# Philosophical Presentation of Pluralism

## Abstract

In part I of the book I gave motivations for adopting pluralism, from the starting point of several well-known philosophies of mathematics. I drew inspiration from them and rejected some of their claims as unwarranted. But we still do not have a clear picture of what pluralism is as a philosophical position in its own right. In this part, I give an initial presentation of the position over the course of four chapters. In this chapter I answer some pressing questions. I begin with the notion of tolerance. This invites discussion on three issues. One is normativity, the second is general organisation of the types of philosophical issues addressed by the pluralist, and the third is restrictions. In particular, I open the issue of how it is that the pluralist will cope with contradiction, and in what respect a paraconsistent logic can help the pluralist.

## Keywords

Mathematical Theory Mathematical Practice Extensional Theory Paraconsistent Logic Peano Arithmetic## References

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