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Kant's Theory of Arithmetic

Year 2019, Volume: 9 Issue: 1, 39 - 58, 28.03.2019
https://doi.org/10.18491/beytulhikme.1439

Abstract

Kant's arithmetic theory is very important both in general mathematical philosophy and in the understanding of critical philosophy. This is because Kant's view of arithmetic theory is a reflection of critical philosophy as a whole. However, in the majority of works on Kant's mathematical philosophy, the relation between geometry and a priori form space is discussed in detail, arithmetic and its relationship with time are relatively neglected. Whereas, to handle Kant's claims about the nature of arithmetic proposals independently within their own dynamics seems necessary and more reasonable. In this direction, we will try to examine Kant's arithmetic theory throughout our work. 

References

  • Bostock, D. (2009). Philosophy of Mathematics An Introduction. Sussex: Wiley-Blackwell Press. Brittan, G. G. (1978). Kant’s Theory of Science. New Jersey: Princeton University Press. Broad, C. D. (1942). Kant’s Theory of Mathematical and Philosophical Reasoning. Proceedings of the Aristotelian Society, Vol. 42, 1-24. Engelhard, K. & Peter, M. (2008). Kant’s Theory of Arithmetic: A Constructive Approach. Journal for General Philosophy of Science, 39 (2), 245-271. Friedman, M. (1992). Kant’s Theory of Geometry. Kant’s Philosophy of Mathematics Modern Essays. (Ed. by Carl J., Posy). London: Kluwer Academic Publishers, 177-220. Hanna, R. (2002). Mathematics for Humans: Kant’s Philosophy of Arithmetics Revisited. European Journal of Philosophy, Vol. 10, 328-352. Kant, I. (1894). Dissertation on The Form and Principles of The Sensible and The Intelligible World. Kant’s Inaugural Dissertation of 1770. (Trn. by William J. E.). New York: Columbia College. Kant, I. (1999). Correspondence. (Trn. and Ed. by Arnulf Zweig). Cambridge: Cambridge University Press. Kant, I. (2009). Critique of Pure Reason. (Trn. Paul Guyer and Allen Wood). Cambridge: Cambridge University Press. Kant, I. (1970). Philosophical Correspondence 1759-99. (Ed. by Arnulf Zweig). Chicago: The University of Chicago Press. Kant, I. (2004). Prolegomena to Any Future Metaphysics. (Trn. and Ed. by G. Hatfield). Cambridge: Cambridge University Press. Kneebone, G. T. (1963). Mathematical Logic and the Foundation of Mathematics An Introductory Survey. London: D. Van Nostrand Company. Leibniz, G. W. & Clarke, S. (2000). Correspondence. (Ed. by Roger Ariew). Cambridge: Hacket Publishing Company. Leibniz, G. W. (1996). New Essays on Human Understanding. (Ed. by P. Remnant, J. Bennett). Cambridge: Cambridge University Press. Martin, G. (1955). Kant’s Metaphysics and Theory of Science. (Trn. by P. Lucas). Manchester: Manchester University Press. Parsons, C. (1969). Kant’s Philosophy of Arithmetic. Philosophy, Science and Method. (Ed. by S. Morgenbesser, P. Suppes, M. White). New York: St Martin’s Press. Posy, C. J. (1992). Introduction: Mathematics in Kant’s Critique of Pure Reason. Kant’s Philosophy of Mathematics Modern Essays. (Ed. by Carl J. Posy). London: Kluwer Academic Publishers. Prichard, H. A. (1906). Kant’s Theory of Knowledge. Oxford: Clarendon Press. Risjord, M. (1990). The Sensible Foundation for Mathematics: A Defense of Kant’s View. Studies in History and Philosophy of Science, 21 (1), 123-143. Shabel, L. (2006). Kant’s Philosophy of Mathematics. The Cambridge Companion to Kant and Modern Philosophy. (Ed. by Paul Guyer). Cambridge: Cambridge University Press, 94-128. Shabel, L. (2003). Mathematics in Kant’s Critical Philosophy Reflections on Mathematical Practice. London: Routledge. Smith, N. K. (1918). A Commentary to Kant’s Critique of Pure Reason. London: Macmillan. Sutherland, D. (2006). Kant on Arithmetic, Algebra, and Proportions. Journal of the History of Philosophy, Vol. 44, 533-558. Weber, A. (1993). Felsefe Tarihi. (Çev. H. Vehbi Eralp). İstanbul: Sosyal Yayınları. Yaldır, H. & Güner, N. (2012). Immanuel Kant’s Philosophy of Mathematics in Terms of His Theory of Space and Time. Kaygı, Vol. 18, 45-70.
Year 2019, Volume: 9 Issue: 1, 39 - 58, 28.03.2019
https://doi.org/10.18491/beytulhikme.1439

Abstract

References

  • Bostock, D. (2009). Philosophy of Mathematics An Introduction. Sussex: Wiley-Blackwell Press. Brittan, G. G. (1978). Kant’s Theory of Science. New Jersey: Princeton University Press. Broad, C. D. (1942). Kant’s Theory of Mathematical and Philosophical Reasoning. Proceedings of the Aristotelian Society, Vol. 42, 1-24. Engelhard, K. & Peter, M. (2008). Kant’s Theory of Arithmetic: A Constructive Approach. Journal for General Philosophy of Science, 39 (2), 245-271. Friedman, M. (1992). Kant’s Theory of Geometry. Kant’s Philosophy of Mathematics Modern Essays. (Ed. by Carl J., Posy). London: Kluwer Academic Publishers, 177-220. Hanna, R. (2002). Mathematics for Humans: Kant’s Philosophy of Arithmetics Revisited. European Journal of Philosophy, Vol. 10, 328-352. Kant, I. (1894). Dissertation on The Form and Principles of The Sensible and The Intelligible World. Kant’s Inaugural Dissertation of 1770. (Trn. by William J. E.). New York: Columbia College. Kant, I. (1999). Correspondence. (Trn. and Ed. by Arnulf Zweig). Cambridge: Cambridge University Press. Kant, I. (2009). Critique of Pure Reason. (Trn. Paul Guyer and Allen Wood). Cambridge: Cambridge University Press. Kant, I. (1970). Philosophical Correspondence 1759-99. (Ed. by Arnulf Zweig). Chicago: The University of Chicago Press. Kant, I. (2004). Prolegomena to Any Future Metaphysics. (Trn. and Ed. by G. Hatfield). Cambridge: Cambridge University Press. Kneebone, G. T. (1963). Mathematical Logic and the Foundation of Mathematics An Introductory Survey. London: D. Van Nostrand Company. Leibniz, G. W. & Clarke, S. (2000). Correspondence. (Ed. by Roger Ariew). Cambridge: Hacket Publishing Company. Leibniz, G. W. (1996). New Essays on Human Understanding. (Ed. by P. Remnant, J. Bennett). Cambridge: Cambridge University Press. Martin, G. (1955). Kant’s Metaphysics and Theory of Science. (Trn. by P. Lucas). Manchester: Manchester University Press. Parsons, C. (1969). Kant’s Philosophy of Arithmetic. Philosophy, Science and Method. (Ed. by S. Morgenbesser, P. Suppes, M. White). New York: St Martin’s Press. Posy, C. J. (1992). Introduction: Mathematics in Kant’s Critique of Pure Reason. Kant’s Philosophy of Mathematics Modern Essays. (Ed. by Carl J. Posy). London: Kluwer Academic Publishers. Prichard, H. A. (1906). Kant’s Theory of Knowledge. Oxford: Clarendon Press. Risjord, M. (1990). The Sensible Foundation for Mathematics: A Defense of Kant’s View. Studies in History and Philosophy of Science, 21 (1), 123-143. Shabel, L. (2006). Kant’s Philosophy of Mathematics. The Cambridge Companion to Kant and Modern Philosophy. (Ed. by Paul Guyer). Cambridge: Cambridge University Press, 94-128. Shabel, L. (2003). Mathematics in Kant’s Critical Philosophy Reflections on Mathematical Practice. London: Routledge. Smith, N. K. (1918). A Commentary to Kant’s Critique of Pure Reason. London: Macmillan. Sutherland, D. (2006). Kant on Arithmetic, Algebra, and Proportions. Journal of the History of Philosophy, Vol. 44, 533-558. Weber, A. (1993). Felsefe Tarihi. (Çev. H. Vehbi Eralp). İstanbul: Sosyal Yayınları. Yaldır, H. & Güner, N. (2012). Immanuel Kant’s Philosophy of Mathematics in Terms of His Theory of Space and Time. Kaygı, Vol. 18, 45-70.
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Details

Primary Language English
Subjects Philosophy
Journal Section Articles
Authors

Aykut Küçürparmak This is me 0000-0002-5565-9377

Publication Date March 28, 2019
Published in Issue Year 2019 Volume: 9 Issue: 1

Cite

APA Küçürparmak, A. (2019). Kant’s Theory of Arithmetic. Beytulhikme An International Journal of Philosophy, 9(1), 39-58. https://doi.org/10.18491/beytulhikme.1439