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THE LOGIC AND TOPOLOGY OF KANT’S TEMPORAL CONTINUUM

Published online by Cambridge University Press:  29 January 2018

RICCARDO PINOSIO  and
MICHIEL VAN LAMBALGEN
RICCARDO PINOSIO*
Affiliation:
ILLC and Department of Philosophy, University of Amsterdam
MICHIEL VAN LAMBALGEN*
Affiliation:
ILLC and Department of Philosophy, University of Amsterdam
*
*ILLC AND DEPARTMENT OF PHILOSOPHY UNIVERSITY OF AMSTERDAM P.O. BOX 94242, 1090 GE AMSTERDAM, THE NETHERLANDS E-mail: [email protected]
†ILLC AND DEPARTMENT OF PHILOSOPHY UNIVERSITY OF AMSTERDAM P.O. BOX 94242, 1090 GE AMSTERDAM, THE NETHERLANDS E-mail: [email protected]
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Abstract

In this paper we provide a mathematical model of Kant’s temporal continuum that yields formal correlates for Kant’s informal treatment of this concept in the Critique of Pure Reason and in other works of his critical period. We show that the formal model satisfies Kant’s synthetic a priori principles for time (whose consistence is not obvious) and that it even illuminates what “faculties and functions” must be in place, as “conditions for the possibility of experience”, for time to satisfy such principles. We then present a mathematically precise account of Kant’s transcendental theory of time—the most precise account to date.

Moreover, we show that the Kantian continuum which we obtain has some affinities with the Brouwerian continuum but that it also has “infinitesimal intervals” consisting of nilpotent infinitesimals; these allow us to capture Kant’s theory of rest and motion in the Metaphysical Foundations of Natural Science.

While our focus is on Kant’s theory of time the material in this paper is more generally relevant for the problem of developing a rigorous theory of the phenomenological continuum, in the tradition of Whitehead, Russell, and Weyl among others.

Keywords

01A5003B4403F9906F3554E55spatio-temporal eventscontinua constructed from eventsKant’s philosophy of timetime as generated by self-affection through motionnilpotent infinitesimals
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 1 , March 2018 , pp. 160 - 206
Copyright
Copyright © Association for Symbolic Logic 2018 

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