Page:An Enquiry Concerning the Principles of Natural Knowledge.djvu/122

 assume that each event has a definite demarcation we know that the laws of nature ordinarily assumed in science will issue in ascribing to each event a definite boundary which will be a spatial surface prolonged into three dimensions by reason of its time-extension. Thus the possibilities of the spatial contact of surfaces are reproduced in the three-dimensional boundaries of events. Abstractive classes exist whose converging ends converge to elements [instantaneous points, or routes, or etc.] on the surface of one of the members of the class. In such a case, as we pass down the abstractive class towards its converging end, after some definite member x of the class the remaining members, all extended over by x, have some form of internal contact with the boundary of x. The closest form of such contact is to be injoined in x. But there will also be more abstract types of point-contact or of line-contact which we have not defined here, but know about from their occurrence in geometry. If we merely exclude such cases without explicit definition, we are really appealing to fundamental relations and properties which have not been explicitly. recognised. We must use definitions based solely upon those properties of the relation K which have been made explicit. We cannot explicitly take account of point-contact till points have been defined.

32. Abstractive Elements. 32.1 A ‘finite abstractive element deduced from the formative condition σ’ is the set of events which are members of σ-primes, where σ is a formative condition regular for primes. The element is said to be ‘deduced’ from its formative condition σ.

An ‘infinite abstractive element deduced from the