Formalizing Kant’s Rules

Journal of Philosophical Logic 48:1-68 (2019)
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This paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. These acts are not propositions; they do not have truth-values. Our formalization is related to the input/ output logics, a family of logics designed to capture relations between elements that need not have truth-values. In this paper, we introduce KL3 as a formalization of Kant’s conception of rules as conditional imperatives and permissives. We explain how it differs from standard input/output logics, geometric logic, and first-order logic, as well as how it translates natural language sentences not well captured by first-order logic. Finally, we show how the various distinctions in Kant’s much-maligned Table of Judgements emerge as the most natural way of dividing up the various types and sub-types of rule in KL3. Our analysis sheds new light on the way in which normative notions play a fundamental role in the conception of logic at the heart of Kant’s theoretical philosophy.

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Author Profiles

Richard Evans
Cambridge University
Andrew Stephenson
University of Southampton

Citations of this work

Does Logic Have a History at All?Jens Lemanski - forthcoming - Foundations of Science:1-23.

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References found in this work

Critique of Pure Reason.Immanuel Kant - 1998 - Cambridge: Cambridge University Press. Edited by J. M. D. Meiklejohn. Translated by Paul Guyer & Allen W. Wood.
Critique of Pure Reason.Immanuel Kant - 1781 - Mineola, New York: Macmillan Company. Edited by J. M. D. Meiklejohn.
Kant and the exact sciences.Michael Friedman - 1992 - Cambridge, Mass.: Harvard University Press.

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