6 Universals

What lets Ramsey ignore nominalism in ‘Theories’ is his denial in ‘Universals’ (1925) that our distinction between particulars and universals shows any intrinsic difference between them. First, it cannot be based on the subject–predicate distinction, e.g. between ‘Socrates’ and ‘is wise’ in ‘Socrates is wise’: for the subject of the equivalent ‘wisdom is a characteristic of Socrates’ is wisdom, which is not a particular (1990a: 14). Also, in molecular propositions like ‘Socrates is wise or Plato is foolish’, the subject–predicate distinction generates complex universals, like being wise unless Plato is foolish. But Ramsey argues that if these existed, then (for example) that a universal R relates a to b, that a has the complex property Rb and that b has aR would ‘be three different propositions because they have different sets of constituents, and yet they are … but one, namely that a has R to b. So the theory of complex universals is responsible for an incomprehensible trinity, as senseless as that of theology’ (1990a: 14). Similarly with Socrates’ apparent property of being wise-unless-Plato-is-foolish and Plato’s of being foolish-unless-Socrates-is-wise. If, as Ramsey assumes, the proposition that Socrates is wise or Plato is foolish can have only one set of constituents, there can be no such complex properties.

Predicates can therefore distinguish universals from particulars only in atomic propositions, and even then the distinction will not imply an intrinsic difference unless that difference would explain our impression that (for example) ‘Socrates is a real independent entity, wisdom … a quality of something else’ (1990a: 19). But no such difference will do this. For our impression comes from associating ‘wise’ only with propositions of the atomic form ‘x is wise’ while associating ‘Socrates’ with all propositions containing it, including the molecular ‘Socrates is neither wise nor just’. Yet we could as easily associate ‘wise’ with this and all other propositions containing it, and restrict ‘Socrates’ to the atomic form ‘Socrates is q’, where q is a universal: a form which, without complex universals, can no more include ‘Socrates is neither wise nor just’ than ‘x is wise’ can include ‘neither Socrates nor Plato is wise’ (1990a: 20–1). So no intrinsic difference between universals and particulars can be inferred from – since none will explain – our associating atomic forms with predicates but not subjects.

Why then do we do that, thus making universals seem less ‘real and independent’ than particulars? Ramsey’s explanation is this. A predicate symbol ‘φ’ can stand alone only if it names a real universal, not if it abbreviates (for example) ‘has R to a or S to b’. This we must abbreviate to ‘φx’, to distinguish it from the two-place ‘… has R to a or … has S to b’, written ‘φ(x,y)’. But since it is irrelevant to an extensional logic whether or not ‘φ’ names a universal, we always write ‘φ’ as ‘φx’, ‘φ(x,y)’, etc., thus associating all predicates with atomic forms (1990a: 26–8).

We cannot therefore infer from this practice that particulars differ intrinsically from universals. A logician can take ‘any type of objects whatever as the subject of his reasoning, and call them individuals, meaning by that simply that he has chosen this type to reason about’ (1990a: 30). We naturally choose easily discriminable objects, such as those with locations in space and time, to quantify over first; but what makes them particulars is simply that we choose them, not why. But then the fact that objects of certain types fail to count as particulars, just because we choose to exclude them from the range of our first-order quantifiers, is no reason to deny, as nominalists do, that they exist. The existence of universals – that is, of whatever we leave for our second-order quantifiers to range over – is no more problematic than that of particulars.