# Higher-Order Contingentism, Part 3: Expressive Limitations

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## Abstract

Two expressive limitations of an infinitary higher-order modal language interpreted on models for higher-order contingentism – the thesis that it is contingent what propositions, properties and relations there are – are established: First, the inexpressibility of certain relations, which leads to the fact that certain model-theoretic existence conditions for relations cannot equivalently be reformulated in terms of being expressible in such a language. Second, the inexpressibility of certain modalized cardinality claims, which shows that in such a language, higher-order contingentists cannot express what is communicated using various instances of talk of ‘possible things’, such as ‘there are uncountably many possible stars’.

## Keywords

Contingentism Higher-order modal logic Expressivity## Notes

### Acknowledgments

In addition to those thanked in the acknowledgements of Part 1, I would like to thank a reviewer for comments on Part 3, and the editor, Frank Veltman, for all his help with the publication of the three parts.

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