  A class of decision problems related to inconsistency proofs for formal
theories is used to show that under a constructive interpretation of
computational complexity classes, an assumption referred to as the MW thesis
implies that one may explicitly construct decision problems in NP which are not
algorithmically solvable. In particular, in this interpretation the MW thesis
implies P $\neq$ NP. It is argued that MW is a naturally valid, yet also
naturally unformalizable principle.
