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of
thoughts implies a capacity for Mary loves John thoughts is that the two
kinds of thoughts have the same constituents; correspondingly, the reason
that a capacity for John loves Mary thoughts does not imply a capacity for
Peter loves Mary thoughts is that they don’t have the same constituents.
Who could really doubt that this is so? Systematicity seems to be one of
the (very few) organizational properties of minds that our cognitive science
actually makes some sense of.
If your favourite cognitive architecture doesn’t support a productive
cognitive repertoire, you can always argue that since minds are really finite,
they aren’t literally productive. But systematicity is a property that even
quite finite conceptual repertoires can have; it isn’t remotely plausibly a
methodological artefact. If systematicity needs compositionality to
explain it, that strongly suggests that the compositionality of mental
representations is mandatory. For all that, there has been an acrimonious
argument about systematicity in the literature for the last ten years or so.
One does wonder, sometimes, whether cognitive science is worth the
bother.
Some currently popular architectures don’t support systematic
representation. The representations they compute with lack constituent
structure; a fortiori they lack compositional constituent structure. This is
true, in particular, of ‘neural networks’. Connectionists have responded to
this in a variety of ways. Some have denied that concepts are systematic.
Some have denied that Connectionist representations are inherently
unstructured. A fair number have simply failed to understand the problem.
The most recent proposal I’ve heard for a Connectionist treatment of
systematicity is owing to the philosopher Andy Clark (1993). Clark says
that we should “bracket” the problem of systematicity. “Bracket” is a
technical term in philosophy which means try not to think about.
I don’t propose to review this literature here. Suffice it that if you
assume compositionality, you can account for both systematicity and
productivity; and if you don’t, you can’t.Whether or not productivity and
systematicity prove that conceptual content is compositional, they are
clearly substantial straws in the wind. I find it persuasive that there are
98 Prototypes and Compositionality
continental drift explains why (e.g.) South America fits so nicely into Africa. It does so,
however, not by entailing that South America fits into Africa, but by providing a theoretical
background in which the fact that they fit comes, as it were, as no surprise. Similarly, mutatis
mutandis, for the explanation of systematicity by compositionality.
Inferences from systematicity to compositionality are ‘arguments to the best
explanation’, and are (of course) non-demonstrative; which is (of course) not at all the same
as their being implausible or indecisive. Compare Cummins 1996, which appears to be
confused about this.
quite a few such straws, and they appear all to be blowing in the same
direction.
The Best Argument for Compositionality
The best argument for the compositionality of mental (and linguistic)
representation is that its traces are ubiquitous; not just in very general
features of cognitive capacity like productivity and systematicity, but also
everywhere in its details. Deny productivity and systematicity if you will;
you still have these particularities to explain away.
Consider, for example: the availability of (definite) descriptions is surely
a universal property of natural languages. Descriptions are nice to have
because they make it possible to talk (mutatis mutandis, to think) about a
thing even if it isn’t available for ostension and even if you don’t know its
name; even, indeed, if it doesn’t have a name (as with ever so many real
numbers). Descriptions can do this job because they pick out unnamed
individuals by reference to their properties. So, for example, ‘the brown
cow’ picks out a certain cow; viz. the brown one. It does so by referring to
a property, viz. being brown, which that cow has and no other cow does
that is contextually relevant. Things go wrong if (e.g.) there are no
contextually relevant cows; or if none of the contextually relevant cows is
brown; or if more than one of the contextually relevant cows is brown . . .
And so forth.
OK, but just how does all this work? Just what is it about the syntax and
semantics of descriptions that allows them to pick out unnamed
individuals by reference to their properties? Answer:
i. Descriptions are complex symbols which have terms that express
properties among their syntactic constituents;
and
ii. These terms contribute the properties that they express to determine
what the descriptions that contain them specify.
It’s because ‘brown’ means brown that it’s the brown cow that ‘the brown
cow’ picks out. Since you can rely on this arrangement, you can be
confident that ‘the brown cow’ will specify the local brown cow even if you
don’t know which cow the local brown cow is; even if you don’t know that
it’s Bossie, for example, or that it’s this cow. That, however, is just to say
that descriptions succeed in their job because they are compositional. If
English didn’t let you use ‘brown’ context-independently to mean brown,
and ‘cow’ context-independently to mean cow, it couldn’t let you use ‘the
brown cow’ to specify a brown cow without naming it.
Prototypes and Compositionality 99
Names, by contrast, succeed in their job because they aren’t
compositional; not even when they are syntactically complex. Consider
‘the Iron Duke’, to which ‘Iron’ does not contribute iron, and which you
can therefore use to specify the Iron Duke even if you don’t know what he
was made of. Names are nicer than descriptions because you don’t have to
know much to specify their bearers, although you do have to know what
their bearers are called. Descriptions are nicer than names because,
although you do have to know a lot to specify their bearers, you don’t have
to know what their bearers are called.What’s nicer than having the use of
either names or descriptions is having the use of both. I agree that, as a
piece of semantic theory, this is all entirely banal; but that’s my point, so
don’t complain. There is, to repeat, no need for fancy arguments that the
representational systems we talk and think in are in large part
compositional; you find the effects of their compositionality just about
wherever you look.
I must apologize for having gone on at such length about the arguments
pro and con conceptual compositionality; the reason I’ve done so is that,
in my view, the status of the statistical theory of concepts turns, practically
entirely, on this issue. And statistical theories are now the preferred
accounts of concepts practically throughout cognitive science. In what
follows I will take the compositionality of conceptual repertoires for
granted, and try to make clear how the thesis that concepts are prototypes
falls afoul of it.
Why Concepts Can’t Be Prototypes12
Here’s why concepts can’t be prototypes: whatever conceptual content is,
compositionality requires that complex concepts inherit their contents
from those of their constituents, and that they do so in a way that explains
their productivity and systematicity. Accordingly, whatever is not inherited
from its constituents by a complex concept is ipso facto not the content of
that concept. But: (i) indefinitely many complex concepts have no
prototypes; a fortiori they do not inherit their prototypes from their
constituents. And, (ii) there are indefinitely many complex concepts whose
prototypes aren’t related to the prototypes of their constituents in the ways
that the compositional explanation of productivity and systematicity
requires. So, again, if concepts are compositional then they can’t be
prototypes.
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12 Some of the next several pages is condensed from Fodor and Lepore 1994, q.v. for a
more extended treatment.