 This version of the singular term argument might seem even more powerful than the mathematical-object version of the singular term argument sketched in  section 4.1,  because in this case, it doesn't seem that there is as much room for paraphrase nominalism. We saw in  section 4.1  that there are a number of programs for paraphrasing the statements of mathematics, but there are no obvious strategies for paraphrasing ordinary belief ascriptions. One might think this could be done by taking sentences of the form ‘S believes that p’ to mean ‘If there existed propositions, then S would believe that p’; but this sort of view is even less plausible here than it is in the mathematical case. It is just wildly implausible to suppose that when common folk say things like ‘Clinton believes that his presidency was successful’, they mean to be making hypothetical claims about what the person in question would believe in some alternate situation.