The present work aims to establish the unity of logic in the same sense as Girard's well-known work yet without having recourse to polarities. Our motivations are to reduce various logics into a single one, clarify the dichotomy between linearity and non-linearity (resp. intuitionisity and classicality) in logic, and further prove that actually we do not need polarities for the unity of logic. Our starting conjecture is that there would be mathematically precise operations of unlinearization and classicalization on logic such that the unlinearization of classical linear logic (CLL) (resp. intuitionistic linear logic (ILL}) coincides with classical logic (CL) (resp. intuitionistic logic (IL)), and the classicalization of IL (resp. ILL) with CL (resp. CLL), where the two operations are compatible in the sense of the evident commutativity. Nevertheless, CLL, in contradiction to the name, is actually not the classicalization of ILL, and CL is not the unlinearization of CLL, both of which are obvious from a game-semantic analysis. The main contribution of the present work is then to prove the conjecture in terms of sequent calculi except that CLL is replaced with its negative fragment, which let us call classical linear logic negative (CLLN).