Divisibility
Divisibility
The property in virtue of which a whole (whether physical, psychical or mathematical) may be divided into parts which do not thereby necessarily sever their relation with the whole. Divisibility usually implies not merely analysis or distinction of parts, but actual or potential resolution into parts. From the beginning philosophers have raised the question whether substances are infinitely or finitely divisible. Ancient materialism conceived of the physical atom as an indivisible substance. Descartes, however, and after him Leibniz, maintained the infinite divisibility of substance. The issue became the basis of Kant’s cosmological antinomy (Crit. of pure Reason), from which he concluded that the issue was insoluble in metaphysical terms. In recent decades the question has had to take account of (1) researches in the physical atom, before which the older conception of physical substance has steadily retreated; and (2) the attempt to formulate a satisfactory definition of infinity (q.v.). — O.F.K.