- In the Parmenides young Socrates, after declaring his faith in the theory of Forms, is asked by Parmenides what he takes the extent of the realm of the Forms to be (130 a-d). That question has confronted not merely Platonists, but every Realist about universals1, ever since. My suggestion has been that the Empiricist, at least, should answer that for the most part it is not up to the philosopher to answer the question. There is much that he can say about the nature of the question and the form that answers should take. This work, long as it is, has only begun to grapple with the problems involved. But the content of the answer must be determined, not by abstract reasoning, but by the natural sciences with their ultimate dependence upon observation and experiment.
- However, as the discussion has developed, what has been presented is not simply a theory of universals2 but a first philosophy or ontology, a theory of the nature of reality in its most general aspect. Not every topic which a first philosophy might be expected to cover has been covered, but comprehensiveness may be too much to expect. Perhaps it should not even be sought.
- At any rate, if what has been offered is a first philosophy, it may be appropriate to conclude by considering where the main difficulty for this philosophy appears to lie. I think that the answer to this question is clear. It is the difficulty which faces any Empiricist philosophy: the problem of necessary truth. Can an Empiricist give a satisfactory account of the logically necessary truths of mathematics, of logic, of philosophy itself, especially first philosophy?
- The problem disappears if there are no necessary truths, if the whole distinction between logically necessary and contingent truths is not a real one. This is the view of W.V. Quine, denier of distinctions. But I find this extreme Empiricist view difficult to accept. The "Rational sciences" of logic and mathematics can be, and are, developed in a purely a priori manner. This would not be possible if their propositions had no different logical status from those of the natural sciences.
- It is clear, then, that what is required is an Empiricist theory of necessary truth. If an Empiricist theory of necessary truth can be developed at all, it is clear what general form it must take. The source of necessity must be located in the words, or concepts, in which the propositions are expressed. What the details of this theory are to be, and how various powerful objections to such a theory are to be overcome, I do not know. One objection, however, which I cannot take seriously is the contention that the notions of meaning, and hence synonymy, are irremediably confused.
- But what of the theory of universals3 put forward in this book? A great deal of our argument has consisted in the rejection of alleged a priori necessities. It has been pointed out that there are logical possibilities open where earlier theories saw only contradiction. An example is the rejection in this book of the necessity for simple universals4. Logical Atomism proclaims their necessity. But we have argued that logic cannot determine the matter.
- Nevertheless, at a few points our arguments seemed to bind rather than to loose. A conspicuous example is the link between particularity and universality. It was argued that every particular must have properties and relations (though no particular properties and relations). Equally it was argued that every property and relation must be a property and relation of some particular (though not of any particular particular).
- The connection between particularity and universality is so close that we can do no more than draw Scotus' 'formal distinction' between them. Here we seem to be in the presence of a logical necessity in things. Yet we are committed to the denial of any de re logical necessity. Can we find some account of this distinction, and of our knowledge of it, which is compatible with Empiricism?
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