## Mathematical Pluralism

### Author

Edward N. Zalta
### Reference

forthcoming, *Noûs*.

### Abstract

Mathematical pluralism can take one of three forms: (1) every
consistent mathematical theory consists of truths about its own domain
of individuals and relations; (2) every mathematical theory,
consistent or inconsistent, consists of truths about its own (possibly
uninteresting) domain of individuals and relations; and (3) the
principal philosophies of mathematics are each based upon an insight
or truth about the nature of mathematics that can be validated. (1)
includes the multiverse approach to set theory. (2) helps us to
understand the significance of the distinguished non-logical
individual and relation terms of even inconsistent theories. (3) is a
metaphilosophical form of mathematical pluralism and hasn't been
discussed in the literature. In what follows, I show how the analysis
of theoretical mathematics in object theory exhibits all three forms
of mathematical pluralism.

[Author's preprint available online in PDF]