Paraconsistent vagueness: a positive argument

Supervaluationism is a well known theory of vagueness. Subvaluationism is a less well known theory of vagueness. But these theories cannot be taken apart, for they are in a relation of duality that can be made precise. This paper provides an introduction to the subvaluationist theory of vagueness in connection to its dual, supervaluationism.

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.

2015

We say that a sentence A is a permissive consequence of a set of premises ! whenever, if all the premises of ! 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.

In Williamson's 'Vagueness', he presents an epistemic view of vagueness. However, this view causes an anti-intuitive consequence. Neither epistemicists nor semanticists have given a satisfactory solution. Higher-order vagueness is one of the core issue in the research area of vagueness, on characterizing which Williamson rejects semantic views of vagueness mainly by their failure. However he himself does not characterize higher-order vagueness good enough. In this paper I find the essential reason of that anti-intuitive consequence, and offer a margin model of knowledge. This model is not only suitable for describing higher-order vagueness, but also can avoid the anti-intuitive consequence. 1 Epistemicism Epistemicism is a view about vagueness. Vagueness is phenomenon causing the sorites paradox. A typical example of the sorites paradox is: a grain of wheat does not make a heap, and if so then two grains of wheat do not make a heap, and if so then three grains of wheat do not make a heap, and so on ad infinitum. Thus we can say that ten thousand grains of wheat do not make a heap, which is clearly false. The fact is that we know one grain of wheat does not make a heap and we also know that ten thousand grains of wheat do make a heap, but we do not know whether a hundred grains of wheat make a heap. Therefore we call a hundred grains of wheat a borderline case of the predict 'heap'. The semantic view used to be the study's mainstream in the area of vagueness, which treats vagueness as a semantic phenomenon. Generally, people who hold the view think that the vague predicates such as 'tall', 'red', 'heap' and 'bold' are partially or unusually defined, which means the truth of propositions like 'a hundred grains of wheat make a heap' are void or something except Truth and Falsity. However, a different view on vagueness has become very active due to Williamson's monograph Vagueness published in 1994. In this book, he defends a view named epistemicism, and in this view, the semantics of vagueness predicts are precise but unknowable. There are two main standpoints of epistemicism: one is that the bivalence principle remains valid for vague propositions, and the other is that KK principle fails when knowledge is inexact for inexact knowledge is governed by the margin for error principles. In this paper I will not talk about the defense of the bivalence principle. We can just presuppose it. The margin for error principles and the failure of KK principle, on the contrary, will be explicated introduced for our purpose. The margin for error principles are actually reliability conditions for inexact knowledge. Williamson holds that when our knowledge is inexact, only if we leave a margin for error, the belief saying something is the case could be reliable enough to be knowledge. A belief has a margin for error means that in all situations similar enough to the actual situation, the thing is still the case. Let us look at an example, and we will see why inexact knowledge should be governed by the margin for error principles.

2017

Vagueness is a phenomenon whose manifestation occurs most clearly in linguistic contexts. And some scholars believe that the underlying cause of vagueness is to be traced to features of language. Such scholars typically look to formal techniques that are themselves embedded within language, such as supervaluation theory and semantic features of contexts of evaluation. However, when a theorist thinks that the ultimate cause of the linguistic vagueness is due to something other than language-for instance, due to a lack of knowledge or due to the world's being itself vague-then the formal techniques can no longer be restricted to those that look only at within-language phenomena. If, for example a theorist wonders whether the world itself might be vague, it is most natural to think of employing many-valued logics as the appropriate formal representation theory. I investigate whether the ontological presuppositions of metaphysical vagueness can accurately be represented by (finitely) many-valued logics, reaching a mixed bag of results.

Vagueness and Language Use. Palgrave McMillan, Oxford, 2010

This paper discusses Fara's so-called 'Paradox of Higher-Order Vagueness' concerning supervaluationism. In the paper I argue that supervaluationism is not committed to global validity, as it is largely assumed in the literature, but to a weaker notion of logical consequence I call 'regional validity'. Then I show that the supervaluationist might solve Fara's paradox making use of this weaker notion of logical consequence. The paper is discussed by Delia Fara in the same volume.

Vagueness and Language Use, 2011

There is an intuitive appeal to truth-value gaps in the case of vagueness. The idea is that the facts that determine the meaning of vague expressions (facts about use, most likely) left unsettled for a range of cases whether the expression applies. This sort of semantic unsettledness has been taken for a long time as a proper motivation for truth-value gaps; since it is unsettled whether the expression applies the correspoding sentence is neither true nor false.

2010

"ABSTRACT: The paper presents a new theory of higher-order vagueness. This theory is an improvement on current theories of vagueness in that it (i) describes the kind of borderline cases relevant to the Sorites paradox, (ii) retains the ‘robustness’ of vague predicates, (iii) introduces a notion of higher-order vagueness that is compositional, but (iv) avoids the paradoxes of higher-order vagueness. The theory’s central building-blocks: Borderlinehood is defined as radical unclarity. Unclarity is defined by means of competent, rational, informed speakers (‘CRISPs’) whose competence, etc., is indexed to the scope of the unclarity operator. The unclarity is radical since it eliminates clear cases of unclarity and, that is, clear borderline cases. This radical unclarity leads to a (bivalence-compatible, non-intuitionist) absolute agnosticism about the semantic status of all borderline cases. The corresponding modal system would be a non-normal variation on S4M. To view paper, click on "View on hdl.handle.net" below."

In this paper we propose to take seriously the claim that at least some kinds of paraconsistent negations are subcontrariety forming operators. We shall argue that from an intuitive point of view, by considering paraconsistent negations that way, one needs not worry with true contradictions and the like, given that "true contradictions" are not involved in these paraconsistent logics. Our strategy consists in showing that the natural translation for subcontrariety in formal languages is not a contradiction in natural language, and vice versa. This move shall provide for an intuitive interpretation for paraconsistent negation, which we also discuss here. By putting all those pieces together, we hope a clearer sense of paraconsistency can be made, one which may free us from the need to tame contradictions.

I develop a new theory of vagueness, which repudiates the notion of local indeterminacy (or borderline case) and replaces it with the notion of global indeterminacy.