We argue that Godel's completeness theorem is equivalent to completability of
consistent theories, and Godel's incompleteness theorem is equivalent to the
fact that this completion is not constructive, in the sense that there are some
consistent and recursively enumerable theories which cannot be extended to any
complete and consistent and recursively enumerable theory. Though any
consistent and decidable theory can be extended to a complete and consistent
and decidable theory. Thus deduction and consistency are not decidable in
logic, and an analogue of Rice's Theorem holds for recursively enumerable
theories: all the non-trivial properties of such theories are undecidable
