It has been maintained by such philosophers as Quine and Goodman that purely ‘extensional’ language suffices for all the purposes of properly formalized scientific discourse. Those entities that were traditionally called ‘universals’ – properties, concepts, forms, etc. – are rejected by these extensionalist philosophers on the ground that ‘the principle of individuation is not clear’. It is conceded that science requires that we allow something tantamount to quantification over non-particulars (or, anyway, over things that are not material objects, not space-time points, not physical fields, etc.), but, the extensionalists contend, quantification over sets serves the purposes nicely. The ‘ontology’ of modern science, at least as Quine formalizes it, comprises material objects (or, alternatively, space-time points), sets of material objects, sets of sets of material objects, …, but no properties, concepts; or forms. Let us thus examine the question: can the principle of individuation for properties ever be made clear?

Properties and reduction

It seems to me that there are at least two notions of ‘property’ that have become confused in our minds. There is a very old notion for which the word ‘predicate’ used to be employed (using ‘predicate’ as a term only for expressions and never for properties is a relatively recent mode of speech: ‘Is existence a predicate?’ was not a syntactical question) and there is the notion for which I shall use the terms ‘physical property’, ‘physical magnitude’, ‘physical relation’, etc., depending on whether the object in question is one-place, a functor, more than one-place, etc.