How to Blunt the Sword of Compositionality

ConceptsDthe elementary building-blocks of thoughtDhave long been a focus of research in psychology, and it shows. A naturalistically minded philosopher who goes shopping for a theory of concepts finds herself faced with a fairly dizzying array of options, including definition theories, prototype theories, exemplar theories, theory theories, and an assortment of hybrids. It is with some sense of relief, perhaps, that she learns of a deviceDwhat I shall call, follow-ing Fodor 1998a, the asword of compositionalityoDwith which to cut down the space of possibilities. In particular, the sword is supposed to greatly sim-plify the selection task by eliminating in one fell swoop the largest and most influential class of theories currently on the market. The aim of this paper is to test the credibility of this rather bold supposition. To get a sense of what's at stake here requires a quick survey of the theoret-ical terrain. Most contemporary thinking about concepts is informed by the lexical semantics tradition, which approaches the study of concepts via the nat-ural language expressions that encode them. Of special importance to this study are lexical concepts, that is, concepts encoded by monomorphemic words like `cat'or `bachelor'. Non-lexical conceptsDconcepts encoded either by polymor-phemic words ~`housebroken', `unmarried'! or by phrases ~`cat fur', `bachelor party'!Dare understood to be built up somehow from lexical ones, and hence are explanatorily posterior to them. Theories of concepts in the lexical semantics tradition can be sorted using a binary decision tree with three branches. First there is the question of atom-ism. Atomists say that lexical concepts are by and large semantically primi-tive or unstructured, in that they have the content they do independently of their relations to particular other concepts ~Fodor 1998a!. Anatomists deny this, opting instead for the idea that concepts generally exhibit semantic structure of some sort. Second there is the question of classicalism. Classical anatomist theories dictate that the kind of structure possessed by concepts is definitional