TY - BOOK

T1 - Applying mathematics

T2 - Immersion, inference, interpretation

AU - Bueno, Otávio

AU - French, Steven

N1 - Publisher Copyright:
© Otavio Bueno and Steven French 2018.

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

UR - http://www.scopus.com/inward/record.url?scp=85051157323&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051157323&partnerID=8YFLogxK

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 -