  is true, there are in fact no mathematical objects and thus in particular no numbers. But there is no contradiction here. We must distinguish between the language LM in which mathematicians make their claims and the language LP in which nominalists and other philosophers make theirs. The statement (1) is made in LM. But the nominalist’s assertion that (1) is true but that there are no abstract objects is made in LP. The nominalist’s assertion is thus perfectly coherent provided that (1) is translated non-homophonically from LM into LP.  And indeed, when the nominalist claims that the truth-values of sentences of LM are fixed in a way which doesn’t appeal to mathematical objects, it is precisely this sort of non-homophonic translation she has in mind. The view mentioned in the previous note provides an example.