Synthese 163 (2):119 - 131 (2008)
This paper compares the statement ‘Mathematics is the study of structure’ with the actual practice of mathematics. We present two examples from contemporary mathematical practice where the notion of structure plays different roles. In the first case a structure is defined over a certain set. It is argued firstly that this set may not be regarded as a structure and secondly that what is important to mathematical practice is the relation that exists between the structure and the set. In the second case, from algebraic topology, one point is that an object can be a place in different structures. Which structure one chooses to place the object in depends on what one wishes to do with it. Overall the paper argues that mathematics certainly deals with structures, but that structures may not be all there is to mathematics.
|Keywords||structuralism mathematics WAYS|
|Categories||categorize this paper)|
References found in this work BETA
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford University Press.
Mathematics Without Numbers: Towards a Modal-Structural Interpretation.Geoffrey Hellman - 1989 - Oxford University Press.
Citations of this work BETA
Categories for the Working Mathematician: Making the Impossible Possible.Jessica Carter - 2008 - Synthese 162 (1):1-13.
Invariants and Mathematical Structuralism.Georg Schiemer - 2014 - Philosophia Mathematica 22 (1):70-107.
Mathematical Forms and Forms of Mathematics: Leaving the Shores of Extensional Mathematics.Jean-Pierre Marquis - 2013 - Synthese 190 (12):2141-2164.
John P. Burgess. Rigor and Structure. Oxford: Oxford University Press, 2015. ISBN: 978-0-19-872222-9 ; 978-0-19-103360-5 . Pp. Xii + 215. [REVIEW]Richard Pettigrew - 2016 - Philosophia Mathematica 24 (1):129-136.
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