Category-Theoretic Realism: A Linguistic Approach to the Philosophy of Mathematics

Dissertation, The University of Western Ontario (Canada) (1998)
  Copy   BIBTEX

Abstract

On what basis can we justify the inclusion of mathematical concepts and theories as legitimate objects of philosophical study? One answer to this question is: mathematical concepts and theories ought to be included because they are indispensable for describing the physical world. But what if a particular mathematical concept or theory has no such application? Are its corresponding statements to be counted as meaningless? Are its corresponding objects to be taken as mere linguistic fictions? One way of avoiding these conclusions is provided by the set-theoretic foundationalist: Mathematical concepts, insofar as they reduce to set-theoretic concepts, are meaningful and hence are to be regarded as legitimate objects of philosophical study. The problem with this approach is that it leads to a conflict between truth and meaning: some mathematical statements are true for one interpretation of set theory yet false for another. ;I show that if we shift our philosophical focus from what mathematical theories are about to what mathematical theories say and if we take category theory as the language of mathematics , then we can justify the inclusion of mathematical concepts and theories as legitimate objects of philosophical study. Thus, I argue that the current debate over the status of mathematical objects and statements is resolved by adopting a linguistic approach to the philosophical analysis of mathematical concepts and theories. In particular, I show how category theory can be taken as the language used to specify and organize the common structural features of mathematical discourse. Category theory, then, provides the means for representing and justifying our talk of mathematical existence, meaning and truth from within a given mathematical theory.

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 102,323

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Semantic Realism.Elaine Landry - 1998 - The Paideia Archive: Twentieth World Congress of Philosophy 34:6-12.
Category theory: The language of mathematics.Elaine Landry - 1999 - Philosophy of Science 66 (3):27.
Figures, Formulae, and Functors.Zach Weber - 2013 - In Sun-Joo Shin & Amirouche Moktefi (eds.), Visual Reasoning with Diagrams. Basel: Birkhaüser. pp. 153--170.
What Is Structuralism? and Other Questions.Michael D. Resnik - 1997 - In Michael David Resnik (ed.), Mathematics as a science of patterns. New York ;: Oxford University Press.
Towards a Fictionalist Philosophy of Mathematics.Robert Knowles - 2015 - Dissertation, University of Manchester

Analytics

Added to PP
2015-02-04

Downloads
1 (#1,950,106)

6 months
1 (#1,826,059)

Historical graph of downloads

Sorry, there are not enough data points to plot this chart.
How can I increase my downloads?

Author's Profile

Elaine Landry
University of California, Davis

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references