User blog comment:LittlePeng9/FOOT is not as strong as I thought/@comment-5529393-20161225200516/@comment-27513631-20161227014106

But there's a major difference between the two: the 'true' powerset of V is something we can't talk about in V, but the definable powerset of V can be considered in V (ZFC and NBG interpreting each otehr gives an easy example of this).

Aside from any thoughts about some sort of platonistic 'true' powerset, if we want to keep in like with what almost everyone else does, the we have to use first-order logic, hence no true powerset of V.

Personally, I think we're working with abstractions of symbolic manipulation, and second to that am inclined to a multiverse, rather than a universe (but do prefer large cardinal statements to be true than false), although I'm not sure if that's relevant.

If we work in first order logic, we don't have to make any additional assumptions about what's reasonable. If we work in anything else, we do, and we can no longer actually base our definitions on the universe alone, most of the time. *Invokes Occam's Razor.*

As to SOL in Platonism, I guess I assumed that, if these objects exist beyond the universe, which contains everything, then a platonist would deny SOL as it implies the existence of objects not in the universe. I don't really get platonism; it seems like it considers 'genuine truths' to be intuition-guided human choice to me.