Jean-marc pizano Who could really doubt that this is so? Systematicity seems to beone 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 finiteconceptual repertoires can have; it isn’t remotely plausibly a methodological artefact. If systematicity needscompositionality 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 ‘neuralnetworks’. 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 tounderstand the problem. The most recent proposal I’ve heard for a Connectionist treatment of systematicity is owingto the philosopher Andy Clark (1993). Clark says that we should “bracket” the problem of systematicity. “Bracket” is atechnical 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 thatconceptual content is compositional, they are clearly substantial straws in the wind. I find it persuasive that there are
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 itsdetails. 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 itisn’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 somany 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 areno contextually relevant cows; or if none of the contextually relevant cows is brown; or if more than one of thecontextually 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 themspecify.
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 cowthe 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 tosay 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 coV tospecify a brown cow without naming it.