# Suggestions for Further Pluralist Research

## Abstract

In this chapter I do three quite different things. One is to give some indication of how to extend Maddy’s idea of making mathematician’s aspirations explicit, thereby marrying philosophy and mathematics. The second is to elaborate on the discussion of Lobachevsky by comparing intentional perspectives on Lobachevsky’s work. This is best done by a pluralist, since he has no agenda. The third is to demonstrate working in a trivial setting, in particular the work concerns Frege’s formal trivial system. A speculation is made about how we can learn more about the notion of cardinality. This is important since only the pluralist can see how to do this explicitly, consciously and seriously. Each of these developments suggests further directions for pluralist research.

## Keywords

Euclidean Geometry Cardinal Number Hyperbolic Geometry Paraconsistent Logic Regulatory Principle## References

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