Prototypes and Compositionality 95

ction.
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
are individuated by their syntax and their contents, and the syntax and
contents of each complex concept is finitely reducible to the syntax and
contents of its (primitive) constituents.
This seems as good an opportunity as any to say something about the
current status of this line of thought. Of late, the productivity argument
has come under two sorts of criticism that a cognitive scientist might find
persuasive:
—The performance/competence argument. The claim that conceptual
repertoires are typically productive requires not just an idealization to
infinite cognitive capacity, but the kind of idealization that presupposes a
memory/program distinction. This presupposition is, however, tendentious
in the present polemical climate. No doubt, if your model for cognitive
architecture is a Turing machine with a finite tape, it’s quite natural to
equate the concepts that a mind could entertain with the ones that its
program could enumerate assuming that the tape supply is extended
arbitrarily. Because the Turing picture allows the size of the memory to
vary while the program stays the same, it invites the idea that machines are
individuated by their programs.
But this way of drawing a ‘performance/competence’ distinction seems
considerably less natural if your model of cognitive architecture is (e.g.) a
neural net. The natural model for ‘extending’ the memory of a network
(and likewise, mutatis mutandis, for other finite automata) is to add new
nodes. However, the idea of adding nodes to a network while preserving
its identity is arguably dubious in a way that the idea of preserving the
identity of a Turing machine tape while adding to its tape is arguably not.8
The problem is precisely that the memory/program distinction isn’t
available for networks. A network is individuated by the totality of its
nodes, and the nodes are individuated by the totality of their connections,
direct and indirect, to one another.9 In consequence, ‘adding’ a node to a
network changes the identity of all the other nodes, and hence the identity
Prototypes and Compositionality 95
8 If the criterion of machine individuation is I(nput)/O(utput) equivalence, then a finite
tape Turing machine is a finite automaton. This doesn’t, I think, show that the intuitions
driving the discussion in the text are incoherent. Rather it shows (what’s anyhow
independently plausible) that I/O equivalence isn’t what’s primarily at issue in discussions
of cognitive architecture. (See Pylyshyn 1984.)
9 Nodes may have intrinsic properties over and above their connectivity (e.g. their rest
level of excitation). The discussion in the text abstracts from such niceties.
of the network itself. In this context, the idealization from a finite cognitive
performance to a productive conceptual capacity may strike the theorist
as begging precisely the architectural issues that he wants to stress.
—The finite representation argument. If a finite creature has an infinite
conceptual capacity, then, no doubt, the capacity must be finitely
determined; that is, there must be a finite set of sufficient conditions, call
it S, such that a creature has the capacity if S obtains. But it doesn’t follow
by any argument I can think of that satisfying S depends on the creature’s
representing the compositional structure of its conceptual repertoire; or
even that the conceptual repertoire has a compositional structure. For all
I know, for example, it may be that sufficient conditions for having an
infinite conceptual capacity can be finitely specified in and only in the
language of neurology, or of particle physics. And, presumably, notions
like computational state and representation aren’t accessible in these
vocabularies. It’s tempting to suppose that one has one’s conceptual
capacities in virtue of some act of intellection that one has performed.
And then, if the capacity is infinite, it’s hard to see what act of intellection
that could be other than grasping the primitive basis of a system of
representations; of Mentalese, in effect. But talk of grasping is tendentious
in the present context. It’s in the nature of intentional explanations of
intentional capacities that they have to run out sooner or later. It’s entirely
plausible that explaining what determines one’s conceptual capacities
(figuratively, explaining one’s mastery of Mentalese) is where they run out.
One needs to be sort of careful here. I’m not denying that Mentalese has
a compositional semantics. In fact, I can’t actually think of any other way
to explain its productivity, and writing blank checks on neurology (or
particle physics) strikes me as unedifying. But I do think we should reject
the following argument: ‘Mentalese must have a compositional semantics
because mastering Mentalese requires grasping its compositional
semantics.’ It isn’t obvious that mastering Mentalese requires grasping
anything.
The traditional locus of the inference from finite determination to finite
representation is, however, not Mentalese but English (see Chomsky 1965;
Davidson 1967). Natural languages are learned, and learning is an ‘act of
intellection’ par excellence. Doesn’t that show that English has to have a
compositional semantics? I doubt that it does. For one thing, as a number
of us have emphasized (see Chapter 1; Fodor 1975; Schiffer 1987; for a
critical discussion, see Lepore 1997), if you assume that thinking is
computing, it’s natural to think that acquiring a natural language is
learning how to translate between it and the language you compute in.
Suppose that language learning requires that the translation procedure be
‘grasped’ and grasping the translation procedure requires that it be finitely
96 Prototypes and Compositionality
and explicitly represented. Still, there is no obvious reason why translation
between English and Mentalese requires having a compositional theory of
content for either language.Maybe translation to and from Mentalese is a
syntactical process: maybe the Mentalese translation of an English
sentence is fully determined given its canonical structural descriptions
(including, of course, lexical inventory).
I don’t really doubt that English and Mentalese are both productive; or
that the reason that they are productive is that their semantics is
compositional. But that’s faith in search of justification. The polemical
situation is, on the one hand, that minds are productive only under a
tendentious idealization; and, on the other hand, that productivity doesn’t
literally entail semantic compositionality for either English or Mentalese.
Somebody sane could doubt that the argument from productivity to
compositionality is conclusive.
The Systematicity Argument for Compositionality
‘Systematicity’ is a cover term for a cluster of properties that quite a
variety of cognitive capacities exhibit, apparently as a matter of
nomological necessity.10 Here are some typical examples. If a mind can
grasp the thought that P ® Q, it can grasp the thought that Q ® P; if a
mind can grasp the thought that ~(P & Q), it can grasp the thought that
~P and the thought that ~Q; if a mind can grasp the thought that Mary
loves John, it can grasp the thought that John loves Mary . . . etc.Whereas
it’s by no means obvious that a mind that can grasp the thought that P®
Q can also grasp the thought that R ® Q (not even if, for example, (P ®
Q) ® (R ® Q). That will depend on whether it is the kind of mind that’s
able to grasp the thought that R. Correspondingly, a mind that can think
Mary loves John and John loves Mary may none the less be unable to think
Peter loves Mary. That will depend on whether it is able to think about
Peter.
It seems pretty clear why the facts about systematicity fall out the way
they do: mental representations are compositional, and compositionality
explains systematicity.11 The reason that a capacity for John loves Mary
Prototypes and Compositionality 97
10 It’s been claimed that (at least some) facts about the systematicity of minds are
conceptually necessary; ‘we wouldn’t call it thought if it weren’t systematic’ (see e.g. Clark
1991). I don’t, in fact, know of any reason to believe this, nor do I care much whether it is
so. If it’s conceptually necessary that thoughts are systematic, then it’s nomologically
necessary that creatures like us have thoughts, and this latter necessity still wants explaining.
11 It’s sometimes replied that compositionality doesn’t explain systematicity since
compositionality doesn’t entail systematicity (e.g. Smolensky 1995). But that only shows
that explanation doesn’t entail entailment. Everybody sensible thinks that the theory of