Page:An Enquiry Concerning the Principles of Natural Knowledge.djvu/130

 116 III. METHOD OF EXTENSIVE ABSTRACTION instantaneous three-dimensional whole of nature. The set of abstractive elements and abstractive classes covered by both of two non-parallel moments is the locus which is their common intersection. Such a locus will be called a level in either moment. A level is in fact an instantaneous plane in the instantaneous space of any moment in which it lies. But we reserve the conventional spatial terms, such as plane/ for the time-less spaces to be defined later. Accordingly the word level is used here. -2 An indefinite number of non-parallel moments will intersect each other in the same level, forming their complete intersection; and one level will never be merely a (logical) part of another level. Let three mutually intersecting moments (M 19 M 2 and M 3, say) intersect in the levels l23, l31, l12. Then three cases can arise: either (i) the levels are all identical [this will happen if any two are identical], or (ii) no pair of the levels intersect, or (iii) a pair of the levels, say l31 and l12, intersect. In case (i) the three moments are called co-level. In case (ii) there are special relations of parallelism of levels, to be considered later. In case (iii) the locus of abstractive elements and abstractive classes which forms the intersection of l31 and l12 will be called a rect ; let this rect be named r123. Then r123 is also the complete intersection of l12 and l23, and of l23 and l31, and of the three moments M1, M2, M3. When three moments have a rect as their complete intersection they are called co-rect. A rect is an in stantaneous straight line in the instantaneous three- dimensional space of any moment in which it lies. But, as before, the conventional space-nomenclature is avoided in connection with instantaneous spaces.