
TL;DR
This paper examines the nature of revolutions in mathematics versus empirical science, analyzing whether mathematical revolutions can be inglorious and how they compare to scientific ones.
Contribution
It offers a resolution to the debate on whether mathematical revolutions can be inglorious by analyzing specific mathematical revolutions and their characteristics.
Findings
Mathematical revolutions can be inglorious, challenging traditional views.
The distinction between glorious and inglorious revolutions applies to mathematics.
The paper clarifies methodological differences between scientific and mathematical revolutions.
Abstract
In their account of theory change in logic, Aberdein and Read distinguish 'glorious' from 'inglorious' revolutions--only the former preserves all 'the key components of a theory' [1]. A widespread view, expressed in these terms, is that empirical science characteristically exhibits inglorious revolutions but that revolutions in mathematics are at most glorious [2]. Here are three possible responses: 0. Accept that empirical science and mathematics are methodologically discontinuous; 1. Argue that mathematics can exhibit inglorious revolutions; 2. Deny that inglorious revolutions are characteristic of science. Where Aberdein and Read take option 1, option 2 is preferred by Mizrahi [3]. This paper seeks to resolve this disagreement through consideration of some putative mathematical revolutions. [1] Andrew Aberdein and Stephen Read, The philosophy of alternative logics, The…
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Taxonomy
TopicsPhilosophy and History of Science · Philosophy and Theoretical Science · Epistemology, Ethics, and Metaphysics
