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Kamp
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and Partee 1995; Osherson and Smith 1996). But, as far as I can see, the
undertaking is pointless. For one thing, it bears emphasis that the
appropriate information for recalibrating a complex concept comes from
the world, not from the content of its constituents. If it happens that they
paint fire engines in funny shades of red, then typical fire engine red won’t
be typical red. To decide whether the colour of a certain engine is typical,
you’d therefore need to recalibrate RED to FIRE ENGINE; and to do
that, you’d need to know the facts about what shades of red fire engines
are painted. Nothing about the concepts RED or FIRE ENGINE, per se,
could tell you this; so nothing about these concepts, per se, could predict
the typicality of a given sample of fire-engine red. In this sense,
“recalibrated” compositionality, even if we knew how to compute it,
wouldn’t really be compositionality. Compositionality is the derivation of
the content of a complex concept just from its structure and the content
of its constituents; that’s why compositionality explains productivity and
systematicity.
Still worse, if possible: identifying the relevant reference set for a
complex concept itself depends on a prior grasp of its compositional
structure. In the case of STRIPED APPLE, for example, the reference set
for the recalibration of STRIPE is the striped apples. How do we know
that? Because we know that STRIPED APPLE applies to is the intersection
of the striped things and the apple things. And how do we know
that? Because we know the compositional semantics of STRIPED
APPLE. Computing typicality for a complex concept by “recalibrating”
its constituents thus presupposes semantic compositionality; it presupposes
that we already know how the content of the concept depends on the
content of the concept’s constituents. So, recalibration couldn’t be what
makes concepts compositional, so it couldn’t be what makes them
systematic and productive. So what is recalibration for? Search me.
By the way, these pet fish sorts of arguments ramify in ways that may
not be immediately apparent; compositionality is a sharp sword and
cutteth many knots.15 For example, it’s very popular in philosophical
circles (it’s the last gasp of Empiricist semantics) to suppose that there are
such things as ‘recognitional concepts’; RED and SQUARE, for example,
and likewise, I suppose, DOG and TREE, and many, many others.
Peacocke 1992 is a locus classicus for this thesis, but any philosopher who
says there are ‘criteria’ for the application of a concept is likely to be
intending to claim that the concept is recognitional. All told, that includes
quite a lot of philosophers and quite a lot of concepts.
104 Prototypes and Compositionality
15 An expanded version of the argument I’m about to sketch can be found in Fodor
forthcoming a; q.v.
A concept is recognitional, in the intended sense, only if the ability to
identify its instances in favourable circumstances is among its conceptconstitutive
possession conditions. Thus, being able to identify squares is
part and parcel of having the concept SQUARE; it’s constitutive of the
content—hence of the identity—of the concept. So the story goes. Notice
that having SQUARE doesn’t require the ability to identify any and every
square (consider a square as big as the universe). Likewise, somebody
could be thoroughly a possessor of the concept BIRD and none the less
not know whether to apply it to ostriches (to say nothing of pterodactyls).
So the story must be (indeed, is) that having a recognitional concept
requires being able to recognize good (clear, paradigmatic, etc.) instances
of the concept. You don’t have BIRD unless you are inclined to take
sparrows and the like to be birds.
But, now, the pet fish/striped apple/male nurse worries return full force.
If, in particular, nothing is constitutive of conceptual content unless it
composes, then recognitional capacities can’t be constitutive of conceptual
content. For someone could have the appropriate recognitional capacities
with respect to FISH (he sees at a glance that trout, tuna, and the like are
fish) and could have the appropriate recognitional capacities with respect
to PET (he sees at a glance that poodles, Siamese kittens, and the like are
pets), but be quite at a loss to identify even paradigmatic pet fish (e.g. even
goldfish) as such. Because being a paradigm doesn’t compose, recognitional
capacities don’t compose either. So the same argument that shows that
paradigms aren’t constituents of content shows that recognitional
capacities aren’t either; hence that there aren’t any recognitional concepts.
Compositionality is a sharp sword which cutteth many knots. (Or have I
mentioned that?)
The long and short: either concepts qua prototypes aren’t compositional
or, if they are, their compositionality is parasitic upon concepts
qua something other than prototypes. Conceptual contents, however, must
be compositional; nothing else could explain why concepts are systematic
and productive. So concepts aren’t prototypes. This is too sad for words.
A theory of concepts has two things to explain: how concepts function as
categories, and how a finite mind can have an infinite and systematic
conceptual capacity. Prototypes do a not-bad job of explaining the first
(though, notoriously, they’re not so good at penguins and ostriches being
birds). Anyhow, they do noticeably better than definitions. But they are
hopeless at the second job; so I am claiming.
It may occur to you, however, that my evidence for this claim has thus
far consisted exhaustively of the enumeration of counter-examples; and it
may likewise strike you that that kind of evidence isn’t ultimately
persuasive. No doubt, there are technical problems about uncats and pet
Prototypes and Compositionality 105
fish; but it’s a profound methodological principle (owing, I believe, to Jim
Higginbotham) that for technical problems there are technical solutions.
Maybe there is, after all, some way around the apparent failures of prototypes
to compose? Given all the evidence that people do have prototypes,
isn’t the identification of prototypes with concepts a programme that’s
worth persisting in? Surely, the proper response to a counter-example is to
explain it away? Or simply to ignore it?
That is a methodology with which I am deeply sympathetic. But it
doesn’t apply in the present case since there is independent reason to doubt
that the examples of failures of prototypes to compose are merely
apparent. It’s not just that, prima facie, the identification of contents with
prototypes fails for certain cases; it’s that there’s a pretty convincing
diagnosis of the failures which, if correct, shows why the project can’t
succeed. Here’s the diagnosis.
Prototype theories of conceptual content are, as we’ve seen, instances
of inferential role theories of conceptual content. Their only fundamental
argument with the classical, definitional version of IRS is over which
inferences are content-constitutive: classical theorists say it’s the defining
ones, prototype theories say that it’s the statistically reliable ones. But so
long as IRS is common ground for everyone concerned, this is an
argument that the classical theorists are bound to win. That’s because,
except for definitional inferences, inferential roles themselves don’t compose.
Compositionality says that, whatever content is, constituents must yield
theirs to their hosts and hosts must derive theirs from their constituents.
Roughly, the first half is required because whatever is true of cows as such
or of brown things as such is ipso facto true of brown cows. And the
second half is required because, if the content of BROWN COW is not
fully determined by the content of BROWN and the content of COW
(together with syntactic structure), then grasping BROWN and COW isn’t
sufficient for grasping BROWN COW, and the standard explanation of
productivity is undone.
Now, complying with the first half of this constraint is easy for IRS
since BROWN contributes to BROWN COW not only its contentconstitutive
inferences (whichever those may be), but every inference that
holds of brown things in general.16 If whatever is a cow is an animal, then
brown cows are animals a fortiori. If whatever is brown is square, then, a
fortiori, every brown cow is a square cow.
But the second half of the compositionality constraint is tricky for an
106 Prototypes and Compositionality
16 If all of BROWN’s inferential role is content-constitutive, so be it; BROWN
contributes its whole inferential role to BROWN COW, so compositionality isn’t violated.
Holism is compatible with compositionality. As far as I know, that’s its only virtue.