In J. C. Beall (ed.), New Essays on the Semantics of Paradox. Oxford University Press (2003)
|Abstract||Philosophers disagree about whether vagueness requires us to admit truth-value gaps, about whether there is a gap between the objects of which a given vague predicate is true and those of which it is false on an appropriately constructed sorites series for the predicate—a series involving small increments of change in a relevant respect between adjacent elements, but a large increment of change in that respect between the endpoints. There appears, however, to be widespread agreement that there is some sense in which vague predicates are gappy which may be expressed neutrally by saying that on any appropriately constructed sorites series for a given vague predicate there will be a gap between the objects of which the predicate is deﬁnitely true and those of which it is deﬁnitely false. Taking as primitive the operator ‘it is deﬁnitely the case that’, abbreviated as ‘D’, we may stipulate that a predicate F is deﬁnitely true (or deﬁnitely false) of an object just in case ‘DF (a)’, where a is a name for the object, is true (or false) simpliciter.1 This yields the following conditional formulation of a ‘gap principle’: (DΦ(x) ∧ D¬Φ(y)) → ¬R(x, y). Here ‘Φ’ is to be replaced with a vague predicate, while ‘R’ is to stand for a sorites relation for that predicate: a relation that can be used to construct a sorites series for the predicate—such as the relation of being just one millimetre shorter than for the predicate ‘is tall’. Disagreements about the sense in which it is correct to say that vague predicates are gappy can then be recast as disagreements about how to understand the deﬁnitely operator. One might give it, for example, a pragmatic construal such as ‘it would not be misleading to assert that’; or an epistemic construal such as ‘it is known that’ or ‘it is knowable that’; or a semantic construal such as ‘it is true that’.|
|Keywords||vagueness observational predicates supervaluationism truth-value gap higher-order vagueness sorites paradox|
|Through your library||Configure|
Similar books and articles
Pablo Cobreros (2010). Paraconsistent Vagueness: A Positive Argument. Synthese 183 (2):211-227.
Susanne Bobzien (2002). Chrysippus and the Epistemic Theory of Vagueness. Proceedings of the Aristotelian Society 102 (1):217-238.
Michael Tye (1994). Why the Vague Need Not Be Higher-Order Vague. Mind 103 (409):43-45.
Achille C. Varzi (2003). Higher-Order Vagueness and the Vagueness of ‘Vague’. Mind 112 (446):295–298.
Elia Zardini (2013). Higher-Order Sorites Paradox. Journal of Philosophical Logic 42 (1):25-48.
Diana Raffman (2009). Demoting Higher-Order Vagueness. In Sebastiano Moruzzi & Richard Dietz (eds.), Cuts and Clouds. Vaguenesss, its Nature and its Logic. Oxford University Press.
Diana Raffman (forthcoming). Vagueness and Observationality. In Giuseppina Ronzitti (ed.), Vagueness: A Guide. Springer.
Nicholas J. J. Smith (2005). Vagueness as Closeness. Australasian Journal of Philosophy 83 (2):157 – 183.
Added to index2009-01-28
Total downloads28 ( #44,147 of 549,196 )
Recent downloads (6 months)4 ( #19,303 of 549,196 )
How can I increase my downloads?