Prototypes and Compositionality 107

virtue.
IRS. If nothing can belong to the content of BROWN COW except what
it inherits either from BROWN or from COW, then the content of
BROWN COW can’t be its whole inferential role. For, of course, all sorts
of inferences can hold of brown cows (not qua brown or qua cows but)
simply as such. That’s because all sorts of things can be true of brown
cows that aren’t true either of brown things in general or of cows in
general; that they are brown cows is an egregious example.
If an X-kind of inference is required to be such that constituents
contribute all their X-inferences to their hosts, and hosts inherit their Xinferences
only from their constituents, then only defining inferences will
do as candidates for X: the inferential role of a complex concept is
exhaustively determined by the inferential roles of its constituents only
with respect to its defining inferences.17 That statistical inferences fail to
compose is just a special case of this general truth. The pet fish problem
is therefore not a fluke. Either the classical, definitional version of IRS is
right, or no version can be.
So here’s the impasse: prototypes are public (i.e. they are widely shared)
and they are psychologically real, so they do meet two of the nonnegotiable
conditions that concepts are required to meet; but they aren’t
compositional. Definitions would be compositional if there were any, but
there aren’t, so they’re not. As things stand, there is no version of the
inferential role theory of conceptual content for which compositionality and
psychological reality can both be claimed. I think there must be something
wrong with inferential role theories of content.
A modest proposal:
—“All right, all right; but if constituent concepts don’t contribute their
definitions or their prototypes to their complex hosts, what do they
contribute?”
—Duck soup. They contribute what they mean; e.g. the properties that
they express.What PET contributes to PET FISH is the property of being
a pet; what FISH contributes to PET FISH is the property of being a fish.
It’s because PET contributes pet to PET FISH and FISH contributes fish
to PET FISH that PET FISH entails PET and FISH. And it’s because pet
and fish exhaust the content of PET FISH that {PET, FISH} entails
PET FISH. There are, to be sure, hard cases for this sort of analysis
(what do RISING and TEMPERATURE contribute to THE RISING
Prototypes and Compositionality 107
17 More precisely, only with respect to conceptually necessary inferences. (Notice that
neither nomological nor metaphysical necessity will do; there might be laws about brown
cows per se, and (who knows?) brown cows might have a proprietary hidden essence.) I
don’t know what a Classical IRS theorist should say if it turns out that conceptually
necessary inferences aren’t ipso facto definitional or vice versa. That, however, is his problem,
not mine.
TEMPERATURE?), but they are just the cases that are hard for compositionality
on any known view.
—“Oh bother, why didn’t I think of that?”
—Presumably because the metaphysics that you had in mind says that
meaning is constituted by inferential roles; in which case, the present
proposal is no better off than the ones that we’ve just been discussing. By
contrast, informational semantics contemplates the metaphysical
possibility that there should be something that a concept means (e.g. a
property that it expresses) even though the concept enters into no
constitutive inferential relations at all. My advice is, therefore: if you want
to say what compositionality appears to require you to—that what a
concept contributes to its hosts is what it means—you’d better mean by
‘what it means’ not its inferential role but something like the information
that it carries, where, by assumption, RED carries information about
redness.
Inferential role semantics is bankrupt. Because cognitive science has
swallowed Inferential Role Semantics whole, its treatment of concepts is
bankrupt too; it keeps writing cheques on a theory of meaning that isn’t
there. It is very naughty to write cheques that you can’t cash, and it’s past
time for cognitive science to kick the habit. Chapters 6 and 7 will be about
that.
APPENDIX 5A
Meaning Postulates
Prototypes dissociate two issues that definition theories treat together:
What is the structure of a lexical concept? and What modal inferences do
you have to accept to have the lexical concept X? On the definition story,
both these questions get answered by reference to the relations between
concepts and their parts: lexical concepts typically have constituent
structure, much like phrasal concepts; and if the concept C is a constituent
of the concept X, then you don’t have X unless you believe that Xs are
necessarily Cs. The argument between definitions and prototypes is over
the second of these claims.
But it’s worth noting that the question whether lexical concepts have
constituent structure can be dissociated from both the question whether
inferences constitute content and whether what makes an inference
content-constitutive is something about its modality. Inferential role
semantics doesn’t have to claim that lexical concepts are structurally complex
if it doesn’t want to. In particular, it doesn’t have to claim that the
108 Prototypes and Compositionality
inferences which constitute a concept’s content are defined over its
constituent structure.
There may be several motivations for separating the question whether
(and which) inferences constitute content from the question whether
typical lexical concepts are structurally complex. Some philosophers do so
because they want to hold on to intuitions of analyticity in face of the
mounting empirical evidence that lexical concepts generally behave like
atoms by either linguistic or psychological criteria. And there’s an
independent, semantical argument as well; it’s known in the lexical
semantics literature as the ‘residuum problem’.
In the most familiar cases, lexically governed inferences are supposed to
follow from definitions by an analogue to simplification of conjunction.
Thus, ‘bachelor’ entails unmarried because its definition is ‘male and
unmarried’ and the ‘and’ works in the usual truth-conditional way. This
treatment fits naturally with the idea that concepts are bundles of semantic
features, each of which express a property of the (actual or possible) things
that the concept subsumes.
Now, it’s natural to assume that if there is a property corresponding to
the feature bundle ‘F1, F2, . . ., Fn’, then there should also be a property
corresponding to the bundle ‘F1, F2, . . ., Fn–1’. So, for example, what’s left
when you take the unmarried out of the definition of ‘bachelor’ is the
definition of ‘male’; and what’s left when you take the male out of the
definition of ‘bachelor’ is the definition of ‘unmarried’. Just as the result
of simplifying a conjunctive predicate is always itself a predicate, so the
result of simplifying a feature bundle is always itself a feature bundle.
But there are cases of lexically governed entailment which appear not
to follow this model; ‘red ® colour’ is a paradigm. According to the
definition story, this inference should be the simplification of a complex
concept (the definition of ‘red’) which has the form: ‘F1, . . .,
COLOUR, . . .’; but, on reflection, it’s hard to see what could go in for
the ‘F1’. A male is something that is just like a bachelor but not necessarily
married; but what is just like red but not necessarily a colour? If you take
the ‘COLOUR’ out of the definition of ‘red’, what you’re left with doesn’t
seem to be a possible meaning; the residuum of ‘red ® coloured’ is
apparently a surd. Or, to put it the other way round, it looks like the only
thing that could combine with ‘COLOURED’to mean red is ‘RED’. That,
however, can’t be what the lexical semanticist is proposing. To have ‘RED’
in the definition of ‘red’ would make ‘COLOUR’ redundant, since if
‘RED’ means red, it thereby entails ‘COLOUR’. If the definition of ‘red’
includes RED, that’s all it includes, so in effect the proposal that it does
concedes the concept to atomism.
It might be possible to treat such cases as mere curiosities specific to