Skip to main content
×
×
Home

A FORMALIZATION OF KANT’S TRANSCENDENTAL LOGIC

  • T. ACHOURIOTI (a1) and M. VAN LAMBALGEN (a1)
Abstract

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.

Copyright
Corresponding author
*INSTITUTE FOR LOGIC, LANGUAGE AND COMPUTATION/DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF AMSTERDAM, OUDE TURFMARKT 141, 1012GC, AMSTERDAM. E-mail:m.vanlambalgen@uva.nl
References
Hide All
Avigad, J., Dean, E., & Mumma, J. (2009). A formal system for euclid’s Elements. Review of Symbolic Logic, 2(4), 700768.
Bartlett, F. C. (1968). Thinking: An Experimental and Social Study. London: Allen and Unwin.
Boricic, B. R. (1985). On sequence-conclusion natural deduction systems. Journal of Philosophical Logic, 14, 359377.
Bruner, J. S. (1973). Beyond the Information Given. New York, NY: W. W. Norton.
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.
Coquand, T.A completeness proof for geometric logic. Technical report, Computer Science and Engineering Department, University of Gothenburg. Available from: http://www.cse.chalmers.se/coquand/formal.html. Retrieved September 29, 2010.
Friedman, M. (1992). Kant and the Exact Sciences. Cambridge, MA: Harvard University Press.
Goldblatt, R. (2006). Topoi. The Categorial Analysis of Logic. Mineola, NY: Dover.
Hodges, W. (1993). Model Theory. Cambridge, MA: Cambridge University Press.
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.
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.
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.
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.
Kitcher, P. W. (1990). Kant’s Transcendental Psychology. New York: Oxford University Press.
Longuenesse, B. (1998). Kant and the Capacity to Judge. Princeton, NJ: Princeton University Press.
MacFarlane, J. (2000). What does it mean to say that logic is formal? PhD Thesis, University of Pittsburgh.
Palmgren, E. (2002). An intuitionistic axiomatisation of real closed fields. Mathematical Logic Quarterly, 48(2), 297299.
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.
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.
Rosenkoetter, T. (2009). Truth criteria and the very project of a transcendental logic. Archiv fuer Geschichte der Philosophie, 61(2), 193236.
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.
Strawson, P. F. (1966). The Bounds of Sense: An Essay on Kant’s “Critique of Pure Reason”. London: Methuen.
Stuhlmann-Laeisz, R. (1976). Kants Logik. Berlin: De Gruyter.
Thompson, M. (1953). On Aristotle’s square of opposition. The Philosophical Review, 62(2), 251265.
Treisman, A. M., & Gelade, G. (1980). A feature-integration theory of attention. Clarendon Press, 12, 97136.
van Lambalgen, M., & Hamm, F. (2004). The Proper Treatment of Events. Oxford: Blackwell.
Watkins, E. (2004). Kant and the Metaphysics of Causality. Cambridge: Cambridge University Press.
Wolff, M. (1995). Die Vollstaendigkeit der kantischen Urteilstafel. Frankfurt am Main: Vittorio Klostermann.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 166 *
Loading metrics...

Abstract views

Total abstract views: 731 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 16th July 2018. This data will be updated every 24 hours.