I admit that there is a quite peculiar obstacle in the way of an understanding with my reader. By a kind of necessity of language, my expressions, taken literally, sometimes miss my thoughts; I mention an object when what I intend is a concept[-sense]. I fully realize that in such cases I was relying on the reader who would be ready to meet me half-way—who does not begrudge me a pinch of salt.

But Frege underestimated (or understates) the problem. If he is right in his insistence that the description refers to an object, this undercuts his whole explanation of the unity of the proposition. Merely reflect for a moment on (*). This is now simply false. We seem forced into the view that concept-senses are objects, even though they cannot be.3

It is not just the unity of propositions which generates this situation for Frege.4 In Fregean semantics, both the senses and referents of predicates are functions, and the same problem arises for normal cases of functional application.Thus, for Frege, ‘the father of ’ refers to the function that maps each person to their father (and each non-person to something else), and has a corresponding sense. Call this a function-sense. So ‘the father of Frege’ refers to Herr Frege sr., and its sense is an object-sense—a unitary thing. It has this because the sense of ‘Frege’ fills the gap in the sense of ‘father of ’. But the sense of ‘father of ’, according to Frege’s criterion, is an object(-sense), and so it does not have a gap at all. The situation is exactly the same.

Frege’s problem, then, is this. If concept-senses and function-senses are to play their role in accounting for the unity of complexes, they cannot be objects. But they are. One might avoid Frege’s problem simply by rejecting his account of meaning.The situation in which Frege finds himself is, however, but anexample of amuch deeper problem which cannot be avoided in this way. At root, the problem is not about meaning at all. It is about how parts cooperate to form a unity of any kind. Let me spell this out.5

3 See, further, Priest (1995a), ch. 12. The chapter shows how the problem gives rise to the distinction between saying and showing in Wittgenstein’s Tractatus, together with its final spectacular self-destruction.

4 Which makes any solution to the problem in terms of predication—such as that in Gaskin (1995)—beside the point.

5 Frege’s problem is, in fact, a version of a much older problem concerning properties (the traditional name for Frege’s concepts). We say ‘Socrates runs’. ‘Runs’ denotes the property of running. That is a thing. But ‘Socrates runs’ is not a congeries of two things. The two cooperate. In the sentence, one must understand ‘runs’ as essentially predicative, ‘is running’, which is not an object. Properties themselves are both objects and not objects.One can get around this to a certain extent, by taking it that there is only one lexical item with a predicative function: ‘instantiates’. (As in ‘Socrates instantiates the property of running’.) But one is still stuck with the phenomenon for the relation of instantiation. I will return to this matter in discussing Heidegger in Chapter 4.

One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness by Graham Priest