Otwarty dostęp

Theological Underpinnings of the Modern Philosophy of Mathematics.


Zacytuj

Albertson, D. (2014). Mathematical theologies: Nicholas of Cusa and the legacy of Thierry of Chartres. New York, NY: Oxford University Press.10.1093/acprof:oso/9780199989737.001.0001Search in Google Scholar

Beck, L.W. (1991). Foreword. In K.C. Köhnke, The rise of Neo-Kantianism: German academic philosophy between idealism and positivism (pp. ix–xiii). Cambridge, UK: Cambridge University Press.Search in Google Scholar

Bloor, D. (1991). Knowledge and social imagery (2nd ed.). Chicago, IL: University of Chicago Press (First published 1976).Search in Google Scholar

Bolzano, B. (1973). Theory of Science (J. Berg, Ed., B. Terrell, Trans.). Dordrecht, Holland: D. Reidel Publishing Company. (Original work published 1837)10.1007/978-94-010-2513-3Search in Google Scholar

Boniface, J. (2005). Leopold Kronecker’s conception of the foundations of mathematics. Philosophia Scientiæ, cahier spécial 5, 143–156. Retrieved from http://philosophiascientiae.revues.org/384.Search in Google Scholar

Breger, H. (2005). God and mathematics in Leibniz’s thought (pp. 485–498). In T. Koetsier & L. Bergmans (Eds.), Mathematics and the divine: A historical study. Amsterdam: Elsevier B.V.Search in Google Scholar

Bueno, O., & Vickers, P. (Eds.). (2014). Is Science Inconsistent? Synthese, 191, 2887–3158 (A special issue).10.1007/s11229-014-0463-9Search in Google Scholar

Byers, W. (2007). How mathematicians think: using ambiguity, contradiction, and paradox to create mathematics. Princeton, NJ: Princeton University Press.Search in Google Scholar

Cantor, G. (1932). Über unendliche lineare Punktmannigfaltigkeiten, Nr. 5: Grundlagen einer allgemeinen Mannigfaltigkeitslehre. In G. Cantor, Gesammelte Abhandlungen mathematischen und philosophischen Inhalts (E. Zermelo, Ed.) (pp. 165–209). Berlin: Springer. Original work published 1883. English translation (Ewald, 1996, pp. 878–920).Search in Google Scholar

Colyvan, M. (2008). Who’s afraid of inconsistent mathematics? ProtoSociology, 25, 24–35.10.5840/protosociology2008252Search in Google Scholar

Colyvan, M. (2009). Applying inconsistent mathematics. In O. Bueno & Ø. Linnebo (Eds.), New waves in philosophy of mathematics (pp. 160–172). Basingstoke: Palgrave MacMillan.Search in Google Scholar

Comte, A. (1934). Cours de philosophie positive. Tome 1: Les préliminaires généraux et la philosophie mathématique. (6 éd.). Paris: Alfred Costes. (Original work published 1830)Search in Google Scholar

Comte, A. (1851). The philosophy of mathematics: Translated from the Cours de philosophie positive by W.M. Gillespie. New York, NY: Harper & Brothers. (Original work published 1830)Search in Google Scholar

Dedekind, R. (1893). Was sind und was sollen die Zahlen? 2. Auflage. Braunschweig: Vieweg. First published 1888. English translation under the name “The nature and meaning of numbers” (Dedekind, 1901, pp. 29–115).Search in Google Scholar

Dedekind, R. (1901). Essays on the theory of numbers, authorized trans. W.W. Beman. Chicago: Open Court.Search in Google Scholar

Dedekind, R. (1932). Gesammelte mathematische Werke, Hrsg. von R. Fricke, E. Noether & Ö. Ore. (Band 3). Braunschweig: Vieweg.Search in Google Scholar

Descartes, R. (1985). The philosophical writings of Descartes, vol. I and II (J. Cottingham, R. Stoothoff, & D. Murdoch, Trans.). Cambridge University Press.Search in Google Scholar

Descartes, R. (1991). The philosophical writings of Descartes, vol. III: The correspondence (J. Cottingham, R. Stoothoff, D. Murdoch, & A. Kenny, Trans.). Cambridge University Press.10.1017/CBO9781107340824Search in Google Scholar

Detlefsen, M. (1998). Constructive existence claims. In M. Schirn (Ed.), The philosophy of mathematics today (pp. 307–336). New York, NY: Oxford University Press.Search in Google Scholar

Diderot, D. (1995). Detailed explanation of the system of human knowledge. In J. le R. d’Alembert, Preliminary discourse to the Encyclopedia of Diderot (R.N. Schwab, Trans., with the collaboration of W.E. Rex) (pp. 143–157). Chicago, IL: University of Chicago Press. (Original work published 1751)Search in Google Scholar

Eldridge, M. (2004). Naturalism. In A.T. Marsoobian & J. Ryder (Eds.), The Blackwell guide to American philosophy (pp. 52–72). Oxford, UK: Blackwell Publishing.Search in Google Scholar

Ernest, P. (1991). The philosophy of mathematical education. London, UK: Routledge Falmer.Search in Google Scholar

Ernest, P. (1998). Social constructivism as a philosophy of mathematics. Albany, NY: SUNY Press.Search in Google Scholar

Ewald, W.B. (1996). From Kant to Hilbert: A source book in the foundations of mathematics. New York, NY: Oxford University Press.Search in Google Scholar

Ferreirós, J. (2007a). Labyrinth of thought: A history of set theory and its role in modern mathematics (2nd rev. ed.). Berlin: Birkhäuser. (First published 1999)Search in Google Scholar

Ferreirós, J. (2007b). ʹΟ Θεὸς ʹΑριϑμετίζει: The rise of pure mathematics as arithmetic with Gauss. In C. Goldstein, N. Schappacher, & J. Schwermer (Eds.), The shaping of arithmetic after C.F. Gauss’s Disquisitiones Arithmeticae (pp. 234–268). Berlin: Springer.10.1007/978-3-540-34720-0_8Search in Google Scholar

Ferreirós, J. (2008). The crisis in the foundations of mathematics. In T. Gowers (Ed.), The Princeton companion to mathematics (pp. 142–156), Princeton, NJ: Princeton University Press.Search in Google Scholar

Frege, G. (1979). Posthumous writings (H. Hermes et al., Eds., P. Long & R. White, Trans.). Oxford, UK: Basil Blackwell.Search in Google Scholar

Frege, G. (1984). Collected papers on mathematics, logic, and philosophy (B. McGuinness, Ed.). Oxford, UK: Basil Blackwell.Search in Google Scholar

Frege, G. (1996). Diary: Written by Professor Dr Gottlob Frege in the time from 10 March to 9 May 1924 (G. Gabriel & W. Kienzler, Ed. and comm., R.L. Mendelsohn, Trans.). Inquiry: An Interdisciplinary Journal of Philosophy, 39, 303–342.Search in Google Scholar

Galilei, G. (1967). Dialogue concerning the two chief world systems (2nd rev. ed.). Berkeley, CA: University of California Press.10.1525/9780520342941Search in Google Scholar

Gersh, S.E. (1978). From Iamblichus to Eriugena: An investigation of the prehistory and evolution of the Pseudo-Dionysian tradition. Leiden: E.J. Brill.Search in Google Scholar

Gersh, S.E. (1996). Concord in discourse: Harmonics and semiotics in late classical and early medieval Platonism. Berlin: Mouton de Gruyter.10.1515/9783110819182Search in Google Scholar

Giaquinto, M. (2002). The search for certainty: A philosophical account of foundations of mathematics. New York, NY: Oxford University Press.Search in Google Scholar

Heidegger, M. (2002). Nietzsche’s word: “God is dead”. In M. Heidegger, Off the beaten track (J. Young & K. Haynes, Eds. and trans.) (pp. 157–199). Cambridge, UK: Cambridge University Press. (Original work written 1943 and published 1950)Search in Google Scholar

Hilbert, D. (1902). Mathematical problems (Lecture delivered before the International Congress of Mathematicians at Paris in 1900). Bulletin of the American Mathematical Society, 8, 437–479 (Original work published 1900)Search in Google Scholar

Hilbert, D. (1926). Über das Unendliche. Mathematische Annalen, 95, 161–190. English translation (van Heijenoort, 1967, pp. 367–392).10.1007/BF01206605Search in Google Scholar

Hilbert, D. (1992). Natur und mathematisches Erkennen: Vorlesungen, gehalten 19191920 in Göttingen (D.E. Rowe, Ed.). Basel: Birkhäuser.Search in Google Scholar

Huttinga, W. (2014). “Marie Antoinette” or mystical depth?: Herman Bavinck on theology as queen of the sciences. In J. Eglinton & G. Harinck (Eds.), Neo-Calvinism and the French revolution (pp. 143–154). London, UK: Bloomsbury T&T Clark.Search in Google Scholar

Kanigel, R. (1991). The man who knew infinity: A life of the genius Ramanujan. New York, NY: Charles Scribner’s Sons.Search in Google Scholar

Kant, I. (1998). Critique of pure reason (P. Guyer & A.W. Wood, Trans. and ed.). New York, NY: Cambridge University Press. (Original work published 1781/1787)10.1017/CBO9780511804649Search in Google Scholar

Kepler, J. (1997). The harmony of the world. Philadelphia, PA: American Philosophical Society. (Original work published 1619)Search in Google Scholar

Kline, M. (1980). Mathematics: the loss of certainty. New York, NY: Oxford University Press.Search in Google Scholar

Kovač, S. (2008). Gödel, Kant, and the path of a science. Inquiry, 51, 147–169.10.1080/00201740801956861Search in Google Scholar

Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery (J. Worrall & E. Zahar, Eds.). Cambridge, UK: Cambridge University Press.10.1017/CBO9781139171472Search in Google Scholar

Lakoff, G., & Núñez, R.E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York, NY: Basic Books.Search in Google Scholar

Leibniz, G.W. (1989). Philosophical essays (R. Ariew & D. Garber, Eds. and trans.). Indianapolis, IN: Hackett Publishing Company.Search in Google Scholar

Lorenz, K. (1941). Kants Lehre vom Apriorischen im Lichte gegenwärtiger Biologie. Blätter für Deutsche Philosophie, 15, 94–125. English translation (Lorenz, 2009).Search in Google Scholar

Lorenz, K. (2009). Kant’s doctrine of the a priori in the light of contemporary biology. In M. Ruse (Ed.), Philosophy after Darwin: Classic and contemporary readings (pp. 231–247). Princeton, NJ: Princeton University Press.Search in Google Scholar

Lossky, V. (2012). Théologie dogmatique. Paris: Cerf.Search in Google Scholar

Mancosu, P. (1998). From Brouwer to Hilbert: The debate on the foundations of mathematics in the 1920s. New York, NY: Oxford University Press.Search in Google Scholar

Map of the system of human knowledge. In D. Goodman et al. (Project directors) The Encyclopedia of Diderot & d’Alembert: Collaborative Translation Project. University of Michigan. Retrieved from http://quod.lib.umich.edu/d/did/tree.html (Original work published 1751)Search in Google Scholar

Martineau, H. (1896). The positive philosophy of Auguste Comte, freely translated and condensed, in three volumes. London: George Bell & Sons.Search in Google Scholar

Menzel, C. (2001). God and mathematical Objects. In R.W. Howell &W.J. Bradley (Eds.), Mathematics in a postmodern age: A Christian perspective (pp. 65–97). Grand Rapids, MI: Eerdmans.Search in Google Scholar

Mill, J.S. (1974). Collected works. Vol. VIII: A system of logic, ratiocinative and inductive. Books IVVI and appendices (J.M. Robson, Ed.). Toronto: University of Toronto Press. (Original work published 1843)Search in Google Scholar

Molière (18??). Don Juan. In The dramatic works of Molière, rendered into English by H. Van Laun, a new edition, complete in six volumes (Vol. 3, pp. 69–133). Philadelphia: George Barrie.Search in Google Scholar

Mortensen, C. (2013). Inconsistent mathematics. In E.N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. Retrieved from http://plato.stanford.edu/entries/mathematics-inconsistent/ (First published 1996, substantive revision 2013)Search in Google Scholar

O’Meara, D.J. (1989). Pythagoras revived: Mathematics and philosophy in late Antiquity. New York, NY: Oxford University Press.Search in Google Scholar

Pascal, B. (1654). Le Mémorial. In Les Pensées de Blaise Pascal. Retrieved from http://www.penseesdepascal.fr/Hors/Hors1-moderne.phpSearch in Google Scholar

Posy, C.J. (1998). Brouwer versus Hilbert: 1907–1928. Science in Context, 11, 291–325.10.1017/S0269889700003021Search in Google Scholar

Pyenson, L. (1982). Relativity in Late Wilhelmian Germany: The appeal to a preestablished harmony between mathematics and physics. Archive for History of Exact Sciences, 27, 137–155.10.1007/BF00348346Search in Google Scholar

Quine, W.V. (1981). Success and limits of mathematization. In W.V. Quine, Theories and things (pp. 148–155). Cambridge, MA: Belknap Press of Harvard University Press.Search in Google Scholar

Schaeffer, J.-M. (2007). La fin de l’exception humaine. Paris: Gallimard.Search in Google Scholar

Scott, C.A. (1900). The International Congress of Mathematicians in Paris. Bulletin of the American Mathematical Society, 7, 57–79.10.1090/S0002-9904-1900-00768-3Search in Google Scholar

Sepkoski, D. (2007). Nominalism and constructivism in seventeenth-century mathematical philosophy. New York, NY: Routledge.Search in Google Scholar

Seshu Aiyar, P.V. & Ramachandra Rao, R. (1927). Srinivasa Ramanujan (1887–1920). In S. Ramanujan, Collected papers (G.H. Hardy, P.V. Seshu Aiyar, & B.M. Wilson, Eds.) (pp. xi–xix). Cambridge, UK: Cambridge University Press.Search in Google Scholar

Shaposhnikov, V.A. (2009). Kategoriya chisla v konkretnoj metafizike Pavla Florenskogo [Number as a category in Pavel Florensky’s concrete metaphysics]. In A.N. Krichevets (Ed.), Chislo: Trudy Moskovskogo seminara po filosofii matematiki [Number: Moscow studies in the philosophy of mathematics] (pp. 341–367). Moscow: MAX Press. [In Russian]Search in Google Scholar

Shaposhnikov, V.A. (2014). The applicability problem and a naturalistic perspective on mathematics. In G. Mints & O. Prosorov (Eds.), Philosophy, mathematics, linguistics: Aspects of interaction. Proceedings of the international scientific conference: St. Petersburg, April 21–25, 2014 (pp. 185–197). Saint Petersburg: Euler International Mathematical Institute.Search in Google Scholar

Slaveva-Griffin, S. (2014). Number in the metaphysical landscape. In P. Remes & S. Slaveva-Griffin (Eds.), The Routledge handbook of Neoplatonism (pp. 200–215). New York, NY: Routledge.Search in Google Scholar

Sortorius von Waltershausen, W. (1856). Gauss zum Gedächtniss, Leipzig: S. Hirzel. Système figuré des connaissances humaines. (1751). In ARTFL Encyclopédie Project (R. Morrissey & G. Roe, Eds.). University of Chicago. Retrieved from http://encyclopedie.uchicago.edu/content/système-figuré-des-connaissances-humaines-0Search in Google Scholar

Tapp, C. (2011). Infinity in mathematics and theology. Theology and Science, 9, 91–100.10.1080/14746700.2011.547009Search in Google Scholar

van Heijenoort, J. (1967). From Frege to Gödel: A source book in mathematical logic, 18791931. Cambridge, MA: Harvard University Press.Search in Google Scholar

Vizgin, V.P. (1998). Einstein’s “cosmic religion” and Wigner’s “empirical law of epistemology”. In I.V. Filimonova & V.A. Petrov (Eds.), Fundamental problems of high energy physics and field theory: Proceedings of the XXI workshop on high energy physics and field theory, Protvino, June 2325, 1998 (pp. 90–96). Protvino: Institute for High Energy Physics. Retrieved from http://web.ihep.su/library/pubs/tconf98/ps/vizgin.pdfSearch in Google Scholar

Weber, H. (1893). Leopold Kronecker. Mathematische Annalen, 43, 1–25.10.1007/BF01446613Search in Google Scholar

Weber, Z. (2009). Inconsistent mathematics. In J. Fieser & B. Dowden (Eds.), The Internet Encyclopedia of Philosophy. Retrieved from http://www.iep.utm.edu/math-inc/Search in Google Scholar

Weyl, H. (1921). Über die neue Grundlagenkrise der Mathematik. Mathematische Zeitschrift, 10, 39–79. English translation (Mancosu, 1998, pp. 86–118).10.1007/BF02102305Search in Google Scholar

White, L.A. (1947). The locus of mathematical reality: An anthropological footnote. Philosophy of Science, 14, 289–303.10.1086/286957Search in Google Scholar

Wigner, E. (1960). The unreasonable effectiveness of mathematics in the natural sciences. Communications of Pure and Applied Mathematics, 13, 1–14.Search in Google Scholar

Wilder, R.L. (1981). Mathematics as a cultural system. New York, NY: Pergamon Press.Search in Google Scholar

Wilholt, T. (2006). Lost on the way from Frege to Carnap: How the philosophy of science forgot the applicability problem. Grazer Philosophische Studien, 73, 69–82.10.1163/18756735-073001004Search in Google Scholar

Zakai, A. (2007). The rise of modern science and the decline of theology as the “queen of sciences” in the early modern era. Reformation & Renaissance Review, 9, 125–151. Reprinted in (Zakai, 2010, pp. 51–85).10.1558/rrr.v9i2.125Search in Google Scholar

Zakai, A. (2010). Jonathan Edwards’s philosophy of nature: The re-enchantment of the world in the age of scientific reasoning. London, UK: Continuum T&T Clark.Search in Google Scholar

eISSN:
2199-6059
ISSN:
0860-150X
Język:
Angielski
Częstotliwość wydawania:
4 razy w roku
Dziedziny czasopisma:
Philosophy, other