Return to Logic: the Case for Paraconsistent Logic

Standard logic is explosive, that is, anything follows from a true contradiction. This is a semantic consequence of the fact that standard logic does not admit of true contradictions. However, if a logic admits of true contradictions and therefore does not have explosiveness as a semantic consequence, one can avoid explosiveness and have a paraconsistent logic. The question remains: Is there a true contradiction?

There is. Each person is an individual, that is, is unique, particularly in their perspective. However, the very fact that this is true for every person creates a paradox: in our uniqueness, we are all the same. This is a paradox, a contradiction, but is it true? Can two persons share a perspective? If so, then differences could only come through the constitution of the persons. Is every person internally unique? Even if two persons start out as internally exactly similar and share a perspective, is it inevitable that one of them will change, thus making them both unique?

All that aside, it remains the case that if this contradiction is true, then the justification for explosiveness fails, thus making the logic paraconsistent. This means that not anything follows from a contradiction, so some standard theorems also fail; one of those that fails is "P -> (~P -> Q)".