I think closing my previous question link text on the basis of its not being mathematics would be a mistake. At least there are two famous theorems of contemporary mathematics echo the principle of plenitude (PP), namely The Infinite Monkey Theorem and Kolmogorov's zero-one law (See e.g. link text).
In his most recent posting on FOM, Harvey Friedman used PP to formulate the system OEU and proved the mutual interpretability of ZF and OEU. That means anything that you can prove in ZF, you can prove in OEU as well. Therefore if mathematics can be interpreted in ZF, then mathematics can be interpreted in OEU as well. See his complete posting on FOM link text.
My main questions are: How confident are we that PP and IP are “true” ? More specifically, is it possible to “prove” or justify PP and IP rigorously? If yes, how? If not, why not?
