INDEFINITE. — Besides having the meaning of indeterminate (v. INFINITO), i. denotes a limited magnitude that can grow without end. I. 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 mode of variation of a magnitude, which can always increase, assuming values greater than a predetermined value. For example, i. or (potential) infinities are the geometrical line, the series of integers, a number greater than another arbitrarily predetermined one, etc.
R. Descartes, reserving the term infinite for God, calls indefinite that magnitude whose limits cannot be known (Principia philosophiae, I, nos. 26–27; ed. C. Adam and P. Tannery, VIII, Paris 1897–1910, pp. 14–15). And since no limit of the material world can be imagined, he concludes: «substantiam corpoream indefinite extensam in iis (negli spazi) contineri» (ibid., II, no. 21, p. 52).