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**1 - 5**of**5**### Supervaluationism and Classical Logic

, 2009

"... The supervaluationist theory of vagueness provides a notion of logical consequence that is akin to classical consequence. In the absence of a definitely operator, supervaluationist consequence coincides with classical consequence. In the presence of ‘definitely’, we might find counterexamples to cla ..."

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The supervaluationist theory of vagueness provides a notion of logical consequence that is akin to classical consequence. In the absence of a definitely operator, supervaluationist consequence coincides with classical consequence. In the presence of ‘definitely’, we might find counterexamples to classically valid patterns of inference within supervaluationist reasoning. Foes of supervaluationism emphasize the last result to argue against the supervaluationist theory, concluding that ‘supervaluations invalidate our natural mode of deductive thinking ’ (Williamson, 1994, 152). This and related objections, however, do not consider particular ways in which we might provide systems of deduction for supervaluationist consequence. The present talk considers two ways in which we can carry out this task. Tableaux Supervaluationist semantics for a propositional language containing a definitely operator (‘D ’ henceforth) can be represented as a possible worlds

### Vagueness, tolerance and non-transitive entailment

"... 1 Tolerance and vagueness Vagueness is standardly opposed to precision. Just as gradable adjectives like ‘tall ’ and a quantity modifier like ‘a lot ’ are prototypical vague expressions, mathematical adjectives like ‘rectangular’, and measure phrases like ‘1.80 meter ’ are prototypically precise. Bu ..."

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1 Tolerance and vagueness Vagueness is standardly opposed to precision. Just as gradable adjectives like ‘tall ’ and a quantity modifier like ‘a lot ’ are prototypical vague expressions, mathematical adjectives like ‘rectangular’, and measure phrases like ‘1.80 meter ’ are prototypically precise. But what does it mean for these latter expressions to be precise? On first thought it just means that they are precise, because they have an exact mathematical definition. However, if we want to use these terms to talk about observable objects, it is clear that these mathematical definitions would be useless: if they exist at all, we cannot possibly determine what are the rectangular objects in the precise geometrical sense, or objects that are exactly 1.80 meters long. For this reason, one allows for a margin of measurement error, or a threshold, in physics, psychophysics and other sciences. Assuming that the predicates we use are observational predicates gives rise to another consequence as well. If statements like ‘the length of stick S is 1.45 meters ’ come with a large enough margin of error, the circumstances in which this statement can be made appropriately (or truly, if you don’t want the notion of truth to be empty) might overlap with the circumstances in which the statement ‘the The main ideas of this paper were first presented in a workshop on vagueness at

### Vagueness, Tolerance and Non-Transitive

"... Vagueness is standardly opposed to precision. Just as gradable adjectives like ‘tall’ and a quantity modifier like ‘a lot ’ are prototypically vague expressions, mathematical adjectives like ‘rectangular’, and measure phrases like ‘1.80 meters ’ are prototypically precise. But what does it mean for ..."

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Vagueness is standardly opposed to precision. Just as gradable adjectives like ‘tall’ and a quantity modifier like ‘a lot ’ are prototypically vague expressions, mathematical adjectives like ‘rectangular’, and measure phrases like ‘1.80 meters ’ are prototypically precise. But what does it mean for these latter expressions to be precise? On first thought it just means that they have an exact mathematical definition. However, if we want to use these terms to talk about observable objects, it is clear that these mathematical definitions would be useless: if they exist at all, we cannot possibly determine what are the existing (non-mathematical) rectangular objects in the precise geometrical sense, or objects that are exactly 1.80 meters long. For this reason, one allows for a margin of measurement error, or a threshold, in physics, psychophysics and other sciences. The assumption that the predicates we use are observational predicates gives rise to another consequence as well. If statements like ‘the length of stick S is 1.45 meters ’ come with a large enough margin of error, the circumstances in which this statement is appropriate (or true, if you don’t want the notion of truth to be empty) might overlap with the appropriate circumstances for uttering statements like ‘the length of stick S is 1.50 meters’. Thus, although

### J Philos Logic DOI 10.1007/s10992-010-9165-z Tolerant, Classical, Strict

, 2010

"... Abstract In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, theny should be P whenever y is similar enough to x. The semantics, which makes use of in ..."

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Abstract In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, theny should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases.

### Supervaluationism and necessarily borderline sentences

"... The supervaluationist theory of vagueness is committed to a particular notion of logical consequence known as global validity. According to a recent objection, this notion of consequence is more problematic than is usually thought since i) it bears a commitment to some sort of bizarre inferences, ii ..."

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The supervaluationist theory of vagueness is committed to a particular notion of logical consequence known as global validity. According to a recent objection, this notion of consequence is more problematic than is usually thought since i) it bears a commitment to some sort of bizarre inferences, ii) this commitment threatens the internal coherence of the theory and iii) we might find counterexamples to classically valid patterns of inference even in the absence of a definitely-operator (or similar device). As a consequence, the supervaluationist theory itself is in trouble. This paper discusses the objection.