Logic

LOGIC It is in keeping with the spirit of this book that we should think in some measure in terms of logical behaviour. It seems natural in taking the pragmatic-cum-behavioural view of philosophical issues that we should treat of logic initially as pre-symbolic, or indeed pre-linguistic, and only then tear it out of its pragmatic context and talk of the propositional or predicate calculus (and all the other logics found in the textbooks) in terms of non­pragmatic systems, with much of the built-in muddle that has been so well illustrated by Geach (1968).We accept much of what Geach has said about the “corrup­tions of logic”. We accept, and have already mentioned, the distinction made between naming and predicates. The classic example being that “The Mayor of Cambridge” does not name a particular man in the same way as “The Duke of Cambridge” does name a particular public house. We should naturally distinguish a particular name with a specific reference from a predicate that names a number of different people (even if at dif­ferent times). It may well be difficult always to remember to make this particular distinction, and in certain contexts it may

not matter, but its validity for logic remains. We shall not discuss the many corruptions that have occurred in logic, since this is a matter for the professional logician. But before leaving this point I would like to mention one interesting example of an unac­ceptable syllogism quoted by Geach (p 57):

Some men smoke hashishSome men study logicErg°:Some men who study logic smoke hashish He argues that the invalidity of this syllogism is obvious and he says that the only solution lies in dropping the whole idea that ‘some men’ is ever used to stand for a class consisting of some men. This, I would have thought, was not perhaps the whole answer; the answer is to realise that ‘some men’ designates (or may designate) different classes in different statements - the point being that ‘some men’ does not tell you which men are referred to. It is presumably another example of the confusion that may arise between names and predicates. This, though, will have been an obvious answer which Geach will not have over­looked, and the problem of class interpretation of the quantifiers (Russell, 1938) should have killed it off as is illustrated by the doctrine of distribution: Geach’s point is well-taken.We shall have some discussion of “traditional logic” if only to present a backcloth to “non-traditional logic”, as well as to pro­vide part of what is required in formalisation, which we discuss in the next chapter. But we shall gradually move over into the less traditional and more practical modes of reasoning.Before leaving the arguments of formal logic, particularly in the terms we have accepted Geach’s view in a formal context, let me try to circumnavigate some aspects of his difficulty, by looking at the same matter through ‘pragmatic’ spectacles. In other words, let me try to relate the formal and the factual here, and see how far this helps to clarify the problem.It is usually suggested that Frege was the founder of the modern predicate calculus, indeed it has been said that he was the founding “father of modern mathematical logic, philosophy

of mathematics and philosophy of language”. One can accept this without question, or without agreeing with all that he said, but for our purpose here in the “formal and the factual”, Frege’s influence was to place the emphasis, as did Chomsky for some­what different reasons, on the purely linguistic and, as a result, away from the behavioural.It was Frege who undoubtedly shifted much of the emphasis of philosophy from epistemology to language. This had a great in­fluence on Wittgenstein and the modern linguistic movement in philosophy. But it happened, quite irrationally in most cases, at the expense of the pragmatic approach to language and com­munication and created for many the false idea that the two ap­proaches were mutually exclusive.It is important to be clear that from the point of view of this book, the work which concentrates on providing a foundation for language, and language in terms of formal languages, is nothing but helpful. But confusion occurs if the attempt is made at the expense of the pragmatic/behavioural analysis of language. One does not exclude the other; on the contrary they are comple­mentary to each other. I am not therefore primarily concerned with arguments about, for example, the Fregean assimilation of propositions to proper names, or the arguments (Kripke, 1972; Dummett, 1973; Geach, 1968, 1975, etc.) that has ensued, and a part which we have already discussed.It can be said that if we encounter a proper name we have never met before we need its reference (“meaning”) fixed for us. At the same time we can understand new propositions (not always in fact!), but this fact, when true, is difficult to explain on the Fregean assumption (implicit rather than explicit) that propositions are proper names. The most obvious answer is that they are not. The proper name is a label that acts as a reference and a proposition may well include names, indeed will frequent­ly do so, but the difficulties here are considerable. They are more considerable indeed than it is my concern to analyse in any detail, but a little by way of guidelines should be drawn. The reason for some comment is that “sentences versus words as being primary”, and the clarification of referencing and prediction are all in some manner involved.