Wednesday, October 18, 2017

Mathematics and Its Applications, A Transcendental-Idealist Perspective (NDPR Review)

Coincidental? Alain Badiou's lecture, this, and the fact that this afternoon a brilliant student who is interested in the philosophy of mathematics is coming by so we can think about an independent study and an institutional research-award project on some narrowed down issue or problem within the philosophy of mathematics. Hmmm, pretty cool.

Mathematics and Its Applications, A Transcendental-Idealist Perspective
// Notre Dame Philosophical Reviews // News

2017.10.18 : View this Review Online | View Recent NDPR Reviews

Jairo José da Silva, Mathematics and Its Applications, A Transcendental-Idealist Perspective, Springer, 2017, 275pp., $99.00 (hbk), ISBN 9783319630724.
Reviewed by Mirja Hartimo, University of Jyväskylä, Finland

Jairo José da Silva formulates a transcendental-idealist approach to mathematics. Appropriating (he is explicit about not engaging in any kind of exegesis) some central notions of Husserl's phenomenology, da Silva holds that mathematics is "intentionally posited" in the mathematical community, in communal work that has been carried out for centuries. "Intentional acts," such as intuiting or empty intending, put something with characteristic features and properties in front of the subject (28). If such positing is consistent, the intended object comes into existence (29). This allows viewing the existence of formal objects "on their own terms," as intentionally posited by the mathematicians. This leads da Silva to embrace a structuralist, and also Platonist, view of formal objects, corresponding not to metaphysical...

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