Resnik, Michael D. University Distinguished Professor of Philosophy, University of North Carolina, Chapel Hill
Print publication date: 1999 (this edition)
Published to Oxford Scholarship Online:
Print ISBN-13: 978-0-19-825014-2
doi:10.1093/0198250142.003.0012
 

Michael D. Resnik
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
doi:10.1093/0198250142.003.0012
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Part One Problems and Positions
Part Two Neutral Epistemology
Part Three Mathematics as a Science of Patterns