Galileo’s Mathematical Platonism. (English) Zbl 0849.00015

Czermak, Johannes (ed.), Philosophy of mathematics. Proceedings of the 15th international Wittgenstein-Symposium, August 16-23, 1992, Kirchberg am Wechsel, Austria. Part I. Wien: Hölder-Pichler-Tempsky. Schriftenreihe der Wittgenstein-Gesellschaft. 20/I, 13-22 (1993).
The author wants to make it plausible that Galileo was a mathematical (geometrical) Platonist in the sense that he believed “that reality is essentially mathematical and that science (a mathematical science) tells us how things actually are” (13). Such Platonism is opposed to Aristotelism in which “mathematics is just a tool and is not capable of telling us anything about the actual structure of the world, which simply is not mathematical” (ibid.). Discussing several aspects of Galileo’s philosophy the author shows the metaphysical priority of quantitative properties over qualitative ones. Even Galileo’s experimentalism is subordinate to the primacy of geometry, but the author does not go so far as to advocate Alexandre Koyré’s thesis that all Galilean science was substantially a priori. In concluding the author gives three different ways in which geometry is connected to natural science: (i) Geometry is the structure of reality, (ii) geometry is the essence of scientific method, and (iii) geometry governs the fundamental structure of knowledge.
For the entire collection see [Zbl 0836.00022].


00A30 Philosophy of mathematics
01A40 History of mathematics in the 15th and 16th centuries, Renaissance
01A45 History of mathematics in the 17th century


Galileo; Platonism