Redefining Revolutions

Por • 30 oct, 2018 • Sección: sociologia

Andrew Aberdein

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 Development of Modern Logic (Leila Haaparanta, ed.), Oxford University Press, Oxford, 2009, pp. 613-723.  [2] Donald Gillies (ed.), Revolutions in Mathematics, Oxford University Press, Oxford, 1992.  [3] Moti Mizrahi, Kuhn’s incommensurability thesis: What’s the argument?, Social Epistemology 29 (2015), no. 4, 361-378.

arXiv:1810.07038v1 [math.HO]

History and Overview (math.HO)

 

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