Book ID: CBB814395007

Mathematics and Its Applications: A Transcendental-Idealist Perspective (2018)

unapi

This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism.The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what does it mean to exist, mathematical structures: what are they and how do we know them, how different layers of mathematical structuring relate to each other and to perceptual structures, and how to use mathematics to find out how the world is.The book simultaneously develops along two lines, both inspired and enlightened by Edmund Husserl’s phenomenological philosophy. One line leads to the establishment of a particular version of mathematical structuralism, free of “naturalist” and empiricist bias. The other leads to a logical-epistemological explanation and justification of the applicability of mathematics carried out within a unique structuralist perspective. This second line points to the “unreasonable” effectiveness of mathematics in physics as a means of representation, a tool, and a source of not always logically justified but useful and effective heuristic strategies.

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Reviewed By

Review Arezoo Islami (2019) Review of "Mathematics and Its Applications: A Transcendental-Idealist Perspective". Metascience: An International Review Journal for the History, Philosophy and Social Studies of Science (pp. 77-80). unapi

Citation URI
https://data.isiscb.org/isis/citation/CBB814395007/

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Authors & Contributors
Gao, Shan
Sonne-Hansen, Lise Mariane
Posy, Carl J.
Pedersen, Stig Andur
Omnès, Roland
Millán Gasca, Ana
Concepts
Mathematics
Mathematics and its relationship to science
Philosophy of mathematics
Philosophy of science
Applied mathematics
Epistemology
Time Periods
21st century
20th century, late
17th century
18th century
20th century
Ancient
Places
England
United States
France
Africa
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