Which undecidable mathematical sentences have determinate truth values?

Source abstract

Abstract I will begin by contrasting three metaphysical pictures about mathematics. The first, about which I will have little to say in what follows, is the fictionalist picture. This says that strictly speaking, there are no mathematical entities; still, we can perfectly well reason from premises that postulate such entities, and systematic reasoning from such premises is both intrinsically interesting and highly useful in our practical affairs. On this view, mathematical theories are not literally true. Of course, a fictionalist needs to say something about why these theories are useful if they are not true: in disciplines other than mathematics, the utility of a theory is generally taken as good reason to believe that the theory is at least approximately true, and, if it is not a good reason in the mathematical case, then we need to know what the relevant differences between the mathematical and the non-mathematical are. Myself, I think that there are such relevant differences, and that the fictionalist view can be defended,1 but I will almost completely ignore it in what follows.