Language, thought, logic, and existence

As is well known, we can prove that everything that exists necessarily exists in S5. Perhaps as well known is Kripke’s two-part solution. First we forbid axioms with free variables and second we forbid the use of singular terms. One way to do the latter is via Nominal Description Theory (NDT): a name N is semantically equivalent to the description that mentions the name, e.g. ‘the-bearer-of-“N”’. But how do we reconcile NDT with the thesis of rigid designation? I argue that we need to distinguish a semantic theory that aims to give an account of thoughts (P-semantics) from one that aims to give an account of English sentence types (L-semantics). I then introduce frigidity as the claim that there are no L-semantic singular terms. The causal theory of reference is a P- semantic theory and together with NDT we can then formulate L-semantic descriptions that cap..
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