The concept horse is not a concept. Thus spoke Frege, paradoxically. Why does he say such a thing? Because the subject expression 'the concept horse' refers to an object. It names an object. Concepts and objects on his scheme are mutually exclusive. No concept is an object and conversely. Only objects can be named. No concept can be named. Predicates are not names. If you try to name a concept you will fail. You will succeed only in naming an object. You will not succeed in expressing the predicativity of the concept. Concepts are predicable while objects are not. It is clear that one cannot predicate Socrates of Socrates. We can, however, predicate wisdom of Socrates. It is just that wisdom is not an object.
But now we are smack in the middle of the paradox. For to explain Frege's view I need to be able to talk about the referent of the gappy predicate ' ___ is wise.' I need to be able to say that it is a predicable entity, a concept. But how can I do this without naming it, and thus objectifying it? Ineffability may be the wages of Frege's absolute object-concept distinction.
To savor the full flavor of the paradox, note that the sentence 'No concept can be named' contains the general name 'concept.' It seems we, or rather the Fregeans, cannot say what we or they mean. But if we cannot say what we mean, how do we know that we mean anything at all? Is an inexpressible meaning a meaning? Are there things that cannot be said but only shown? (Wittgenstein) Perhaps we cannot say that concepts are concepts; all we can do is show that they are by employing open sentences or predicates such as '___ is tall.' Unfortunately, this is also paradoxical. For I had to say what the gappy predicate shows. I had to say that concepts are concepts and that concepts are what gappy predicates (predicates that are not construed as names) express.
Why can't concepts be named? Why aren't they a kind of higher-order object? Why can't they be picked out using abstract substantives? Why can't we say that, in a sentence such as 'Tom is sad,' 'Tom' names an object while 'sad' names a different sort of object, a concept/property? Frege's thought seems to be that if concepts are objects, then they cannot exercise their predicative function. Concepts are essentially and irreducibly predicative, and if you objectify them -- think or speak of them as objects -- then you destroy their predicative function. A predicative proposition is not a juxtaposition of two objects. If there is Tom and there is sadness, it doesn't follow that sadness is true of Tom. What makes a property true of its subject? An obvious equivalence: if F-ness is true of a, then *a is F* is true. So we might ask the questions this way: What makes *a is F* true?
The Problem of the Unity of the Proposition and the Fregean Solution
We are brought back to the problem of the unity of the proposition. It's as old as Plato. It is a genuine problem, but no one has ever solved it. (Of course, I am using 'solve' as a verb of success.)
A collection of two objects is not a proposition. The mereological sum Tom + sadness is neither true nor false; propositions are either true or false. The unity of a proposition is a type of unity that attracts a truth value, whereas the unity of a sum does not attract a truth value. The unity of a proposition is mighty puzzling even in the simplest cases. It does no good to say that the copula 'is' in 'Tom is sad' refers to the instantiation relation R and that this relation connects the concept/property to the object, sadness to Tom, and in such a way as to make sadness true of Tom. For then you sire Mr Bradley's relation regress. It's infinite and it's vicious. Note that if the sum Tom + sadness can exist without it being true that Tom is sad, then the sum Tom + R + sadness can also exist without it being true that Tom is sad.
Enter Frege with his obscure talk of the unsaturatedness of concepts. Concepts exist whether or not they are instantiated, but they are 'gappy': if a first-level concept is instantiated by an object, there is no need for a tertium quid to connect concept and object. They fit together like plug and socket, where the plug is the object and the concept the socket. The female receptacle accepts the male plug without the need of anything to hold the two together.
On this approach no regress arises. For if there is no third thing that holds concept and object together, then no worries can arise as to how the third thing is related to the concept on the one side and the object on the other. But our problem about the unity of the proposition remains unsolved. For if the concept can exist uninstantiated, then both object and concept, Tom and sadness, can exist without it being true that Tom is sad.
The dialectic continues on and on. Philosophia longa, vita brevis. Life is brief; blog posts ought to be.
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