A Formal Skeleton of Reason

It has been said that in language and, therefore, ordinary reasoning, laws such as those of duality cannot be considered universally valid. They can be valid, but they are not always valid; their validity is local. Nor is it true that a conjunction is always commutative, that a negation is always strong or involutive, or that the principles of the excluded third and of noncontradiction are valid universally or locally, respectively, expressed in the forms \(p+p'= 1\) and \(p\cdot p'=0\) . These were previously presented and are particular cases of the more general form that will be presented later.