Realism, Reductionism, Determinatism
Allan Hazlett, in his Against Fictionalism, says that if numbers exist then "there is a fact of the matter about which sets numbers are", even if we can't find it out. I don't think realism and reductionsism about numbers implies this kind of determinatism. (Sorry, "determinism" was already taken.)
The point is general. I believe in psychological states, and I believe that psychological states are really just neurophysiological states. But I don't believe that it is possible to isolate a single brain state that realises the pain role, or the believes-that-the-meeting-starts-at-noon role. The problem is that folk psychology is probably far too unspecific to have a unique realisation. (This is not the problem of multiple realisability, or not quite. Multiple realisability is usually taken to be the problem that pain is or might be differently realised in different individuals. It would be interesting to know more about the relation between the two problems.)
Similarly, I believe in mountains, and I believe that mountains are really just mereological sums of rocks, stones, sand, etc. But I don't believe that it is possible to isolate a single sum of rocks etc. that is (determinately) Mt. Everest.