Areté. Revista de Filosofía 31 (1):7-34 (2019)

Manuel Barrantes
Hamilton College
“Structuralism, Fictionalism, and the Applicability of Mathematics in Science”. This article has two objectives. The first one is to review some of the most important questions in the contemporary philosophy of mathematics: What is the nature of mathematical objects? How do we acquire knowledge about these objects? Should mathematical statements be interpreted differently than ordinary ones? And, finally, how can we explain the applicability of mathematics in science? The debate that guides these reflections is the one between mathematical realism and anti-realism. On the other hand, the second objective is to discuss the arguments that use the applicability of mathematics in science to justify mathematical realism, and show that none of them reaches its aim. To this end, we will distinguish three aspects of the problem of the applicability of mathematics: the utility of mathematics in science, the unexpected utility of some mathematical theories, and the apparent indispensability of mathematics in our best scientific theories - in particular, in our best scientific explanations. Finally, I argue that none of these aspects constitutes a reason to adopt mathematical realism.
Keywords Mathematical realism  Realismo matemático  aplicabilidad  applicability  estructuralismo matemático  explicaciones matemáticas  factionalism  ficcionalismo  indispensabilidad  indispensability  mathematical explanations
Categories (categorize this paper)
DOI 10.18800/arete.201901.001
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

Our Archive
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

What Makes a Scientific Explanation Distinctively Mathematical?Marc Lange - 2013 - British Journal for the Philosophy of Science 64 (3):485-511.
Mathematical Explanation in Science.Alan Baker - 2009 - British Journal for the Philosophy of Science 60 (3):611-633.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.

View all 15 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Realismo/Anti-Realismo.Eduardo Castro - 2014 - Compêndio Em Linha de Problemas de Filosofia Analítica.
Mathematical Explanation and Indispensability.Susan Vineberg - 2018 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 33 (2):233-247.
Mathematical Explanation and Indispensability.Vineberg Susan - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):233-247.
The Applicability of Mathematics and the Indispensability Arguments.Michele Ginammi - 2016 - Lato Sensu, Revue de la Société de Philosophie des Sciences 3 (1).
Mathematical Explanations Of Empirical Facts, And Mathematical Realism.Aidan Lyon - 2012 - Australasian Journal of Philosophy 90 (3):559-578.
Confirmational Holism and its Mathematical (W)Holes.Anthony Peressini - 2008 - Studies in History and Philosophy of Science Part A 39 (1):102-111.
Indispensability, Causation and Explanation.Sorin Bangu - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):219-232.
Scientific Realism and the Indispensability Argument for Mathematical Realism: A Marriage Made in Hell.Jacob Busch - 2011 - International Studies in the Philosophy of Science 25 (4):307-325.
Indispensability Argument and Anti-Realism in Philosophy of Mathematics.Feng Ye - 2007 - Frontiers of Philosophy in China 2 (4):614-628.


Added to PP index

Total views
22 ( #441,260 of 2,324,555 )

Recent downloads (6 months)
4 ( #231,818 of 2,324,555 )

How can I increase my downloads?


My notes