Abstract
It’s not clear what supervaluationists should say about propositional content. Does a vague sentence, e.g., ‘Harry is bald’, express one proposition, or a barrage of propositions, or none at all? Or is the matter indeterminate? The supervaluationist canon is not decisive on the issue; authoritative passages can be cited in favor of each of the proposals just mentioned. Furthermore, some detractors have argued that supervaluationism is incapable of providing any coherent account of propositional content. This paper considers each of the proposals for how many propositions are expressed by a vague sentence: none, some, all, or it’s indeterminate. Most of these proposals turn out to be unworkable in the metalanguage. I conclude that orthodox supervaluationists—those who identify truth with supertruth—must either relax the standard requirement that propositions be bivalent, or else alter the standard relation between sentences and propositions in which a sentence inherits its truth-conditions from the proposition it expresses. The best option going forward for the orthodox supervaluationist is perhaps the most surprising—amend the requirement that propositions be bivalent. I argue that propositions having supervaluational truth-conditions are best suited to fill the propositional roles in the semantic theory of a vague language. These propositions admit of truth-value gaps, and gappy propositions are controversial, but I argue that they earn their keep.
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Notes
Fine (1975, p. 270).
See Varzi (2007) for a taxonomy of supervaluationist logics.
Another way to make the same point, in the terminology of Burgess and Sherman (2014), is that there is work to be done in determining which metasemantic theories support supervaluationist semantics for the object-language.
Weatherson (2003) is another direct attempt to address the problems of propositional content raised here. Weatherson (2003, pp. 482–483) says precisification should be applied to a language as a whole, rather than to a single sentence or single term. He thinks this is a point of disagreement with Keefe, but Keefe (2000, pp. 162, 189) in fact agrees that precisification should be applied to the entire language. Weatherson then seems to share Keefe’s commitment to supervaluating “S expresses P” statements in the way that I criticize here. See also note 6 below.
That brief consideration occurs in the exchange between Schiffer (1998, 2000a, b) and García-Carpintero (2000, 2010). In the course of criticizing supervaluationism’s handling of indirect speech reports, Schiffer considers vague (non-bivalent) propositions and argues that they cannot adequately explain de re ascriptions such as ‘There is where Al said Ben was.’ In response, García-Carpintero (2010, p. 349) takes up these propositions that have supervaluational truth-conditions, along with a Frege-inspired doctrine of referential shift, in order to explain the relevant de re ascriptions. So, the position I defend here is in agreement with part of García-Carpintero’s proposal, though I do not consider the specific problem of de re ascriptions. Thanks to an anonymous reviewer at this journal for correcting an oversight on this point.
There are other views that employ admissible models in the semantics of vague languages, e.g. Asher et al. (2009). Some of my discussion may apply to such views, but some of it may not.
If you think it is impossible to extend or precisify the meaning of a term without changing that meaning, then you have sympathy with Fodor and Lepore (1996), as I do. But this is how supervaluationists put things.
I’m following Williamson (1994, p. 145) in treating LEM as the object language schema “A or not-A” and the principle of bivalence as the metalinguistic principle that, for any object language statement \(\upvarphi \), either \(\upvarphi \) is true or \(\upvarphi \) is false. Supertruth Semantics does not affirm bivalence.
Here and throughout, I will assume a fixed context for the evaluation of any vague sentence. Most vague sentences will have various candidate contents in various contexts. “In context c” could be added in the appropriate places.
One cannot in fact list the candidate contents of (3) because there can be neither a determinately first member nor a determinately last member—if there were either, this would create sharp cut-offs for the extension and antiextension of ‘is tall’, in which case there would be no higher-order vagueness for that term. Also, the propositions listed in (3a–d) are not necessarily bivalent, as candidate contents must be. It is in fact quite difficult to pick out an individual proposition that is necessarily bivalent that is about anything other than mathematical entities. This is because one cannot use vague terms to pick out such a proposition, and most natural language terms are vague—see the next note.
In the literature, arguments for the ubiquity of vagueness in natural language are brief. Cf. Williamson (1994, p. 165), Schiffer (2003, p. 4), Keefe (2000, p. 3), and Fine (1975, p. 266). The idea is that one sees the ubiquity of vagueness as soon as one begins to look for it. A fully adequate argument for the point would proceed by exhaustive enumeration; I spare the reader.
The metalanguage has a semantics that obeys Supertruth Semantics, so the truth of a metalanguage statement is truth on all admissible models. Which models are these? Keefe supervaluates the metalanguage over the same models used to supervaluate the object-language, so I will follow that practice. That seems to be the only practice that fits with the results of Keefe’s supervaluation of speech reports.
Because Supertruth Semantics supports the inference from “\(\upvarphi \) is supertrue” to “\(\upvarphi \) is true simpliciter,” I will use the abbreviation “\(\upvarphi \) is (super)true” for the phrase “\(\upvarphi \) is supertrue and therefore true simpliciter.” Mutatis mutandis for “\(\upvarphi \) is (super)false.”
Recall, from note 12, that I am pretending that (3a–d) are necessarily bivalent, even though they are not.
Determinacy operators and the semantics of ‘determinately’ are vexing. For present purposes, the determinacy operator may be ignored because Keefe’s theory makes ‘D\({\upphi }\)’ equivalent to ‘\(\upphi \) is supertrue’ (2010, pp. 208–211). So we are free to conduct the discussion in terms of supertruth without mentioning D and without losing anything.
There may be an argument that the current proposal is consistent with a weaker reading of Propositional Semantics. But a weaker reading would yield the principle that the proposition expressed by a sentence plays some part or other in determining the truth-conditions of that sentence. That principle is all-encompassing, and is therefore uninteresting. Even proponents of truth-conditional pragmatics can affirm the weak reading of Propositional Semantics, so the weak reading is not an apt criterion for delineating traditional propositional semantics. The interesting version of Propositional Semantics is the strict reading that makes the propositions expressed the exclusive determiners of sentential truth-conditions.
One might take Fine’s (1975, p. 277) comments on actual meaning and potential meaning to support the None Proposal.
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Acknowledgments
For helpful comments on drafts of this paper, thanks to Graeme Forbes, Graham Oddie, Michael Tooley, Raul Saucedo, Garrett Bredeson, Matthew Babb, David Neely, Peter van Elswyk, Cameron Domenico Kirk-Giannini, Rebecca Chan, Alex Zambrano, and Kelly Weirich. Thanks to Alex Lloyd for help with proofreading.
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Rohrs, B. Supervaluational propositional content. Synthese 194, 2185–2201 (2017). https://doi.org/10.1007/s11229-016-1051-y
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DOI: https://doi.org/10.1007/s11229-016-1051-y