INDEFINITE. — In addition to having the meaning of indeterminate (v. INFINITE), the term "indefinite" indicates a limited magnitude that can grow without end. It coincides with the mathematical concept of potential or genetic infinity, simply called infinity (to be distinguished from actual or transfinite infinity introduced into mathematics by G. CANTOR with set theory). Potential infinity is not a magnitude but the manner in which a magnitude varies, which can always increase, assuming values greater than any preassigned value. For example, potential infinities or infinitudes are the geometric line, the series of whole numbers, a number greater than any other arbitrarily fixed number, etc.
R. DESCARTES, reserving the term "infinite" for God, calls "indefinite" that magnitude whose limits cannot be known (Principia philosophiae, I, nn. 26-27; ed. C. Adam and P. Tannery, VIII, Paris 1897-1910, pp. 14-15). And since one cannot imagine a limit to the material world, he concludes: «substantiam corpoream indefinite extensam in iis (in those spaces) contineri» (ibid., II, n. 21, p. 52).