INDEFINITE. - Besides having the meaning of indeterminate (v. INFINITE), i. denotes a limited magnitude that can grow without end. I. coincides with the mathematical concept of potential or genetic infinity, called simply infinity (to be distinguished from the 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 larger than a predetermined value. For example, i. or (potential) infinities are the geometric line, the series of whole numbers, a number larger than another predetermined at will, etc.

R. Descartes, reserving the term infinite to God, calls indefinite that magnitude whose limits one cannot manage to know (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 of the material world, he concludes: «substantiam corpoream indefinite extensam in iis (negli spazi) contineri» (ibid., II, n. 21, p. 52).

Bibliography3 works

BIBL.: L. Couturat, De l'infini mathématique, Paris 1896; F. Enriques, I problemi della scienza, Bologna 1925, p. 14 ff.; A. Fraenkel, Einleitung in die Mengenlehre, 3rd ed., Berlin 1928.

Roberto Masi

@incollection{ec6_indefinito, author = {Masi, Roberto}, title = {Indefinito}, booktitle = {Enciclopedia Cattolica}, volume = {VI}, pages = {1794}, note = {Cited by column}, publisher = {Ente per l’Enciclopedia Cattolica e per il Libro Cattolico}, address = {Città del Vaticano}, year = {1951}, url = {https://azioneromana.com/article/indefinito} }

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Indefinite

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