Vagueness and Modality

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.

B. Morison & K. Ierodiakonou (eds), Episteme, etc. , 2012

ABSTRACT: The purpose of this paper is to challenge some widespread assumptions about the role of the modal axiom 4 in a theory of vagueness. In the context of vagueness, axiom 4 usually appears as the principle ‘If it is clear (determinate, definite) that A, then it is clear (determinate, definite) that it is clear (determinate, definite) that A’, or, more formally, CA → CCA. We show how in the debate over axiom 4 two different notions of clarity are in play (Williamson-style "luminosity" or self-revealing clarity and concealeable clarity) and what their respective functions are in accounts of higher-order vagueness. On this basis, we argue first that, contrary to common opinion, higher-order vagueness and axiom 4 are perfectly compatible. This is in response to claims like that by Williamson that, if vagueness is defined with the help of a clarity operator that obeys axiom 4, higher-order vagueness disappears. Second, we argue that, contrary to common opinion, (i) bivalence-preservers (e.g. epistemicists) can without contradiction condone axiom 4 (by adopting what elsewhere we call COLUMNAR HIGHER-ORDER VAGUENESS), and (ii) bivalence-discarders (e.g. open-texture theorists, supervaluationists) can without contradiction reject axiom 4. Third, we rebut a number of arguments that have been produced by opponents of axiom 4, in particular those by Williamson. (The paper is pitched towards graduate students with basic knowledge of modal logic.)

this volume) do two main things in their insightful paper. 1 They defend the intelligibility of the idea of metaphysical indeterminacy, and they present a new theoryof metaphysical indeterminacy, one which is fully classical and bivalent. Their main project is the second one, but I will also pause for some time on the first. While for the most part talking about indeterminacy, I will also compare the more narrowissue of vagueness. Keeping the distinction between indeterminacy and vagueness sharply in mind will prove analytically useful at various points.

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.

2011

Peter van asks: when do some things compose a further thing? Those who accept unrestricted theories of composition hold that composition either always occurs or never occurs; those who instead accept restricted theories claim that composition occurs sometimes but not always. Van Inwagen infamously defends a restricted theory, organicism, according to which some things compose a further thing iff their activity constitutes a life. But since it is oftentimes indeterminate whether the activity of certain things constitutes a life, organicism entails that it is oftentimes indeterminate whether composition occurs. Such indeterminacy is not rooted in semantic indecision or our epistemic limitations: it is metaphysical indeterminacy.

Philosophy and Phenomenological Research, 2017

This is a paper about the nature of metaphysical laws and their relation to the phenomenon of vagueness. Metaphysical laws are introduced as analogous to natural laws, and metaphysical indeterminism is modeled on causal indeterminacy. This kind of indeterminacy is then put to work in developing a novel theory of vagueness and a solution to the sorites paradox.

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.

philosophy.stanford.edu

Forthcoming in Canadian Journal of Philosophy I will here present a number of problems concerning the idea that there is ontological vagueness, and the related claim that appeal to this idea can help solve some vagueness-related problems. A theme underlying the discussion will be the distinction between vagueness specifically and indeterminacy more generally (and, relatedly, the distinction between ontological vagueness and ontological indeterminacy). Even if the world is somehow ontologically indeterminate it by no means follows that it is, properly speaking, ontologically vague. 1

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."