Hostname: page-component-cb9f654ff-qc88w Total loading time: 0 Render date: 2025-08-23T12:57:43.639Z Has data issue: false hasContentIssue false
  • English
  • Français

Arbitrary combination and the use of signs in mathematics: Kant’s 1763 Prize Essay and its Wolffian background

Published online by Cambridge University Press:  01 January 2020

Katherine Dunlop
Katherine Dunlop*
Affiliation:
Department of Philosophy, University of Texas at Austin, Austin, TX, USA
*
*Email: kdunlop@utexas.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

In his 1763 Prize Essay, Kant is thought to endorse a version of formalism on which mathematical concepts need not apply to extramental objects. Against this reading, I argue that the Prize Essay has sufficient resources to explain how the objective reference of mathematical concepts is secured. This account of mathematical concepts’ objective reference employs material from Wolffian philosophy. On my reading, Kant’s 1763 view still falls short of his Critical view in that it does not explain the universal, unconditional applicability of mathematical concepts.

Keywords

Kant’s philosophy of mathematicsKant’s pre-Critical philosophyChristian Freiherr von Wolffformalism in mathematics

Information

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 44 , Issue 5-6: Special Issue: Mathematics in Kant’s Critical Philosophy , December 2014 , pp. 658 - 685
Copyright
Copyright © Canadian Journal of Philosophy 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Anderson, R. Lanier. 2005. “The Wolffian Paradigm and its Discontents.” Archiv für Geschichte der Philosophie 87: 22–74.Google Scholar
Arndt, H. W. 1965. “Christian Wolffs Stellung zur ‘Ars Characteristica Combinatoria’.” Studi e ricerche di storia della filosofia (Torina) 71: 1–12.Google Scholar
Basso, Paola. 2011. “Le mythe de la démonstrabilité résiste-t-il encore?” Astérion 9 (n.p.)Google Scholar
Boyer, Carl. 1956. History of Analytic Geometry. Reprint New York: Dover, 2004.Google Scholar
Capozzi, Mirella. 1981. “Kant on Mathematical Definition.” In Italian Studies in the Philosophy of Science. Boston Studies in the Philosophy and History of Science, edited by Chiara, M. L. Dalla. Vol. 47, 423–452. Dordrecht: Reidel.CrossRefGoogle Scholar
Capozzi, Mirella. 2011. “Philosophy and Writing.” Quaestio 11: 307–350.CrossRefGoogle Scholar
Carson, Emily. 1999. “Kant on the Method of Mathematics.” Journal of the History of Philosophy 37: 629–652.CrossRefGoogle Scholar
Corr, Charles. 1972. “Christian Wolff’s Treatment of Scientific Discovery.” Journal of the History of Philosophy 10: 323–334.CrossRefGoogle Scholar
Desmaizeaux, Pierre, ed. 1720. Recueil de diverse pieces … par Mrs. Leibniz, Clarke, Newton, et autres Auteurs célèbres. Amsterdam: Duillard et Changuion.Google Scholar
Detlefsen, Michael. 2005. “Formalism.” In The Oxford Handbook of Philosophy of Mathematics and Logic, edited by Shapiro, S., 236–317. Oxford: Oxford University Press.CrossRefGoogle Scholar
Dunlop, Katherine. 2012. “Kant and Strawson on the Content of Geometrical Concepts.” Nous 46: 86–126.CrossRefGoogle Scholar
Dunlop, Katherine, “Definitions and Empirical Justification in Christian Wolff’s Theory of Science.” Unpublished Manuscript.Google Scholar
Engfer, H.-J. 1982. Philosophie als Analyse. Studien zur Entwicklung philosophische Analysiskonzeption. Stuttgart: Frommann-Holzboog.Google Scholar
Engfer, H.-J. 1983. “Zur Methodendiskussion bei Wolff und Kant.” In Schneiders, 1983, 48–65.Google Scholar
Guyer, Paul. 1991. “Mendelssohn and Kant.” Philosophical Topics 19: 119–152. Cited as reprinted in Kant on Freedom, Law, and Happiness. Cambridge: Cambridge University Press, 2000.CrossRefGoogle Scholar
Hintikka, Jaakko. 1965. “Kant’s ‘New Method’ of Thought and his Theory of Mathematics.” Ajatus 27: 37–47.Google Scholar
Hintikka, Jaakko. 1967. “Kant on the Mathematical Method.” The Monist 51: 351–372.CrossRefGoogle Scholar
Hintikka, Jaakko. 1974. Knowledge and the Known. Dordrecht and Boston: D. Reidel Pub. Co.CrossRefGoogle Scholar
Körner, Stefan. 1968. The Philosophy of Mathematics. Reprint New York: Dover, 1986.Google Scholar
Leibniz, G. W. 1969. Philosophical Papers and Letters. Translated and edited by L. Loemker.Dordrecht: Reidel.Google Scholar
Leibniz, G. W. 1989. Philosophical Essays. Translated and edited by R. Ariew and D. Garber.Indianapolis: Hackett.Google Scholar
Loemker, Leroy. 1966. “Leibniz’s Conception of Philosophical Method.” First published in Zeitschrift für Philosophische Forschung, Bd. 20 Heft 3-4. Cited as reprinted in Ivor LeClerc, ed., The Philosophy of Leibniz and the Modern World. Nashville: Vanderbilt University Press, 1973.Google Scholar
McRae, Robert. 1995. “The Theory of Knowledge.” In The Cambridge Companion to Leibniz, edited by Jolley, Nicholas, 176–198. Cambridge: Cambridge University Press.Google Scholar
Mittelstrass, Jürgen. 1979. “The Philosopher’s Conception of Mathesis Universalis from Descartes to Leibniz.” Annals of Science 36: 593–610.CrossRefGoogle Scholar
Onof, Christian, and Dennis Schulting (transls.), . 2014. “On Kästner’s Treatises.” Kantian Review 19: 305–313.Google Scholar
Parsons, Charles. 1969. Kant’s Philosophy of Arithmetic. Cited as reprinted in Mathematics in Philosophy. Ithaca, NY: Cornell University Press, 1983.Google Scholar
Parsons, Charles. 2009. Mathematical Thought and its Objects. Cambridge: Cambridge University Press.Google Scholar
Pimpinella, Pietro. 2001. “Cognitio intuitiva bei Wolff und Baumgarten.” In Vernunftkritik und Aufklärung, edited by Oberhausen, M., et al., 265–294. Stuttgart: Frommann-Holzboog.Google Scholar
Pombo, Olga. 1987. Leibniz and the Problem of a Universal Language. Materialien zur Geschichte der Sprachwissenschaft und der Semiotikvol. 3. Münster: Nodus Publikationen.Google Scholar
Rechter, Ofra. 2006. “The View from 1763.” In Intuition and the Axiomatic Method, edited by Carson, E. and Huber, R.. The Netherlands: Springer.Google Scholar
Schwaiger, Clement. 2001. “Symbolische und intuitive Erkenntnis bei Leibniz, Wolff, und Baumgarten.” In Nihil sine ratione. Mensch, Natur und Technik im Wirken von G.W. Leibniz (VII. Internationaler Leibniz-Kongress), edited by Poser, H.. Hanover: Gottfried-Wilhelm-Leibniz-Gesellschaft.Google Scholar
Sepper, Dennis. 2012. “Spinoza, Leibniz, and the Rationalist Reconceptions of Imagination.” In A Companion to Rationalism, edited by Nelon, Alan. Chichester: Wiley-Blackwell.Google Scholar
Shabel, Lisa. 1998. “Kant on the ‘Symbolic Construction’ of Mathematical Concepts.” Studies in History and Philosophy of Science 29: 589–621.CrossRefGoogle Scholar
Shabel, Lisa. 2003. Mathematics in Kant’s Critical Philosophy. New York: Routledge.Google Scholar
Shabel, Lisa. 2006. “Kant’s Philosophy of Mathematics.” In The Cambridge Companion to Kant and Modern Philosophy, edited by Guyer, P., 94–128. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Sutherland, Daniel. 2004. “Kant’s Philosophy of Mathematics and the Greek Mathematical Tradition.” Philosophical Review 113: 157–201.CrossRefGoogle Scholar
Sutherland, Daniel. 2006. “Kant on Arithmetic, Algebra, and the Theory of Proportions.” Journal of the History of Philosophy 44: 533–558.CrossRefGoogle Scholar
Sutherland, Daniel. 2010. “Philosophy, Geometry, and Logic in Leibniz, Wolff, and the Early Kant.” In Discourse on a New Method, edited by Dickson, M. and Domski, M., 155–192. Chicago and LaSalle: Open Court.Google Scholar
Tonelli, Giorgio. 1959. “Der Streit über die mathematische Methode in der Philosophie in der ersten Hälfte des 18.Jahrhunderts.” Archiv für Philosophie 9: 37–66.Google Scholar
Ungeheuer, Gerold. 1983. “Sprache und symbolische Erkenntnis bei Wolff.” In Christian Wolff (1679–1754), edited by W. Schneiders, 9–112. Hamburg: Meiner Verlag.Google Scholar
Weir, Alan. 2011. “Formalism in the Philosophy of Mathematics.” In The Stanford Encyclopedia of Philosophy (Fall 2011 edition), edited by Zalta, E..Google Scholar
Wolff, Christian. (1716) 1965. Mathematisches Lexicon. edited by Hoffmann, J. E.. Hildesheim: Georg Olms.Google Scholar
Wolff, Christian. (1737) 1981. Herrn Christian Wolffs Gesammelte kleine philosophische Schrifften, Dritter Theil. Hildesheim: Georg Olms.Google Scholar
Wolff, Christian. (1738) 1968. Psychologia Empirica, edited by Jean, École. Hildesheim: Georg Olms.Google Scholar
Wolff, Christian. (1740) 1983. Philosophia Rationalis sive Logica, edited by Jean, École. Hildesheim: Georg Olms.Google Scholar
Wolff, Christian. (1742) 1968. Elementa Matheseos Universae. Hildesheim: Georg Olms.Google Scholar
Wolff, Christian. (1750) 1999. Anfangsgründe aller mathematischen Wissenschaften, Erster Theil. Hildesheim: Georg Olms.Google Scholar
Wolff, Christian. (1751) 1983. In Vernünftige Gedanken von Gott, der Welt und der Seele des Menschens, auch allen Dingen überhaupt, edited by Corr, C. A.. Hildesheim: Georg Olms.Google Scholar
Wolff, Christian. (1754) 1965. Vernünftige Gedanken von den Kräften des menschlichen Verstandes, edited by Arndt, H. W.. Hildesheim: Georg Olms.Google Scholar
Wolff, Christian. 1963. Preliminary Discourse Concerning Philosophy in General, edited by Blackwell, R. J.. Indianapolis: Bobbs-Merrill.Google Scholar
Zac, Sylvain. 1974. “Le prix et la mention.” Revue de métaphysique et de morale 79: 473–498.Google Scholar