Mathematics and Reality

by Mary Leng

Mary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focussed on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. Leng, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized.

Genres: Philosophy, Mathematics

290 pages, Paperback

First published April 1, 2010

Reviews

[emily · Rating 4 out of 5]

mary leng writes and formulates her arguments so well; even if they were a little redundant at times, it definitely made sure that points landed and the reader fully understood. perhaps only the one time she lost me was when she talked about constructive empiricism, but i think that's more of my end and not being informed as to the specifics of that stance re: philosophy of science. there was also a point in the essay when she used the word 'fictional' to mean something other than it usually does in normal speech, which kind of made for clunky writing, but i agree in thinking there was no better option.