PRELIMINARY REMARKS

The Naturalist theory of possibility now to be advanced will be called a Combinatorial theory. It traces the very idea of possibility to the idea of the combinations – all the combinations – of given, actual elements. Combination is to be understood widely. It includes the notions of expansion (perhaps ‘repetition’ is a less misleading term) and also contraction.

It is to be emphasized that the central idea is not original, although naturally I hope I will be making some contribution to the details. The central idea is in the Tractatus, and it is one of the central ideas of the Tractatus. Perhaps its charter is 3.4:

I myself encountered the Combinatorial idea, and was converted, in Brian Skyrms's article ‘Tractarian Nominalism’ (1981), which is reprinted at the end of this book as an appendix. But a Combinatorial conception of possibility was put forward earlier by Max Cress well (1972) and before that at least toyed with, quite a vigorous toying, by Quine (1969, pp. 147–52). The Combinatorial theory of Cresswell and Quine does not involve the fictionalist element that mine will have.

I shall develop the theory in a particular way, a way determined by my own metaphysical views, in particular by my acceptance of (in re) universals (see Armstrong 1978a, b). It seems a peculiarly apt way to develop a Combinatorial theory.