Higher-Order Contingentism, Part 3: Expressive Limitations

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’. This is a post-peer-review, pre-copyedit version of an article published in Journal of Philosophical Logic. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10992-017-9443-0