Abstract
I consider two possible sources of vagueness. The first is indeterminacy about which intension is expressed by a word. The second is indeterminacy about which referent (extension) is determined by an intension. Focusing on a Fregean account of intensions, I argue that whichever account is right will matter to whether vagueness turns out to be a representational phenomenon (as opposed to being “in the world”). In addition, it will also matter to whether supervaluationism is a viable semantic framework. Based on these considerations, I end by developing an argument against supervaluational semantics that depends, instead, on anti-Fregean (Millian) assumptions.
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Notes
- 1.
Russell (1923).
- 2.
I use “object” liberally to apply to the referent of our words including properties, relations, and their extensions.
- 3.
I want to put aside Frege’s own views on the question of vagueness. Frege (1892) seems to think that concepts without determinate extensions don’t have Bedeutung. Commentators have pointed out that since the Bedeutung of a sentence is a truth-value, all sentences containing vague terms would lack a truth-value on Frege’s view. This is a costly conclusion. See Puryear (2013) and the references therein for further discussion.
- 4.
Jc Beall (2010) discusses “vague intensions” but treats them as having empty extensions (like Frege did). This is a costly move.
- 5.
Lewis (1993) holds that each precise object is a planet (which predicts there are countless planets in the vicinity of Venus). An alternative view says that each precise object is indeterminately a planet. I will assume the latter view.
- 6.
- 7.
- 8.
Russell (1923, p. 154).
- 9.
I am using “concept” here the way psychologists use it, to denote a mental entity not an abstract object or universal.
- 10.
Frege (1956).
- 11.
- 12.
Taking any sense, it will be a constituent of some proposition P. But now this proposition will be a constituent of some necessary proposition which is the disjunction of P and some truth of mathematics.
- 13.
There is a lot of literature challenging this last assertion. See King (2007) for a discussion challenging this last line of reasoning.
- 14.
Recall that we are making the simplifying assumption that the options are mutually exclusive and that there are no vague objects.
- 15.
As a simplifying assumption, I ignore tense.
- 16.
Fine (1975).
- 17.
The coordination may extend outside the boundaries of a sentence to an entire discourse or even between a mental state and a report as Brian Weatherson (2003) has pointed out. Weatherson’s paper is a response to Schiffer’s (1998) criticism of supervaluations. For a related response, see Keefe (2010).
- 18.
Schiffer (1998).
- 19.
Schiffer calls these propositions “vague” not “imprecise.”
- 20.
Garcia-Carpintero (2000, 2010) addresses Schiffer’s argument by invoking neo-Fregean machinery. According to his view, “there” and other expression taking on a de re interpretation in attitude contexts do not contribute their ordinary referents to the proposition expressed by that-clause. Instead, other representational entities may appear in the proposition expressed.
- 21.
Schiffer’s argument focuses on the “says” relation and I focus on “belief.” What follows is an adaptation of Schiffer’s argument to suit our purposes. One difference is that Schiffer does not focus on Fregean propositions but his argument carries over.
- 22.
- 23.
For simplicity, I ignore tense and context sensitivity.
- 24.
See also Hawthorne (2005).
- 25.
Roy Sorensen (2000) develops a different sort of puzzle for direct reference and supervaluations.
- 26.
See Williamson (1994, ch. 8).
- 27.
Discussions of margins of error in vagueness almost always concern sorites series. The case of Venus does not obviously admit of a sorites series but I see no reason why the same ideas cannot apply here.
- 28.
See Williamson (2007). However, the claim is derived from a more basic one.
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Pinillos, Á. (2014). Attitudes, Supervaluations, and Vagueness in the World. In: Akiba, K., Abasnezhad, A. (eds) Vague Objects and Vague Identity. Logic, Epistemology, and the Unity of Science, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7978-5_7
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