Page:An Enquiry Concerning the Principles of Natural Knowledge.djvu/123

 formative condition σ’ is the set of events which are members of σ-antiprimes, where σ is a formative condition regular for antiprimes. The element is said to be ‘deduced’ from its formative condition σ.

The abstractive elements are the set of finite and infinite abstractive elements.

32.2 An abstractive element deduced from a regular formative condition σ is such that every abstractive class formed out of its members either covers all σ-primes [element finite] or is covered by all σ-antiprimes [element infinite]. Thus it represents a set of equivalent routes of approximation guided by the condition that each route is to satisfy the condition σ.

32.3 An abstractive element will be said to ‘inhere’ in any event which is a member of it. Two elements such that there are abstractive classes covered by both are said to ‘intersect’ in those abstractive classes.

One abstractive element may cover another abstractive element. The elements of the utmost simplicity will be those which cover no other abstractive elements. These are elements which in euclidean phrase may be said to be ‘without parts and without magnitude.’ It will be our business to classify some of the more important types of elements. The elements of the greatest complexity will be those which can cover elements of all types. These will be ‘moments.’

A point of nomenclature is important. We shall name individual abstractive elements by capital latin letters, classes of elements by capital or small latin letters, and also, as heretofore, events by small latin letters. K will continue to denote the fundamental relation of extension from which all the relations here considered are derived.