The Stanford Encyclopedia of Philosophy’s entry on concepts explains three commonly held views of concepts. On the first, concepts are taken to be psychological entities that serve as constituents of the mental representations that feature in the representational theory of mind. On the second, concepts are understood in terms of concept possession which is explained as a sort of ability had by cognitive agents. Finally, on the third, concepts are understood as abstract objects roughly identified with the constituents of propositions. On this view, a concept can be said to contribute a Fregean sense to the thought which is the proposition of which it is a constituent. In this post, I want to suggest that, if we accept some prima facie unobjectionable claims about mental representations and the representative character of language, then on either of these three understandings of concepts we are left with the result that concepts, cognizers and individuals (that is, concrete, abstract or mental objects) stand in the following relation: concepts are (or can be used as) sortals of individuals for cognizers.
I won’t spend too much time spelling out each of these three views, as I think the SEP does well at this. But I will quote some of the relevant parts of the entry. We get a good thumbnail sketch of the first position in the following,
Many advocates of RTM [Representational Theory of Mind] take the mental representations involved in beliefs and other propositional attitudes to have internal structure. Accordingly, the representations that figure in Sue’s beliefs would be composed of more basic representations. For theorists who adopt the mental representation view of concepts, concepts are identified with these more basic representations.
The following sketches the concepts-as-abilities view,
According to the abilities view, it’s wrong to maintain that concepts are mental particulars—concepts are neither mental images nor word-like entities in a language of thought. Rather, concepts are abilities that are peculiar to cognitive agents (e.g., Brandom 1994, Dummett 1993, Millikan 2000). The concept CAT, for example, might amount to the ability to discriminate cats from non-cats and to draw certain inferences about cats.
Finally, we have this to give a flavor of the concepts-are-Fregean-senses view,
Concepts are said to be the constituents of propositions. For proponents of this view, concepts mediate between thought and language, on the one hand, and referents, on the other. An expression without a referent (“Pegasus”) needn’t lack a meaning, since it still has a sense. Similarly, the same referent can be associated with different expressions (e.g., “Eric Blair” and “George Orwell”) because they convey different senses. Senses are more discriminating than referents. Each sense has a unique perspective on its referent—a unique mode of presentation. Differences in cognitive content trace back to differences in modes of presentation.
Now, as I said before, I want to argue that on any of these views that, if we take on board (what I hope are) some innocuous assumptions, concepts are sortals of individuals for cognizers. Let’s consider the first view: assume that a cognizer (call him ‘Cy’) with appropriate perceptual abilities is presented with a physical object (call it ‘α‘) of particular size, shape and color in certain conditions (say it’s a green cube with 10cm edges presented under normal lighting) and that the cognizer forms a mental representation of this object. Now we might say that Cy correctly (mentally) represents α iff he mentally represents it as having the certain shape that is does (cubical), the certain color that it does (green) and size that it does (10cm sides). On this view, we might say that among the constituents of Cy’s mental representation are (a mental representation equivalent of) the concept CUBE and (a mental representation equivalent of) the concept GREEN. (I’ll use all CAPS to indicate concepts that are expressed — or corresponding most closely to what is expressed — by the word capitalized on each of the three views that we discuss.)
If Cy can form such mental representations, then he could also represent something to or for himself in the absense of such a presentation. We might ask Cy to imagine a green cube of a certain size, and it seems that he would use the same or at least (in relevant ways) similar constituents in this representation (without a presentation). Of course, we could do this at least two ways. If Cy has associated the predicate ‘is a cube’ with the mental representation he uses to imagine an identify cubes and has associated the predicate ‘is green’ with the mental representation he uses to imagine and identify green things, then we could encourage Cy to represent a green cube of a certain size to himself by saying: “Please think about a green cube with sides of roughly ten centimeters”. Or if Cy didn’t realize that the predicate ‘is a cube’ and ‘is green’ expressed the concepts we normally take them to (perhaps Cy isn’t competent with these predicates), but has competence with enough of a language to be in a position to be able to represent to himself the situation we wished him to — that is a representation as of a green cube with sides of roughly 10cm in length — we might be able to make it the case that he made this representation (perhaps with the aid of demonstrations, etc.).
Now, having said this much, I think we can see that, on the view that concepts are constituents of mental representations, if Cy has the concept expressed by the predicate ‘is a cube’, then Cy can discriminate cubes from non-cubes in actual and counterfactual situations (however those are specified). Specifically, Cy can accurately represent to himself cubes – that is, token CUBE – when he’s presented with cubes or when he’s asked to imagine cubes or asked to determine in some counterfactual situation whether in the situation described whether there is a cube or not. So Cy has the ability to discriminate cubes from non-cubes if he has the concept CUBE. Possession of the concept ensures that, in the right circumstances, Cy can sort objects into cubes and non-cubes. CUBE is a sortal of individuals (in this case physical objects) for a cognizer Cy.
On the second view – concepts-as-abilities, it’s obvious that to possess a concept (like CUBE) is to be able to sort individuals into two groups: cubes and non-cubes.
On the third view – concepts as Fregean Senses – we need to take on a few more assumptions to argue for this thesis. First off, we must assume that the sentences that express Fregean thoughts (or propositions) have truth conditions and so are in some sense representational. If we limit our discussion to sentences which make simple claims of physical objects, such as the claim that the cat is on the mat or that a green cube with sides of roughly 10 cm sits on the table in front of me, then the truth conditions of these sentences have the obvious relation to the representations made by these sentences. The first sentence represents the cat as being on the mat and so in this case, the truth conditions of ‘the cat is on the mat’ is that the cat is, in fact, on the mat. The second sentence, represents the situation in which a green cube with sides of roughly 10cm is on the table; its truth conditions are that a green cube with sides of roughly 10cm is on the table. Second, we must assume that a necessary condition on grasping a particular proposition (or, alternatively, to understand the meaning of a sentence that expresses this proposition) is to know the truth conditions of the sentence that expresses the proposition. Third, we must assume that the content or character of propositions (or the meaning of a sentence) is compositional – that is, the character or content of propositions is somehow dependent on the character or content of the individual constituents of the proposition together with the manner in which these constituents are combined.
Now on this view of concepts, they are the constituent senses of propositions expressed by declarative sentences. From the three assumptions, we can see that a necessary condition on possessing a concept (what does this come to on the third view? perhaps “grasping a sense” – I’m not really even sure how to say this in a properly Fregean manner) is an understanding of how that concept, as a sense, contributes to truth conditions of the sentence which expresses the proposition in which the concept is a constituent. For a simple sentence like ‘alpha is a green cube with sides of roughly 10cm in length’ (where ‘alpha’ is a singular referring term denoting the individual α), the concept expressed by the predicate ‘is a cube’ presumably contributes being a cube to the truth conditions of the sentence – the sentence is true only if α is a cube, and to understand the sentence one must know its truth conditions. If a cognizer knows these truth conditions, she will know when they are met and when they are not. If α is a green cube, the truth conditions are met. If α is a green sphere , the truth conditions are not met. Specifically, one must know, at least, whether the individual picked out by ‘alpha’ (that is, α) is cubical or not. Since the character or content of a proposition is compositional, if a cognizer grasps the sense of the proposition in which the concept CUBE features, then the cognzier would understand other propositions in which CUBE featured given that she understood each of the other concepts in those propositions. We’ve assumed that this understanding requires knowing the truth conditions of each of the sentences that express these propositions and a necessary condition on that seems to be the ability to discriminate cubes from non-cubes in actual and counterfactual situations. In other words, grasping or possessing the concept CUBE is to be (a cognizer) in possession of a sortal of individuals. And so on this view and our assumptions, a concept can be used (given that a cognizer grasps the concept) as a sortal of individuals for that cognzier.
– Jesse Butler