Article ID: CBB001320268

Mathematical Method and Newtonian Science in the Philosophy of Christian Wolff (2013)

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is paper aims to illuminate Christian Wolff's view of mathematical reasoning, and its use in metaphysics, by comparing his and Leibniz's responses to Newton's work. Both Wolff and Leibniz object that Newton's metaphysics is based on ideas of sense and imagination that are suitable only for mathematics. Yet Wolff expresses more regard (than Leibniz) for Newton's scientific achievement. Wolff's approval of the use of imaginative ideas in Newtonian mathematical science seems to commit him to an inconsistent triad. For he rejects their use in metaphysics, and also holds that every scientific discipline must follow mathematics' method. A facile resolution would be to suppose Wolff identifies the method of mathematics with the order in which propositions are deduced, or with analysis that reveals the structure of concepts. This would be to assimilate Wolff's view to Leibniz's (on which all mathematical propositions are ultimately derived from definitions, and definitions are justified by conceptual analysis). On this construal, mathematical reasoning involves only the understanding. But Wolff conceives mathematics' method more broadly, to include processes of concept-formation which involve perception and imagination. Thus my way of resolving the tension is to find roles for perception and imagination in the formation of metaphysical concepts.

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Article Massimi, Michela (2013) Philosophy of Natural Science from Newton to Kant. Studies in History and Philosophy of Science (p. 393). unapi

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Authors & Contributors
Garber, Daniel
Rumore, Paola
Connolly, Patrick J.
Howard, Stephen
Pelletier, Arnaud
Schliesser, Erick
Concepts
Metaphysics
Philosophy of science
Philosophy
Mathematics
Newtonianism
Philosophy of mathematics
Time Periods
18th century
17th century
Early modern
16th century
Places
Germany
France
England
Europe
Paris (France)
Institutions
Prussian Academy of Sciences
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