5 research outputs found
Intransitivity and Vagueness
There are many examples in the literature that suggest that
indistinguishability is intransitive, despite the fact that the
indistinguishability relation is typically taken to be an equivalence relation
(and thus transitive). It is shown that if the uncertainty perception and the
question of when an agent reports that two things are indistinguishable are
both carefully modeled, the problems disappear, and indistinguishability can
indeed be taken to be an equivalence relation. Moreover, this model also
suggests a logic of vagueness that seems to solve many of the problems related
to vagueness discussed in the philosophical literature. In particular, it is
shown here how the logic can handle the sorites paradox.Comment: A preliminary version of this paper appears in Principles of
Knowledge Representation and Reasoning: Proceedings of the Ninth
International Conference (KR 2004
Vagueness, Truth and Permissive Consequence
We say that a sentence A is a permissive consequence of a set of premises Γ whenever, if all the premises of Γ hold up to some standard, then A holds to some weaker standard. In this paper, we focus on a three-valued version of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness toward a unified treatment of the paradoxes of vagueness and self-referential truth. For vagueness, st-consequence supports the principle of tolerance; for truth, it supports the requisit of transparency. Permissive consequence is non-transitive, however, but this feature is argued to be an essential component to the understanding of paradoxical reasoning in cases involving vagueness or self-reference