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Published online by Cambridge University Press:  24 February 2011

ILLC/Department of Philosophy, University of Amsterdam
ILLC/Department of Philosophy, University of Amsterdam


Although Kant (1998) envisaged a prominent role for logic in the argumentative structure of his Critique of Pure Reason, logicians and philosophers have generally judged Kant’s logic negatively. What Kant called ‘general’ or ‘formal’ logic has been dismissed as a fairly arbitrary subsystem of first-order logic, and what he called ‘transcendental logic’ is considered to be not a logic at all: no syntax, no semantics, no definition of validity. Against this, we argue that Kant’s ‘transcendental logic’ is a logic in the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first-order logic. The main technical application of the formalism developed here is a formal proof that Kant’s Table of Judgements in Section 9 of the Critique of Pure Reason, is indeed, as Kant claimed, complete for the kind of semantics he had in mind. This result implies that Kant’s ‘general’ logic is after all a distinguished subsystem of first-order logic, namely what is known as geometric logic.

Research Article
Copyright © Association for Symbolic Logic 2011

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Avigad, J., Dean, E., & Mumma, J. (2009). A formal system for euclid’s Elements. Review of Symbolic Logic, 2(4), 700768.Google Scholar
Bartlett, F. C. (1968). Thinking: An Experimental and Social Study. London: Allen and Unwin.Google Scholar
Boricic, B. R. (1985). On sequence-conclusion natural deduction systems. Journal of Philosophical Logic, 14, 359377.CrossRefGoogle Scholar
Bruner, J. S. (1973). Beyond the Information Given. New York, NY: W. W. Norton.Google Scholar
Chang, C. C., & Keisler, H. J. (1990). Model Theory, Studies in Logic and the Foundations of Mathematics, Vol. 73 (third edition). Amsterdam, The Netherlands: North-Holland, First edition: 1973, second edition: 1977.Google Scholar
Coquand, T.A completeness proof for geometric logic. Technical report, Computer Science and Engineering Department, University of Gothenburg. Available from: Retrieved September 29, 2010.Google Scholar
Friedman, M. (1992). Kant and the Exact Sciences. Cambridge, MA: Harvard University Press.Google Scholar
Goldblatt, R. (2006). Topoi. The Categorial Analysis of Logic. Mineola, NY: Dover.Google Scholar
Hodges, W. (1993). Model Theory. Cambridge, MA: Cambridge University Press.CrossRefGoogle Scholar
Hyland, M., & de Paiva, V. (1993). Full intuitionistic linear logic (extended abstract). Annals of Pure and Applied Logic, 64, 273291. doi:10.1016/0168-0072(93)90146-5.Google Scholar
Kant, I. (1992). Lectures on Logic; Translated from the German by J. Michael Young. The Cambridge edition of the works of Immanuel Kant. Cambridge, MA: Cambridge University Press.Google Scholar
Kant, I. (1998). Critique of Pure Reason; Translated from the German by Paul Guyer and Allen W. Wood. (The Cambridge edition of the works of Immanuel Kant). Cambridge, MA: Cambridge University Press.Google Scholar
Kant, I. (2002). Theoretical philosophy after 1781; Edited by Henry Allison and Peter Heath. The Cambridge edition of the works of Immanuel Kant. Cambridge, MA: Cambridge University Press.Google Scholar
Kitcher, P. W. (1990). Kant’s Transcendental Psychology. New York: Oxford University Press.CrossRefGoogle Scholar
Longuenesse, B. (1998). Kant and the Capacity to Judge. Princeton, NJ: Princeton University Press.Google Scholar
MacFarlane, J. (2000). What does it mean to say that logic is formal? PhD Thesis, University of Pittsburgh.Google Scholar
Palmgren, E. (2002). An intuitionistic axiomatisation of real closed fields. Mathematical Logic Quarterly, 48(2), 297299.3.0.CO;2-G>CrossRefGoogle Scholar
Posy, C. J. (2003). Between Leibniz and Mill: Kant’s logic and the rhetoric of psychologism. In Jacquette, D., editor. Philosophy, Psychology and Psychologism, Dordrecht: Kluwer, pp. 5179.Google Scholar
Reich, K. (1932). Die Vollstaendigkeit der kantischen Urteilstafel. Berlin: Schoetz. Translated as The completeness of Kant’s Table of Judgements transl. by Kneller, J., and Losonsky, M. (1992). Stanford University Press.Google Scholar
Rosenkoetter, T. (2009). Truth criteria and the very project of a transcendental logic. Archiv fuer Geschichte der Philosophie, 61(2), 193236.Google Scholar
Steinhorn, C. I. (1985). Borel structures and measure and category logics. In Barwise, J., and Feferman, S., editors. Model-theoretic Logics, chapter 16. New York, NY: Springer-Verlag, pp. 579596.Google Scholar
Strawson, P. F. (1966). The Bounds of Sense: An Essay on Kant’s “Critique of Pure Reason”. London: Methuen.Google Scholar
Stuhlmann-Laeisz, R. (1976). Kants Logik. Berlin: De Gruyter.CrossRefGoogle Scholar
Thompson, M. (1953). On Aristotle’s square of opposition. The Philosophical Review, 62(2), 251265.Google Scholar
Treisman, A. M., & Gelade, G. (1980). A feature-integration theory of attention. Clarendon Press, 12, 97136.Google ScholarPubMed
van Lambalgen, M., & Hamm, F. (2004). The Proper Treatment of Events. Oxford: Blackwell.Google Scholar
Watkins, E. (2004). Kant and the Metaphysics of Causality. Cambridge: Cambridge University Press.Google Scholar
Wolff, M. (1995). Die Vollstaendigkeit der kantischen Urteilstafel. Frankfurt am Main: Vittorio Klostermann.CrossRefGoogle Scholar