The Pythagorean World pp 179-222 | Cite as

# What Mathematics Is About

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## Abstract

The focus of the previous chapter was foundational issues for mathematics; in particular, whether there is one background theory which could serve as the ultimate arbiter of mathematical existence and truth. The outcome was inconclusive. The current situation is that there are many background theories which agree on commonly held intuitions about mathematics but which differ on the status of undecidable propositions such as the continuum hypothesis. Pluralists have arguments to support the view that this will always be the case and that questions of mathematical truth and existence are relative to a chosen background. Universalists believe that, with further work, a preferred set of axioms will emerge which will effectively determine the truth value of all mathematical propositions. Profoundly important steps have been taken by the universalists in their quest for the ultimate background theory and there are signs that a solution is emerging. However, the work is very preliminary and the weight of opinion in the debate is still on the pluralist side.

## Keywords

Mathematical Structure Physical Reality Conceptual Scheme Measurable Cardinal Reflection Principle## References

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