Page:The World and the Individual, First Series (1899).djvu/550

Rh stituent portions. Now let us suppose our particular system N to be a system such as a particular portion, itself infinite, of the Gedankenwelt, would constitute. Namely, let us suppose our system N to be capable of a process of self-representation that first selects a single one of the elements of N (to be called One or element the first), and, that then represents the whole of N by that portion of N which is formed of all the elements of N except One. The result of this mode of self-representation is that N becomes, in the sense before defined, a Kette, represented by a part of itself, N’. This part, N’, by hypothesis, contains all of the N except the chosen first element named One. In consequence, and because of the very same sort of reasoning that we carried out in case of the map of England made within England, N’ will again contain, by virtue of the one principle of its constitution, a further part, N’’, which will be derived from N’ by leaving out a single element of N’, to be called Two, and defined as the second element of the system. Two will be, in fact, the name of that very element in N’ which, in the original mapping of N by N’, was the element that was made to represent, or to image, element One. But the process of expressing the meaning thus involved is now recurrent. For the one plan of representing N by N’, with the omission from N’ of the single element called One, has involved the representing of N’ by N’’, with the omission from N’’ of the single element now called Two, — an element which is merely the image in N’ of One in N. The same plan, however, not so much applied anew, as simply once fully expressed, implies that within N’’ there is an N’’’, an Niv, and so on without end; just as the one plan of mapping England within England involved the endless series of maps. But each of the series of systems N’, N’’, N’’’, etc., differs from the previous one simply by the omission of a