Online research in philosophy

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.

Saul Kripke pointed out that whether or not an utterance gives rise to a liar-like paradox cannot always be determined by checking just its form or content.1 Whether or not Jones’s utterance of ‘Everything Nixon said is true’ is paradoxical depends in part on what Nixon said. Something similar may be said about the sorites paradox. For example, whether or not the predicate ‘are enough grains of coffee for Smith’s purposes’ gives rise to a sorites paradox depends at least in part on what Smith’s purposes are. If Smith’s purpose is to make some coffee to drink, so that he can wake up and start his day, then we would be inclined to accept, and would find it strange to deny the following sorites sentence.

ABSTRACT: Recently a bold and admirable interpretation of Chrysippus’ position on the Sorites has been presented, suggesting that Chrysippus offered a solution to the Sorites by (i) taking an epistemicist position1 which (ii) made allowances for higher-order vagueness.2 In this paper I argue (i) that Chrysippus did not take an epistemicist position, but − if any − a non-epistemic one which denies truth-values to some cases in a Sorites-series, and (ii) that it is uncertain whether and how he made allowances for higher-order vagueness, but if he did, this was not grounded on an epistemicist position.

The theory of consciousness proposed by O'Brien & Opie is open to the Sorites paradox, for it defines a consciousness system internally in terms of computationally relevant units which add up to consciousness only if sufficient in number. The Sorites effect applies on the assumed level of features.

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 past twenty or so years have seen the sorites paradox receive a good deal of philosophical air-time. Yet, in what is surely a sign of a good puzzle, no consensus has emerged. It is perhaps a good time to stop and take stock of the current status of the sorites paradox. My main contention is that the proposals offered to date as ways of blocking the paradox are seriously deficient, and hence there is, at present, no acceptable solution to the sorites. In the final section I argue that, although vagueness is the source of the threat to modus ponens engendered by the sorites, it is also vagueness that protects modus ponens from clear counterexample.

I begin by highlighting the importance of the step size in the induction step of the sorites paradox. A careful analysis reveals that the step size can be characterised as a proper instance of the concept very small . After having accurately described the structure of sorites-susceptible predicates, I argue that the structure of the induction step in the Sorites Paradox is inherently circular. This circularity emerges in the structure of Wang's paradox and also of the classical variations of the paradox with the young, bald, etc. predicates.

Call an argument a ‘happy sorites’ if it is a sorites argument with true premises and a false conclusion. It is a striking fact that although most philosophers working on the sorites paradox find it at prima facie highly compelling that the premises of the sorites paradox are true and its conclusion false, few (if any) of the standard theories on the issue ultimately allow for happy sorites arguments. There is one philosophical view, however, that appears to allow for at least some happy sorites arguments: strict finitism in the philosophy of mathematics. My aim in this paper is to explore to what extent this appearance is accurate. As we shall see, this question is far from trivial. In particular, I will discuss two arguments that threaten to show that strict finitism cannot consistently accept happy sorites arguments, but I will argue that (given reasonable assumptions on strict finitistic logic) these arguments can ultimately be avoided, and the view can indeed allow for happy sorites arguments.

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..