Constructibility, computational complexity and P versus NP

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.