Reality and Human Values in Mathematics

Many mathematicians and philosophers say that mathematical objects have a real existence independent of any human activities or values. But do mathematicians behave as if this were true? This paper applies techniques from linguistics and sociology to show that mathematical discourse involves a highly nuanced assignment of values to objects, which is then used in resolving references to objects; it also discusses the nature of abstraction, and shows how the appearance of reality for mathematical objects arises through the use of conventions from ordinary discourse, including narrative. Results in the paper have implications for the exposition and use of mathematics, for mathematics education, and for philosophy.