In what sense is Kantian principle of contradiction non-classical?

Srećko Kovač

doi:10.12775/LLP.2008.013

Authors

Srećko Kovač Institute of Philosophy, Zagreb

DOI:

https://doi.org/10.12775/LLP.2008.013

Keywords

Kant, paracompleteness, paraconsistency, principle of contradiction, square of oppositions, subject abstraction, labelled tableau

Abstract

On the ground of Kant’s reformulation of the principle of contradiction, a non-classical logic KC and its extension KC+ are constructed. In KC and KC+, ¬(φ ∧ ¬φ),φ → (¬φ → ψ), and φ ∨ ¬φ are not valid due to specific changes in the meaning of connectives and quantifiers, although there is the explosion of derivable consequences from {φ,¬φ} (the deduction theorem lacking). KC and KC+ are interpreted as fragments of an S5-based first-order modal logic M. The quantification in M is combined with a “subject abstraction” device, which excepts predicate letters from the scope of modal operators. Derivability is defined by an appropriate labeled tableau system rules. Informally, KC is mainly ontologically motivated (in contrast, for example, to Jaśkowski’s discussive logic), relativizing state of affairs with respect to conditions such as time.

References

Ciuciura, J., “On the da Costa, Dubikajtis and Kotas’ system of the discursive logic, D*2”, Logic and Logical Philosophy 14 (2005), 235–252.

Fitting, M., First-Order Modal Logic, Kluwer, Dordrecht, Boston, London, 1999.

Fitting, M., “FOIL axiomatized”, Studia Logica 84 (2006), 1–22.

Jaśkowski, S., “Propositional calculus for contradictory deductive systems”, Studia Logica 24 (1969), 143–157. In Polish 1948.

Jaśkowski, S., “A propositional calculus for inconsistent deductive systems”, Logic and Logical Philosophy 7 (1999), 35–56. A modified version of [4].

Jaśkowski, S., “On the discussive conjunction in the propositional calculus for inconsistent deductive systems”, Logic and Logical Philosophy 7 (1999), 57–59. In Polish 1949.

Kant, I., Gesammelte Schriften, vol. 1–, Königlich Preussische Akademie der Wissenschaften, Berlin, 1908–.

Kant, I., Critique of Pure Reason, St Martin’s Press, MacMillan, New York,Toronto, 1965. Transl. by N. Kemp Smith.

Kant, I., Prolegomena to Any Future Metaphysics, Open Court, Chicago, La Salle, 1997. Transl. by P. Carus.

Leibniz, G.W., Die Philosophischen Schriften, vol. 1–7, Olms, Hildesheim, New York, 1978.

Leibniz, G.W., “Nouveaux essais sur l’entendement humain”, in C.I. Gerhardt (ed.), Die Philosophischen Schriften, vol. 5. 1978.

Perzanowski, J., “Parainconsistency, or inconsistency tamed, investigated and exploited”, Logic and Logical Philosophy 9 (2001), 5–24.

Priest, G., Beyond the Limits of Thought, 2nd ed., Oxford University Press, Oxford, New York, 2002.

Priest, G., “Paraconsistent logic”, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, vol. 6, 2002, pp. 287–393.

Puga, L.Z., N.C.A. da Costa, and W.A. Carnielli, “Kantian and non-Kantian logics”, Logique et Analyse 31 (1988), 3–9.

Urchs, M., “On the role of adjunction in para(in)consistent logic”, in M. Coniglio, and I.L. D’Ottaviano (eds.), Paraconsistency: the Logical Way to the Inconsistent, (New York, Basel, 2002), W. Carnielli, Dekker, pp. 487–499.