Online research in philosophy

This paper considers a generalisation of the sorites paradox, in which only topological notions are employed. We argue that by increasing the level of abstraction in this way, we see the sorites paradox in a new, more revealing light—a light that forces attention on cut-off points of vague predicates. The generalised sorites paradox presented here also gives rise to a new, more tractable definition of vagueness.

In this paper, I argue against an influential view of Frege''s writings on indexical and other context-sensitive expressions, and in favour of an alternative. The centrepiece of the influential view, due to (among others) Evans and McDowell, is that according to Frege, context-sensitiveword-meaning plus context combine to express senses which are essentially first person, essentially present tense and so on, depending on the context-sensitive expression in question. Frege''s treatment of indexicals thus fits smoothly with his Intuitive Criterion of difference of sense. On my view, by contrast, Frege stuck by the view which he held in his unpublished 1897 Logic, namely that the senses expressed by the combination of context-sensitive word-meaning and context could just as well be expressed by means of non-context-sensitive expressions: being first person, present tense and so on are properties, in Frege''s view, only of language, not of thought. Given the irreducibility of indexicals – a phenomenon noticed by Castañeda, Perry and others – Frege''s treatment of indexicals thus turns out to be inconsistent with the Intuitive Criterion. I argue that Frege was not aware of the inconsistency because he was not aware of the irreducibility of indexicals. This oversight was possible because the source of Frege''s interest in indexicals, as inother context-sensitive expressions, differed from that of contemporary theorists. Whereas contemporary theorists are most often interested in indexicals (and in Frege''s treatment of them) because they are interested in the indexical versions of Frege''s Puzzle and their relation to psychological explanation, Frege himself was interested in them because they pose a prima facie threat to his general conception of thoughts. The only indexical expression Frege''s view of which the above account does not cover is I insofar as it is associated with special and primitive senses, but Frege did not introduce such senses with a view to explaining theirreducibility of I his real reason for introducing them remains obscure.

A rejoinder to G. Hull’s reply to my Mind 2003. Hull argues that Sorensen’s purported proof that ‘vague’ is vague--which I defended against certain familiar objections--fails. He offers three reasons: (i) the vagueness exhibited by Sorensen’s sorites is just the vagueness of ‘small’; (ii) the general assumption underlying the proof, to the effect that predicates which possess borderline cases are vague, is mistaken; (iii) the conclusion of the proof is unacceptable, for it is possible to create Sorensen-type sorites even for predicates that are paradigmatically precise. I argue that each of these points involves fallacious reasoning.

Vagueness manifests itself (among other things) in our inability to find boundaries to the extension of vague predicates. A semantic theory of vagueness plans to justify this inability in terms of the vague semantic rules governing language and thought. According to a supporter of semantic theory, the inability to find such a boundary is not dependent on epistemic limits and an omniscient being like God would be equally unable. Williamson (Vagueness, 1994 ) argued that cooperative omniscient beings adequately instructed would find a precise boundary in a sorites series and that, for this reason, the semantic theory misses its target, while Hawthorne (Philosophical Studies 122:1–25, 2005 ) stood with the semantic theorists and argued that the linguistic behaviour of a cooperative omniscient being like God would clearly demonstrate that he does not find a precise boundary in the sorites series. I argue that Hawthorne’s definition of God’s cooperative behaviour cannot be accepted and that, contrary to what has been assumed by both Williamson and Hawthorne, an omniscient being like God cannot be a cooperative evaluator of a semantic theory of vagueness.

In this paper I present two arguments against the thesis that we experience qualia. I argue that if we experienced qualia then these qualia would have to be essentially vague entities. And I then offer two arguments, one a reworking of Gareth Evans' argument against the possibility of vague objects, the other a reworking of the Sorites argument, to show that no such essentially vague entities can exist. I consider various objections but argue that ultimately they all fail. In particular I claim that the stock responses to the Sorites argument fail against my reworking of the argument because they require us to make a distinction between a determinate reality and how that reality appears to us, whereas in the case of qualia we can make no such distinction. I conclude that there can be no such things as qualia.

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.

In this paper I offer a critique of the recent popular strategy of giving a contextualist account of vagueness. Such accounts maintain that truth-values of vague sentences can change with changes of context induced by confronting different entities (e.g. different pairs through a sorites series). I claim that appealing to context does not help in solving the sorites paradox, nor does it give us new insights into vagueness per se. Furthermore, the contextual variation to which the contextualist is committed is problematic in various ways. For example, it yields the consequence that much of our everyday (non-soritical) reasoning is fallacious, and it renders us ignorant of what we and others have said.

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..

Jason Stanley has criticized a contextualist solution to the sorites paradox that treats vagueness as a kind of indexicality. His objection rests on a feature of indexicals that seems plausible: that their reference remains fixed in verb phrase ellipsis. But the force of Stanley’s criticism depends on the undefended assumption that vague terms, if they are a special sort of indexical, must function in the same way that more paradigmatic indexicals do. This paper argues that there can be more than one sort of indexicality, that one term might easily have both sorts, and that therefore, and despite Stanley’s worries, vagueness might easily be assimilated to one form.

According to what I will call a contextualist solution to the sorites paradox, vague terms are context-sensitive, and one can give a convincing dissolution of the sorites paradox in terms of this context-dependency. The reason, according to the contextualist, that precise boundaries for expressions like “heap” or “tall for a basketball player” are so difficult to detect is that when two entities are sufficiently similar (or saliently similar), we tend to shift the interpretation of the vague expression so that if one counts as falling in the extension of the property expressed by that expression, so does the other. As a consequence, when we look for the boundary of the extension of a vague expression in its penumbra, our very looking has the effect of changing the interpretation of the vague expression so that the boundary is not where we are looking. This accounts for the persuasive force of sorites arguments.