Mathematics and God’s Point of View1

Król, Zbigniew

doi:10.1515/slgr-2016-0005

Abstract

In this paper the final stages of the historical process of the emergence of actual infinity in mathematics are considered. The application of God’s point of view – i.e. the possibility to create mathematics from a divine perspective, i.e. from the point of view of an eternal, timeless, omniscience and unlimited subject of cognition – is one of the main factors in this process. Nicole Oresme is the first man who systematically used actual infinity in mathematical reasoning, constructions and proofs in geometry.

References

(Bacon 1928) Bacon, R., Opera hactenus inedita Rogeri Baconi, Fasc. 8 Questiones supra libros quatuor Phisicorum Aristotelis Ferdinand M. Delorme O.F.M., Robert Steele (Eds.), Clarendon Press, Oxford (1928).
Search in Google Scholar
(Boyer 1968) Boyer, C. B., The History of the Calculus and its Conceptual Development. (The Concepts of the Calculus.), Willey International Editions (1968).
Search in Google Scholar
(Busard 1965) Busard, H. L. L., Unendlischen Reihen in A est unum calidum, Archive for History of Exact Sciences, vol. 2, no. 5, 387–397 (1965).
Search in Google Scholar
(Busard 2010) Busard, H. L. L., Nicole Oresme, Qustiones super geometriam Euclidis, Franz Steiner Verlag, Stuttgard (2010).
Search in Google Scholar
(Clagett 1968) Clagett, M., Nicole Oresme and the medieval geometry of qualities and motions. A treatise on the uniformity and difformity of intensities known as Tractatus de configurationibus qualitatum et motuum, edited with an introduction, English translation and commentary by Marshall Clagett, The University of Wisconsin Press, Medison, Milwaukee, and London (1968).
Search in Google Scholar
(Cleomedes 1891) Cleomedes, De motu circulari corporum caelestium, Ziegler, H. (ed.), Greek text and Latin translation, Teubner, Leipzig (1891).
Search in Google Scholar
(Cornford 1936) Cornford, F. N., The invention of space, in: Essays in Honour of Gilbert Murray, Allen & Unwin., London (1936).
Search in Google Scholar
(Crosby 1961) Crosby, H. L., Thomas of Bradwardine. His Tractatus de proportionibus. Its significance for the development of mathematical physics, Madison (1961).
Search in Google Scholar
(Cross 1998) Cros, R., Infinity, continuity, and composition: The continuum of Gregory of Rimini, Medieval Philosophy and Theology 7, 89–110 (1998).
Search in Google Scholar
(Czwalina 1927) Czwalina, A., Kleomedes Die Kreisbewegung der Gestirne, in: Ostwald’s Klassiker der exacten Wissenschaften, Engelmann, Leipzig (1927).
Search in Google Scholar
(Droppers 1966) Droppers, G., The questions de sphera of Nicole Oresme. Latin text with English translation, commentary and variants, a thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy, History and History of Science, University of Visconsin (1966).
Search in Google Scholar
(Duhem 1906–13) Duhem, P., Études sur Léonard de Vinci, vol I, II, Ceux qu’il a lus et ceux qui l’ont lu; vol. III Les précurseurs parisiens de Galilée, Paris (1906–13).
Search in Google Scholar
(Edwards 1979) Edwards, C. H., Jr, The historical development of the calculus. Springer-Verlag, New York, Heidelberg, Berlin (1979).10.1007/978-1-4612-6230-5
Search in Google Scholar
(Grant 1961) Grant, E., Nicole Oresme and the Commensurability of Incommensurability of the Celestial Motions, Archive for History of Exact Science 1, 420–458, (1961).10.1007/BF00328576
Search in Google Scholar
(Grant 1966) Grant, E., Nicole Oresme. De proportionibus proportionum and Ad pauca respicientes, edited with Introduction, English translations, and Critical notes by Edward Grant, The University of Wisconsin Press, Madison, Milwaukee, and London (1966).
Search in Google Scholar
(Grant 1969) Grant, E., Medieval and seventeenth-century conceptions of an infinite void space beyond the cosmos, Isis 60(1), 39–60 (1969).10.1086/350448
Search in Google Scholar
(Grant 1971) Grant, E., Nicole Oresme and the Kinematics of Circular Motion. Tractatus de commensurabilitate and incommensurabilitate motuum coeli, edited with an Introduction, English translations, and Commentary by Edward Grant, The University of Wisconsin Press, Madison, Milwaukee, and London (1971).
Search in Google Scholar
(Grant 1982) Grant, E., Much Ado About Nothing. Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution, Cambridge University Press, Cambridge, London, New York, New Rochelle, Melbourne, Sydney (1982).10.1017/CBO9780511895326
Search in Google Scholar
(Grosseteste 1912) Robert Grosseteste, De luce, in: Die Philosophischen Werke des Robert Grosseteste, Bischofs von Lincoln, W., Aschendorff (ed.), (1912), pp. 51–59.
Search in Google Scholar
(Grosseteste 1942) Robert Grosseteste, On Light (De Luce), Translation from the Latin, with an introduction, C. C. Riedl, Marquette University Press, Milwaukee, Wisconsin (1942).
Search in Google Scholar
(Hardie 2007) Hardie, R. P. & Gaye, R. K., Physics by Aristotle, translated by R. P. Hardie and R. K. Gaye, e BooksAdelaide. Retrieved 2007, from: http://classics.mit.edu/Aristotle/physics.3.iii.html.
Search in Google Scholar
(Król 2013) Król, Z., Infinity in mathematics: Development of Platonic ideas and methods in mathematics in late Antiquity and the Middle Ages, Humanistyka i Przyrodoznawstwo, 19, 121–135 (2013).
Search in Google Scholar
(Król 2015) Król, Z. Platonism and the Development of Mathematics. Geometry and Infinity, IFiS PAN, Warsaw 2015.
Search in Google Scholar
(Mair 1938) Mair, J., Le Traité DE L’INFINI de Jean Mair, Hubert Elie (ed.), J. Vrin, Paris (1938).
Search in Google Scholar
(Murdoch 1957) Murdoch, J. E., Geometry and the continuum in the fourteenth century: A philosophical analysis of Thomas Bradwardines’s tractatus De Continuo, a PH.D. thesis submitted to the Graduate School of the University of Wisconsin (1957).
Search in Google Scholar
(Murdoch 1968) Murdoch, J. E., The Medieval Euclid: Salient Aspects of the Translations of the Elements by Adelard of Bath and Campanus of Novara, in XIIe Congres International d’Histoire des Sciences, Revue de Synthese, 3e série, 49–52, 67–94, Paris (1968).
Search in Google Scholar
(Murdoch 1987) Murdoch, J. E., Thomas Bradwardine: mathematics and the continuity in the fourteenth century, in: Grant, E., Murdoch, J. E., (eds.), Mathematics and its applications to science and natural philosophy in the Middle Ages, Cambridge University Press, Cambridge, London, New York, New Rochelle, Melbourne, Sidney (1987), pp. 103–137 (1987).
Search in Google Scholar
(Oresme 1965) Nicole Oresme, The Questiones super de celo of Nicole Oresme, Kren, C. (ed.), Ph.D dissertation, University of Wisconsin (1965).
Search in Google Scholar
(Oresme 1968) Nicole Oresme, Nicole Oresme La Livre du ciel et le monde, Menut, A. D., Denomy, A. J. (eds.), University Wisconsin Press, Madison (1968).
Search in Google Scholar
(Wodeham 1988) Adam Wodeham, Tractatus de indivisibilibus: A critical edition with Introduction, Translation, and Textual Notes, R. Wood (ed.), Synthese Historical Library, 31, Dordrecht, Boston, and London, Kluwer Academic Publishers (1988).
Search in Google Scholar

Mathematics and God’s Point of View1

Abstract

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