denumerably

Hartman claims that according to a theorem of transfinite mathematics, any collection of material objects is at most denumerably infinite.

But, according to Hartman, people are capable of a denumerably infinite set of predicates, intended in as many ways, which he gives as .

Since has , that is, denumerably many propositional symbols, there are , and therefore uncountably many distinct possible interpretations of .

The syntax of a first-order theory can describe only a denumerable number of sets; hence, only denumerably many sets may be eliminated in this fashion, but this limitation is not binding for the sort of mathematics contemplated here.