Kerry’s position as explicated by Frege in 'On concept and object':
“I have myself expressed the opinion that the relation between the content of the concept and the concept-object [i.e., the extension of the concept, instr.] is, in a certain respect, a peculiar and irreducible one; but this was in no way bound up with the view that the properties of being a concept and of being an object are mutually exclusive. The latter view no more follows from the former than it would follow, if, e.g., the relation of father and so on were one that could not be further reduced, that a man could not be, at once a father and a son (though of course not, e.g., father of the man whose son he was).”
So Kerry maintains that the relation between a concept and its extension is primitive and irreducible. Moreover, he rightly points out that it does not follow from this that something cannot be both a concept and an object anymore than it would follow from the primitiveness of the parent of relation that nothing can be both a father and a son.
Furthermore, Kerry goes on to give us some examples where it seems clear that a concept occurs in subject position and so is the argument of a further concept. Frege says:
“There are, indeed, cases that seem to support his view. I myself have indicted that a concept may fall under a higher[-order] concept―which, however, must not be confused with one concept’s being subordinate to another. Kerry does not appeal to this; instead, he gives the following example: ‘the concept “horse” is a concept easily attained,’ and thinks that the concept ‘horses’ is an object, in fact one of the objects that fall under the concept ‘concept easily attained’.”
It is not clear why Frege believes that Kerry is not appealing to a higher order concept with his example―that seems to be exactly what he is doing. Basically, Kerry’s point is that if you want to say that one concept (say, being a horse) falls under another, higher-order one (say, being easily attained) you formulate a sentence in which the subject term refers to the first concept and the predicate refers to the second. Thus, ‘The concept of being a horse is a concept which is easily attained.” Makes good sense.
Bizarrely, however, Frege rejects Kerry’s argument.
“Quite so; the three words ‘the concept “horse”’, do designate an object, but on that very account they do not designate a concept, as I am using the word. This is in full accord with the criterion I gave―that the singular definite article always indicates an object, whereas the indefinite article accompanies a concept-word.”
Moreover, Frege immediately notes the awkwardness of his view:
“It must indeed be recognized that here we are confronted by an awkwardness of language, which I admit cannot be avoided, if we say that the concept horse is not a concept, whereas, e.g., the city of Berlin is a city, and the volcano Vesuvius is a volcano. Language is here in a predicament that justifies the departure from custom. … In logical discussions one quite often needs to assert something about a concept, and to express this in the form usual for such assertions―viz. to make what is asserted of the concept into the content of the grammatical predicate. Consequently, one would expect that the reference of the grammatical subject would be the concept; but the concept as such cannot play this part, in view of its predicative nature; it must first be converted into an object, or, speaking more precisely, represented by an object.”
What gives? Why on earth does Frege feel compelled to deny that the concept of being a horse is a concept?!
The answer, it turns out, is pretty complex. First, two basic ontological claims:
- Frege argues that there is “a distinction … between what can occur only as an object, and everything else.”
- The only counterexample would seem to be identity claims, but these make use of the ‘is’ of identity, not the ‘is’ of predication.
- Propositions, while having analyses, are not in anything but a metaphorical sense structured or composed from the entities invoked in those analyses.
So, from a logical point of view, the world consists of two (not necessarily distinct) sorts of logically simple categories, objects and propositions. Objects are necessarily referred to by nominal expressions (names) and this is what gives us our wedge into the philosophical analysis of a given proposition. Specifically, when we “remove” the object referred to by a given name, what remains is a predicate. As we have seen, the predicate refers to a concept.
In effect, Frege’s view of concepts falls out of the Context Principle (never ask for the meaning of a word in isolation, but only in the context of an entire proposition): a concept just is what you get when you decompose a proposition by removing one or more objects involved in the analysis of that proposition. Here is the crucial point to understand: the existence of a concept is not independent of the analysis which gives rise to it; concepts are existentially dependent on analyses.
“The distinction between individual and concept seems to me even more important. In language the two merge into one another. … A concept is unsaturated in that it requires something to fall under it; hence it cannot exist on its own. That an individual falls under it is a judgeable content [i.e., proposition, instr.], and here the concept appears as a predicate and is always predicative. In this case, where the subject is an individual, the relation of subject to predicate is not a third thing added to the two, but it belongs to the content of the predicate, which is what makes the predicate unsatisfied. Now I do not believe that concept formation can precede judgement because this would presuppose the independent existence of concepts, but I think of a concept as having arisen by decomposition by way of decomposition from a judgeable content. I do not believe that for any judgeable content there is only one way in which it can be decomposed, or that one of these ways can always claim objective pre-eminence. In the inequality 3 > 2 we can regard either 2 or 3 as the subject. In the former case we have the concept being smaller than 3, in the latter, being greater than 2. We can also regard 3-and-2 [i.e., the ordered pair <3, 2>] as a complex subject. As a predicate we then have the concept of the relation of the greater to the smaller. In general I represent the falling of an individual under a concept by F(x), where x is the subject (argument) and F( ) the predicate (function), and where the empty place in the parentheses indicates unsaturadedness” [Letter to Anton Marty].
So basically a concept is an artifact of a propositional analysis in much the way that the logical form is an artifact of a propositional analysis (in fact, what counts as a concept is part of the logical form of the proposition).