Leibniz and Kant on Mathematical and Philosophical Knowledge

  • Jürgen Mittelstrass
Chapter
Part of the The University of Western Ontario Series in Philosophy of Science book series (WONS, volume 29)

Abstract

Kant’s comments on Leibniz are often marginal in form, but always essential in substance. It is in these comments that Kant distances himself from the philosophical tradition and establishes a new orientation in philosophy in an important way. This is also true of the reference to Leibniz in the (pre-critical) Prize Essay (An Inquiry into the Distinctness of the Fundamental Principles of Natural Theology and Morals, 1764), Kant’s answer to the problem of the application of mathematical proof to the field of metaphysics posed by the Berlin Royal Academy of Sciences. The reference is of epistemological significance with respect to the system of the sciences. Here, Kant makes in a pragmatic form the distinction between mathematical and philosophical knowledge, which when it is later presented in the Critique of Pure Reason, in a systematically more elaborated form, forms an essential part of the ‘transcendental doctrine of method’. The opposing party is, as Kant makes clear, Leibniz with his Identification of both kinds of knowledge. From a systematic point of view, different ideals of knowledge and their realization in different disciplines -- paradigmatically given in conceptions of Leibniz and Kant --are at stake.

Keywords

Mathematical Knowledge Pure Reason Reciprocal Method Complete Concept Philosophical Knowledge 
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Notes

  1. 1.
    Untersuchung über die Deutlichkeit der Grundsätze der natürlichen Theologie und der Moral [1764], commonly referred to as Prize Essay, I. Kant, Gesammelte Schriften, published by the Königlich Preussische Akademie der Wissenschaften, Berlin 1902ff. (cited hereafter as Acad.-Ed.), II, p. 281. I use here the translation of Lewis White Beck (Immanuel Kant, Critique of Practical Reason And Other Writings in Moral Philosophy, Chicago 1949).Google Scholar
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    Critique of Pure Reason B 152ff. Kant emphasizes here the constructivist character of mathematical intuition: “We cannot think a line without drawing it in thought, or a circle without describing it. We cannot represent the three dimensions of space save by setting three lines at right angles to one another from the same point. Even time itself we cannot represent, save in so far as we attend, in the drawing of a straight line (which has to serve as the outer figurative representation of time), merely to the act of the synthesis of the manifold whereby we successively determine inner sense, and in so doing attend to the succession of this determination in inner sense. Motion, as an act of the subject (not as a determination of an object), and therefore the synthesis of the manifold in space, first produces the concept of succession -- if we abstract from this manifold and attend solely to the act through which we determine the inner sense according to its form” (Critique of Pure Reason B 154f.).Google Scholar
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    “spatium…ordo coexistentium phaenomenorum, ut tempus successivorum” (letter of June 16, 1712 to B. Des Bosses, Philos. Schr. II, p. 450). Thus, with regard to the isotropy and homogeneity of space in which no direction and no place can be discriminated by mathematical or physical criteria, Leibniz speaks of abstract space as “the order of situations, when they are conceived as being possible” (fifth letter to S. Clarke, Philos. Schr. VII, p. 415). For the concept of relational space in Leibniz the fact is crucial that space, as a system of relations, possesses the same ideal status already claimed for the concept of physical bodies in the analysis of the continuum, and continued by introduction of the concept of formal atoms.Google Scholar
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    In Newton’s mechanics this concept serves for the definition of absolute movement and also for the definition of inertial movement. The concept had also been originally advocated by Kant (Von dem ersten Grunde des Unterschiedes der Gegenden im Raume [1768], Acad.-Ed. II, pp. 375–384.Google Scholar
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    See my “’Über’transzendental” (footnote 107) and my ‘Rationale Rekonstruktion der Wissenschaftsgeschichte’, in: P. Janich (ed.), Wissen Schaftstheorie und Wissenschaftsforschung, München 1981, pp. 89-111, 137–148.Google Scholar
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    See K. Lorenz, ‘The Concept of Science. Some Remarks on the Methodological Issue ‘Construction’ versus ‘Description’ in the Philosophy of Science’, in: P. Bieri and R.-P. Horstmann and L. Krüger (eds.), Transcendental Arguments and Science. Essays in Epistemology, Dordrecht and Boston and London 1979, pp. 177–190.Google Scholar

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© D. Reidel Publishing Company 1985

Authors and Affiliations

  • Jürgen Mittelstrass
    • 1
  1. 1.Department of PhilosophyUniversity of KonstanzGermany

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