TY - BOOK
T1 - Applying mathematics
T2 - Immersion, inference, interpretation
AU - Bueno, Otávio
AU - French, Steven
N1 - Publisher Copyright:
© Otavio Bueno and Steven French 2018.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - What has been called ‘the unreasonable effectiveness of mathematics’ sets a challenge for philosophers. Some have responded to that challenge by arguing that mathematics is essentially anthropocentric in character whereas others have pointed to the range of structures that mathematics offers. Here a middle way is offered that focuses on the moves that have to be made in both the mathematics and the relevant physics in order to bring the two into appropriate relation. This relation can be captured via the inferential conception of the applicability of mathematics which is formulated in terms of immersion inference and interpretation. In particular the roles of idealizations and of surplus structure in science and mathematics respectively are brought to the fore and captured via an approach to models and theories that emphasizes the partiality of the available information: the partial structures approach. The discussion as a whole is grounded in a number of case studies drawn from the history of quantum physics and extended to contest recent claims that the explanatory role of certain mathematical structures in scientific practice supports a realist attitude towards them. The overall conclusion is that the effectiveness of mathematics does not seem unreasonable at all once close attention is paid to how it is actually applied in practice.
AB - What has been called ‘the unreasonable effectiveness of mathematics’ sets a challenge for philosophers. Some have responded to that challenge by arguing that mathematics is essentially anthropocentric in character whereas others have pointed to the range of structures that mathematics offers. Here a middle way is offered that focuses on the moves that have to be made in both the mathematics and the relevant physics in order to bring the two into appropriate relation. This relation can be captured via the inferential conception of the applicability of mathematics which is formulated in terms of immersion inference and interpretation. In particular the roles of idealizations and of surplus structure in science and mathematics respectively are brought to the fore and captured via an approach to models and theories that emphasizes the partiality of the available information: the partial structures approach. The discussion as a whole is grounded in a number of case studies drawn from the history of quantum physics and extended to contest recent claims that the explanatory role of certain mathematical structures in scientific practice supports a realist attitude towards them. The overall conclusion is that the effectiveness of mathematics does not seem unreasonable at all once close attention is paid to how it is actually applied in practice.
KW - Application of mathematics
KW - Idealization
KW - Mathematical optimism
KW - Structure
KW - Unreasonable effectiveness
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U2 - 10.1093/oso/9780198815044.001.0001
DO - 10.1093/oso/9780198815044.001.0001
M3 - Book
AN - SCOPUS:85051157323
BT - Applying mathematics
PB - Oxford University Press
ER -