# Why the Utility of Mathematical Entities is Unlike the Utility of Theoretical Entities

# Why the Utility of Mathematical Entities is Unlike the Utility of Theoretical Entities

Argues for the legitimacy of using mathematics to draw nominalistic conclusions (ones statable without reference to mathematical entities) from nominalistic premises, without assuming that the mathematics used in this way is true. Instead we assume that mathematics is *conservative*: any inference from nominalistic premises to a nominalistic conclusion that can be made with the help of mathematics could be made without it. (In mathematics, conservativeness is only slightly stronger than consistency: the exact relation between the two is discussed in an appendix.) The role of conservativeness marks a fundamental difference between the use of mathematical entities and the use of the theoretical entities of science. The utility of theoretical entities in science is due solely to their *theoretical indispensability*. Mathematical entities appear to be theoretically indispensable too, but later chapters will argue to the contrary.

*Keywords:*
conservativeness, consistency, mathematical entities, nominalistic statement, theoretical indispensability

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .