Online research in philosophy

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.

I go through, and criticize, Stephen Schiffer's account of vagueness and the sorites paradox. I discuss his notion of a happy-face solution to a paradox, his appeal to vagueness-related partial belief, his claim that indeterminacy is a psychological notion, and his view that the sorites premise and the inference rule of modus ponens are indeterminate.

This paper defends a pragmatical approach to vagueness. The vagueness-adaptive logic VAL is a good reconstruction of and an excellent instrument for human reasoning processes in which vague predicates are involved. Apart from its proof-theory and semantics, a Sorites-treating model based on it is presented, disarming the paradox. The paper opens perspectives with respect to the construction of theories by means of vague predicates.

This paper defends a pragmatical approach to vagueness. The vagueness-adaptive logic VAL is a good reconstruction of and an excellent, instrument for human reasoning processes in which vague predicates are involved. Apart from its proof-theory and semantics, a Sorites-treating model based on it is presented, disarming the paradox. The paper opens perspectives with respect to the construction of theories by means of vague predicates.

In this paper I argue, first, that the only difference between Epistemicism and Nihilism about vagueness is semantic rather than ontological, and second, that once it is clear what the difference between these views is, Nihilism is a much more plausible view of vagueness than Epistemicism. Given the current popularity of certain epistemicist views (most notably, Williamson’s), this result is, I think, of interest.

In the introduction to their vagueness reader, Rosanna Keefe and Peter Smith classified accounts of vagueness with respect to how they handle the sorites paradox. The sorites paradox is set out in the standard way with reference to a sorites se- quence s of objects s1, . . . , sn and an associated vague predicate F . In S, there is a very small and seemingly negligible difference between any two adjacent elements si and si +1 with respect to the dimension that is relevant to satisfying F (for instance, if F is ‘. . . is tall’, then the dimension is height). This suggests that if si satisfies F , then so does si +1. Since S is a sorites sequence for F it is also stipulated that s1 satisfies F and that sn does not. Let ti denote si, 1 ≤ i ≤ n. Then the sorites argument is set up as..

It is taken for granted in much of the literature on vagueness that semantic and epistemic approaches to vagueness are fundamentally at odds. If we can analyze borderline cases and the sorites paradox in terms of degrees of truth, then we don’t need an epistemic explanation. Conversely, if an epistemic explanation suffices, then there is no reason to depart from the familiar simplicity of classical bivalent semantics. I question this assumption, showing that there is an intelligible motivation for adopting a many-valued semantics even if one accepts a form of epistemicism. The resulting hybrid view has advantages over both classical epistemicism and traditional many-valued approaches.

The ancient sorites paradox is traditionally attributed to Eubulides, a contemporary of Aristotle and a member of the Megarian school, who is also credited with inventing the liar paradox. The sorites paradox figures centrally in most discussions of vagueness in philosophy and in logic. In my view, it has profound implications for metaphysics and semantics, as well as for logic. In this paper I will briefly explain why I think so, in a way that draws upon my other [1] writings on vagueness. The paper also will constitute a brief, opinionated, overview of the..

The naive theory of vagueness holds that the vagueness of an expression consists in its failure to draw a sharp boundary between positive and negative cases. The naive theory is contrasted with the nowadays dominant approach to vagueness, holding that the vagueness of an expression consists in its presenting borderline cases of application. The two approaches are briefly compared in their respective explanations of a paramount phenomenon of vagueness: our ignorance of any sharp boundary between positive and negative cases. These explanations clearly do not provide any ground for choosing the dominant approach against the naive theory. The decisive advantage of the former over the latter is rather supposed to consist in its immunity to any form of sorites paradox. But another paramount phenomenon of vagueness is higher-order vagueness: the expressions (such as ‘borderline’ and ‘definitely’) introduced in order to express in the object language the vagueness of the object language are themselves vague. Two highly plausible claims about higher-order vagueness are articulated and defended: the existence of “definitely ω ” positive and negative cases and the “radical” character of higher-order vagueness itself. Using very weak logical principles concerning vague expressions and the ‘definitely’-operator, it is then shown that, in the presence of higher-order vagueness as just described, the dominant approach is subject to higher-order sorites paradoxes analogous to the original ones besetting the naive theory, and therefore that, against the communis opinio , it does not fare substantially better with respect to immunity to any form of sorites paradox.

The purpose of this paper is to challenge some widespread assumptions about the role of the modal axiom S4 in a theory of vagueness. In the context of vagueness, S4 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. In this paper, we argue first that, contrary to common opinion, higher-order vagueness and S4 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 S4, higher-order vagueness disappears. Second, we argue that, contrary to common opinion, (i) bivalence-preservers (e.g. epistemicists) can without contradiction condone S4, and (ii) bivalence-discarders (e.g. open-texture theorists, supervaluationists) can without contradiction reject S4. To this end, we show how in the debate over S4 two different notions of clarity are in play and what their respective functions are in accounts of higher-order vagueness. Third, we rebut a number of arguments that have been produced by opponents of S4, in particular those by Williamson.