Does Realism Make a Difference to Logic?

Abstract

The ancient theory of an identity of some sort between subject and predicate is not merely out of fashion. Rejection of it is just about the cor nerstone of the Fregean analysis of propositions in terms of argument (or arguments) and function. My partenthesis, 'or arguments', is crucial. For while the old subject predicate relation itself might be analysed, or at least rephrased, in terms of argument and function, and while this procedure might be believed in nocuous, it is the extension of this paradigm to the analysis of sentences into functions with two or more arguments which decisively and openly upsets the older scheme, revealing it, so it is held, as being but a small part of the logic opened up by the recognition of polyadic 'predicates', or relations as they are also called. Thus Russell was led to suggest that the traditional subject-predicate relation is a 'monadic' predication.1 But from the traditional standpoint this could only mean that a predication like 'is white' is made twice over. The structure of the intended (putative) relation and of the proposition in tending it seem here to be confused. But in fact in this 'monadic' case although there is, as always, a relation between subject and predicate, i.e., a logical relation or a relation of reason, yet there is no such relation in the situation as described, but only the transcendental non-predicamental rela tion of a substance to its quality. Yet for the mathematical logician the at tributing of something to a subject, because of this relational account of predication, must itself be seen as something relational which the sentence isomorphically reflects. Thus in attributing a two-place predicate, also a dyadic relation, to a subject, as the logician says we do, I seem at one and the same time to predicate 'father of Tom' to John and 'father of to John and Tom as 'an ordered pair'. There is a certain fusion of the linguistic and the real, papered over by an isomorphic or 'picture' theory of meaning. If I say 'John is the father of Tom' the real relation of John to Tom is not the same as John's logical relation to what is predicated of him here, viz., being the father of Tom, i.e., not at all a relation to Tom (to say this relates 'John' but not John is simply wrong; it is John I am thinking and talking about). We can perhaps dimly begin to see how calling the subject