Structuralism and the conformity of mathematics and nature

Stemeroff, Noah

doi:10.1016/j.shpsa.2021.01.004

Cited by 1 publication

(1 citation statement)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…etc. ), what kind of structure the account assumes the physical world to have, the role played by scientific theories in generating that structure, and so on (Nguyen and Frigg, 2017;Bueno and Colyvan, 2011;Bueno, 2016;Bueno and French, 2018;Pincock, 2004aPincock, ,b, 2007Pincock, , 2011Stemeroff, 2021). 2 If we are interested in assessing the plausibility of the mapping account as an account of applied mathematics, however, there is another issue that we must consider.…”

Section: Mapping Accounts and The Mathematical Structure Assumptionmentioning

confidence: 99%

Structure and applied mathematics

McKenna

2022

Synthese

View full text Add to dashboard Cite

Mapping accounts' of applied mathematics hold that the application of mathematics in physical science is best understood in terms of 'mappings' between mathematical structures and physical structures. In this paper, I suggest that mapping accounts rely on the assumption that the mathematics relevant to any application of mathematics in empirical science can be captured in an appropriate mathematical structure. If we are interested in assessing the plausibility of mapping accounts, we must ask ourselves: how plausible is this assumption as a working hypothesis about applied mathematics? In order to do so, we examine the role played by mathematics in the multiscalar modelling of sea ice melting behaviour and examine whether we can indeed capture the mathematics involved in the kind of mathematical structure employed by the mapping account. Along the way, we note that the cases of applied mathematics that appear in discussions of mapping accounts almost exclusively involve the employment of a single clearly circumscribed mathematical field or domain (e.g. 'the use of arithmetic in counting physical objects'). While the core assumption of mapping accounts may appear plausible in such situations, we ultimately suggest that the mapping account is not able to handle the important added complexities involved in our sea ice case study. In particular, the notion of mathematical structure around which such accounts are framed does not seem to be able to capture the way in which some applications of mathematics require that very different pieces of mathematics be related to one another on the basis of both mathematical and empirical information.

show abstract

Section: Mapping Accounts and The Mathematical Structure Assumptionmentioning

confidence: 99%

Structure and applied mathematics

McKenna

2022

Synthese

View full text Add to dashboard Cite

show abstract

Structuralism and the conformity of mathematics and nature

Cited by 1 publication

References 24 publications

Structure and applied mathematics

Structure and applied mathematics

Contact Info

Product

Resources

About