# The Weak Objectivity of Mathematics and Its Reasonable Effectiveness in Science

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## Abstract

Philosophical analysis of mathematical knowledge are commonly conducted within the realist/antirealist dichotomy. Nevertheless, philosophers working within this dichotomy pay little attention to the way in which mathematics evolves and structures itself. Focusing on mathematical practice, I propose a weak notion of objectivity of mathematical knowledge that preserves the intersubjective character of mathematical knowledge but does not bear on a view of mathematics as a body of mind-independent necessary truths. Furthermore, I show how that the successful application of mathematics in science is an important trigger for the objectivity of mathematical knowledge.

## Keywords

Mathematical knowledge Objectivity Platonism Nominalism Applicability of mathematics## Notes

### Acknowledgements

I would like to thank one anonymous reviewer for helpful comments. This work was supported by the Portuguese Foundation for Science and Technology through the FCT Investigator Programme (Grant Nr. IF/01354/2015).

### Compliance with Ethical Standards

### Conflict of interest

The author reports no real or perceived vested interests that relate to this article that could be construed as a conflict of interest.

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