 Balaguer (2001, 2009) argues that Field’s formalistic view can’t be right, and he develops a non-formalistic alternative to it. His argument against the formalistic view is that it cannot account for all of the objectivity that we find in mathematics. Most importantly, the formalistic view entails (incorrectly) that there can be no objectively correct answers to questions that ask about the truth values of mathematical sentences that are undecidable in currently accepted mathematical theories. The most famous example here is probably the continuum hypothesis (CH), which is undecidable in currently accepted set theories, e.g., Zermelo-Fraenkel set theory (ZF). (In other words, ZF is consistent with both CH and ~CH; i.e., ZF+CH and ZF+~CH are both consistent set theories.) Given this, it follows from Field’s view that neither CH nor ~CH is part of the story of mathematics and, hence, that there is no objectively correct answer to the CH question. This, however, seems unacceptable, because it could turn out that mathematicians are going to discover an objectively correct answer to the CH question. For instance, suppose that some mathematician came up with a new axiom candidate AX such that (i) all mathematicians agreed that AX was an intuitively obvious claim about sets, and (ii) ZF+AX entailed CH. If this happened, then mathematicians would say that they had proven CH, and that they had discovered that CH was correct, and so on. Field’s view would force us to say that if we endorsed AX, then CH would become true in the story of mathematics. But this seems to get things wrong. Given the intuitive obviousness of AX, it seems very natural to say that, in this scenario, mathematicians discovered that CH had been true (or “correct”, or true in the story of mathematics, or whatever we want to call it) all along—i.e., that we didn’t just make this up by endorsing a new theory. And, again, it seems that this is what mathematicians would say. So, Balaguer argues, Field’s formalistic view of the objectivity of mathematics is unacceptable.