubiquitous and robust.6 In fact, you can hardly devise a
concept-possession test on which prototype structure fails to have an
appreciable effect. Ask a subject to tell you the first —— that comes into
his head, and it’s good odds he’ll report the prototype for the category —
—: cars for vehicles, red for colours, diamonds for jewels, sparrows for
birds, and so on. Ask which vehicle-word a child is likely to learn first,
and prototypicality is a better predictor than even very good predictors
like the relative frequency of the word in the adult corpus. Ask an
experimental subject to evaluate the truth of ‘a —— is a vehicle’ and he’ll
be fastest where a word for the basic level prototype fills the blank. And
so forth. Even concepts like ODD NUMBER, which clearly do have
definitions, often have prototype structure as well. The number 3 is a
‘better’ odd number than 27 (and it’s a better prime than 2) (see
Armstrong, Gleitman, and Gleitman 1983). The discovery of the massive
presence of prototypicality effects in all sorts of mental processes is one of
the success stories of cognitive science. I shall simply take it for granted in
what follows; but for a review, see Smith and Medin 1981.
So prototypes are practically everywhere and definitions are practically
nowhere. 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 of cognitive science has taken in the last decade or so. But it is
not a good idea. Concepts can’t be prototypes, pace all the evidence that
everybody who has a concept is highly likely to have its prototype as well.
I want to spend some time rubbing this point in because, though it’s
sometimes acknowledged in the cognitive science literature, it has been
very much less influential than I think that it deserves to be. Indeed, it’s
mostly because it’s clear that concepts can’t be prototypes that I think that
concepts have to be atoms.7
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6 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.
7 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 minority opinion
prompted, primarily, by a desire to assimilate a prototype-centred theory of concepts to a
Connectionist view about cognitive architecture. In fact, the identification of concepts with
prototypes is entirely compatible with the “Classical” version of RTM according to which
concepts are the constituents of thoughts and mental processes are defined on the
constituent structure of mental representations.
But though prototypes are neutral with respect to the difference between classical and
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 anything ever gets in cognitive science that prototypes
don’t compose. So it’s as certain as anything ever gets in cognitive science
that 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 the compositionality 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. (‘Normally’ means something
like: with not more than 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 be trivialized, and there’s a hunt
on for ways to make the notion rigorous. But we can bypass this problem
for our present purposes. Since the argument that concepts compose is
primarily that they are productive and systematic, we can simply stipulate
that the claim that concepts compose is true only if the syntax and content
of complex concepts is derived from the syntax and content of their
constituents in a way that explains their productivity and systematicity. I do
so stipulate.
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
94 Prototypes and Compositionality
connectionist architectures, 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
to statistical 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, the structure
of concepts isn’t statistical, then Connectionists have yet another woe to add to their
collection.