Synthese 190 (12):2141-2164 (2013)
|Abstract||In this paper, I introduce the idea that some important parts of contemporary pure mathematics are moving away from what I call the extensional point of view. More specifically, these fields are based on criteria of identity that are not extensional. After presenting a few cases, I concentrate on homotopy theory where the situation is particularly clear. Moreover, homotopy types are arguably fundamental entities of geometry, thus of a large portion of mathematics, and potentially to all mathematics, at least according to some speculative research programs|
|Keywords||Philosophy of mathematics Algebraic geometry Category theory Homotopy theory|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Stojan Obradović & Slobodan Ninković (2009). The Heuristic Function of Mathematics in Physics and Astronomy. Foundations of Science 14 (4):351-360.
Oystein Linnebo, Review of Stewart Shapiro, Philosophy of Mathematics: Structure and Ontology. [REVIEW]
Christopher Pincock (2009). Towards a Philosophy of Applied Mathematics. In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave Macmillan.
Carlo Cellucci (2013). Philosophy of Mathematics: Making a Fresh Start. Studies in History and Philosophy of Science Part A 44 (1):32-42.
René Cori (2000). Mathematical Logic: A Course with Exercises. Oxford University Press.
Jean-Pierre Marquis (1999). Mathematical Engineering and Mathematical Change. International Studies in the Philosophy of Science 13 (3):245 – 259.
Penelope Maddy (1990). Realism in Mathematics. Oxford University Prress.
Mark Colyvan (2012). An Introduction to the Philosophy of Mathematics. Cambridge University Press.
Jean Paul Van Bendegem (2005). Proofs and Arguments: The Special Case of Mathematics. Poznan Studies in the Philosophy of the Sciences and the Humanities 84 (1):157-169.
Alexander Paseau (2005). Naturalism in Mathematics and the Authority of Philosophy. British Journal for the Philosophy of Science 56 (2):377-396.
Stewart Shapiro (2004). Foundations of Mathematics: Metaphysics, Epistemology, Structure. Philosophical Quarterly 54 (214):16 - 37.
Mark Steiner (1998). The Applicability of Mathematics as a Philosophical Problem. Harvard University Press.
Penelope Maddy (2008). How Applied Mathematics Became Pure. Review of Symbolic Logic 1 (1):16-41.
Added to index2012-07-20
Total downloads28 ( #49,832 of 722,839 )
Recent downloads (6 months)1 ( #60,917 of 722,839 )
How can I increase my downloads?