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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. . .
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