Negación dialéctica y lógica transitiva (I)

Abstract

In this essay I bring up the issue of how to deal with dialectical views -especialIy with dialectic negation- from the standpoint of a transitive logic, which is a particular paraconsistent logic.

After briefly tracing the development of the debate between dialectic thinkers and those who, hewing to entrenched logical theories, did out of hand reject any contradictorial proposal -up to recent developments of paraconsistent systems of mathematical logic- I canvass a variety of grounds shoring up the thesis of the contradictoriality of the world. Chief among them is fuzziness. The paper tries to show that fuzziness has nothing to do with uncertainty, and that accepting fuzzy sets and facts not only does not compel us to waive the law of excluded middle, but -on the base of reasonable presuppositions- entails recognition of that law's relevant instances -the ones that purportedly ought to be dropped as true sentences, should fuzziness be acknowledged. True enough, fuzziness plus excluded middle leads to contradiction, i.e. to negation inconsistency. But then fuzziness is -or can he viewed as being- negation inconsistency, since a fuzzy situation is one wherein something neither is nor fails to be the case: which -in virtue of involutivity of simple negation and De Morgan laws- means that something both ia and yet is not the case.
[L.P.]