Kant's Logic

Srećko Kovač

Institute of Philosophy
Zagreb, Croatia



The tutorial will give an introduction into the main features of Kant's formal and transcendental logic, their modern formalization, and their impact on the development of logic.

Logic had been, according to Kant, on a "sure path of a science" since antiquity, but had not reached its pure scientific (systematic) form, being often rhapsodical, and non-systematically mixed with other kinds of knowledge. Kant's program is to give logic a systematic form, founded on the first principles of our knowledge, and that in two steps: (1) reduction of basic logic to formal logic by means of a functional account of logical forms; (2) establishing of a logic of knowledge ("transcendental logic") on the basis of formal logic and analytic of space and time, with independent verification of logical forms and concepts on a fixed (empirically defined) model.

According to Kant's functional account, logical forms should be conceived in the sense of "bringing different representations under a common one" by means of abstract acts (operations) of our faculty of understanding (formal apperception, consciousness). For example, it will be shown how for Kant categorical, hypothetical and disjunctive judgments (as well as their modal counterparts: problematic, assertoric and apodictic judgments) gradually strengthen the conditions of bringing our representations under the formal objective unity of apperception, and in this way gradually implement logical laws. The foundational approach to Kant's logic as based on the theory of formal unity of apperception was developed in a seminal work by K. Reich (1948).

By means of modern formalization, it will be shown that Kant's formal logic has features of paraconsistent and paracomplete logic (see Kovac 2008, together with an axiomatization of the propositional part in Nasieniewski, 2011). A formalization of Kant's logical forms and formal unity of apperception with the use of geometric logic and geometric implication is elaborated by Achourioti and van Lambalgen (2011).

Kant's transcendental logic is a sort of philosophical logic to which, according to Kant's view, formal ontology should be reduced. It will be shown that Kant's transcendental logic includes elements of model theory and type theory, by means of which he solves, for instance, cosmological antinomies. In this part, we will build especially on the ideas by M. Tiles (2004).

Session 1. Kant's formal logic. Functional account of logical forms. Concept, judgment, inference. Relation of judgment (condition of objectivity – assertion): subject – predicate, antecedent – consequent, whole – members. Laws of non-contradiction, sufficient reason, and excluded middle. Modalities. Foundations of logic: formal unity of apperception (analytic, synthetic).

Session 2. Formalization of Kant's predicate logic by means of modal logic and generalized quantifiers (formal system and semantics). Paraconsistency and paracompleteness in Kant's logic.

Session 3. Transcendental logic. A priori – a posteriori, analytic – synthetic. Categories and transcendental ideas, transcendental and empirical reality, antinomies. Formal system and empirical model, type-theoretical distinctions in Kant's transcendental logic. Influences on the posterior history of logic (e.g., Frege, Hilbert, Brouwer, Gödel).

The tutorial is self-contained, not presupposing anything beyond the elementary knowledge of classical and modal logic.




Kant, Immanuel. 1910-. Kant's gesammelte Schriften. Berlin and Leipzig: de Gruyter, etc. Volumes 3 and 4 (Kritik der reinen Vernunft, Prolegomena), 9 (Jäsche-Logik), 16 (Logik), 24 (Vorlesungen über Logik).

Kant, Immanuel, 1998. Logik-Vorlesung. Unveröffentlichte Nachschriften. 1-2. Hamburg: Meiner.

Kant, Immanuel. 1965. Critique of Pure Reason. New York: St Martin's Press, Toronto: Macmillan. Transl. by Norman Kemp Smith.

Kant, Immanuel. 1992. Lectures on Logic. Cambridge (Ma.): Cambridge University Press. Transl. by J. Michael Young.

Kant, Immanuel. 2001. Prolegomena to any Future Metaphysics. 2nd ed. Indianapolis: Hackett. Transl. by James W. Ellington.

Achourioti, T. and van Lambalgen, M. 2011. "A formalization of Kant's transcendental logic". The Review of Symbolic Logic, 4: 254-289.

Brandt, Reinhard. 1991. Die Urteiltafel. Kritik der reinen Vernunft A 67-76; B 92-101. Hamburg: Meiner. - English: The Table of Judgments. Critique of Pure Reason A 67-76; B 92-101, transl. by E. Watkins, Atascadero (Ca.): Ridgeview, 1995.

Béziau, Jean-Yves. 2012. "What is 'formal logic'?", in Proceedings of the XXII Congress of Philosophy, Myung-Hyung-Lee (ed.), Seoul: Korean Philosophical Association, vol. 13, pp. 9-22.

Capozzi, Mirella and Roncaglia, Gino. 2009. "Logic and philosophy of logic from humanism to Kant", in Leila Haaparanta (ed.), The Development of Modern Logic. New York: Oxford University Press, pp. 78-158.

Friedman, Michael. 1992. Kant and the Exact Sciences. Cambridge (Ma.), London: Harvard University Press.

Kovac, Srecko. 2008. “In what sense is Kantian principle of contradiction non-classical”, Logic and Logical Philosophy. 17: 251–274.

Kovac, Srecko. 2014. “Forms of judgment as a link between mind and the concepts of substance and cause (Kant, Gödel)”, in Substantiality and Causality. M. Szatkowski and M. Rosiak (eds.). Berlin: de Gruyter, in print.

Longuenesse, Beatrice. 1998. Kant and the Capacity to Judge: Sensibility and Discursivity in the Transcendental Analytic of the Critique of Pure Reason. Princeton: Princeton University Press. Transl. by Charles T. Wolfe.

Loparic, ˇeljko. 1990. “The logical structure of the first antinomy”. Kant-Studien. 81: 280-303. MacFarlane, John. 2002. “Frege, Kant, and the logic in logicism”. The Philosophical Review. 111: 25–65.

Mosser, Kurt, 2008. Necessity and Possibility: The Logical Strategy of Kant's Critique of Pure Reason. Washington, DC: Catholic University of America Press.

Nasieniewski, Marek, Logiki zdaniowe wyrazalne przez modalnosc. Torun: Wyd. Naukowe UMK, 2011.

Reich, Klaus. 1948. Die Vollständigkeit der kantischen Urteilstafel. 2nd ed. Berlin: Schoetz. - English: The Completeness of Kant's Table of Judgments, transl. by J. Kneller and M. Losonsky, Stanford: Standford University Press, 1992.

Scholz, Heinrich. 1959. Abriß der Geschichte der Logik. Freiburg, München: Alber. - English: Concise History of Logic, transl. by K. F. Leidecker, New York: Philosophical Library, 1961.

Tiles, Mary. 2004. "Kant: From General to Transcendental Logic", in Handbook of the History of Logic, vol. 3, Dov M. Gabbay and John Woods (eds.), Amsterdam, etc: Elsevier, pp. 85-130.

Tolley, Christian. 2012. “The Generality of Kant's Transcendental Logic”. Journal of the History of Philosophy. 50: 417-446.

Wolff, Michael. 1995. Die Vollständigkeit der kantischen Urteilstafel. Frankfurt a. M.: Klostermann.