Partial Truth, Fringes and Motion: Three Applications of a Contradictorial Logic

Abstract

The paper argues that we can make good sense of the idea of contradictory truths -- as implemented in a paraconsistent infinite-valued system of logic, which is here put forward -- in three fields -- which have been claimed to be amenable to contradictorial treatments by the dialectical tradition -- namely those of partial truth, fringes of application of sundry predicates, and motion. The first is that, when a predicate correctly or truthfully applies to a part of some object but not to other parts thereof, it can only be said with partial truth that the object satisfies that predicate or has the property it denotes. The second problem arises because many predicates can be neither completely assigned to some things nor completely withheld from them. The 3d. problem is nothing else but Zeno's paradox of the arrow. The paper's gist is that in all cases true contradictions stem from graduality in things.