Chapter

What Is Structuralism? and Other Questions

Michael D. Resnik

in Mathematics as a Science of Patterns

Published in print December 1999 | ISBN: 9780198250142
Published online November 2003 | e-ISBN: 9780191598296 | DOI: http://dx.doi.org/10.1093/0198250142.003.0012
 What Is Structuralism? and Other Questions

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I explore the relation between structuralism and other theses that I have presented in the rest of the book, in particular, my holism, realism about mathematical objects, and the disquotational account of truth. In developing my theory, I have claimed that there is no fact of the matter as to whether the patterns that the various mathematical theories describe are themselves mathematical objects, so I first try to explain what the locution ‘there is no fact of the matter’ means. Next, I discuss the relativity of key structuralist concepts like sub‐pattern and pattern equivalence, and then explore the possibility of formulating structuralist versions of mathematical theories. Even if my holism precludes me from drawing a sharp distinction between philosophy and science I do not regard my structuralism as a mathematical theory but rather as a philosophical account of mathematics that tries to achieve a deeper understanding of the epistemology and ontology of mathematics. My structuralism is epistemic rather than ontic because it is not an ontological reduction or a foundation for mathematics but a philosophical view about the nature of its objects. So when it is combined with realism concerning mathematical objects, it need not commit one to the existence of structures.

Keywords: disquotation; epistemic; fact of the matter; holism; mathematical object; mathematical structure; mathematical theory; ontic; realism; structuralism

Chapter.  12051 words. 

Subjects: Philosophy of Mathematics and Logic

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