It turns out that for powerful theories of Computer Science, there must exist infinitely many propositions that are inferentially undecidable, that is, can be

It turns out that for powerful theories of Computer Science, there must exist infinitely many propositions that are inferentially undecidable, that is, can be neither proved nor disproved. However, the propositions cannot be specified constructively and so are not very interesting. Currently, there seem to be no propositions interesting to practical Computer Science that are provably inferentially undecidable.