METAPHYSICS turn out to be functions The link between mathematical functions and predicates such as ‘ killed ’ or ‘ is lighter than ’ is made in a striking passage of ‘Function and Concept’ where we are invited to consider the function ‘x2 ¼ 1’ The first question that arises here is what the values of this function are for different arguments Now if we replace x successively by À1, 0, 1, we get: (À1)2 02 12 22 ¼1 ¼1 ¼1 ¼1 Of these equations the first and third are true, the others false I say ‘the value of our function is a truth-value’ and distinguish between the truth-values of what is true and what is false (CP 144) Once this move has been made, it is possible for Frege to define a concept as a function whose value for every argument is a truth-value A concept will then be the extra-linguistic counterpart of a predicate in language: what is represented, for instance, by the predicate ‘ is a horse.’ Concepts, like numbers, are quite independent of mind or matter: we not create them, we discover them; but we not discover them by the operation of our senses They are objective, though they not have the kind of reality (Wirklichkeit) that belongs to the physical world of cause and effect Frege’s realism is often called Platonism, but there is a significant difference between Plato’s Ideas and Frege’s concepts For Plato, the Ideal Horse was itself a horse: only by being itself a horse could it impart horsiness to the non-ideal horses of the everyday world.4 Frege’s concept horse, by contrast, is something very unlike a horse Any actual horse is an object, and between objects and concepts there is, for Frege, a great gulf fixed Not only is the concept horse not a horse, it is, Frege tells us, not a concept This remark at first hearing brings us up short; but there is nothing really untoward about it Prefacing ‘horse’ with ‘the concept’ has the effect of turning a sign for a concept into a sign for an object, just as putting quotation marks round the word ‘swims’ turns the sign for a verb into a noun which, unlike a verb, can be the subject of a sentence We can See vol I, p 208 180