Abstract
According to the plurivaluationist, our vague discourse doesn’t have a single meaning. Instead, it has many meanings, each of which is precise—and it is this plurality of meanings that is the source of vagueness. I believe plurivaluationist positions are underdeveloped and for this reason unpopular. This paper attempts to correct this situation by offering a particular development of plurivaluationism that I call supersententialism. The supersententialist leverages lessons from another area of research—the Problem of the Many—in service of the plurivaluationist position. The Problem reveals theoretical reasons to accept that there are many cats where we thought there was one; the supersententialist claims that we are in a similar situation with respect to languages, propositions and sentences. I argue that the parallel suggested by the supersententialist reveals unappreciated advantages and lines of defense for plurivaluationism.
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Notes
I am considering the view that Smith calls classical plurivaluationism. For ease of presentation, I drop the ‘classical’ qualification. Note, however, that as Smith uses the term, unqualified plurivaluationists are not committed to the claim that the many meanings are classical or precise. Nor are they committed to the claim that the plurality of meanings is the source of vagueness. (Smith ultimately defends a view he calls fuzzy plurivaluationism, which differs from classical plurivaluationism in denying both of these claims.)
Although Smith is the first to delineate (classical) plurivaluationism from supervaluationism, he does not endorse the view. Instead he endorses fuzzy plurivaluationism (see fn. 1). Lewis (1969, 1970, 1975) and Burns (1991) are read by Smith (2008) as endorsing plurivaluationism. (Although I disagree with this reading: see the end of Sect. 6 and fn. 27.) In the course of discussing a problem with speech reports and semantic plasticity, Dorr and Hawthorne (2014, §5 (esp. p. 333)) discuss a view of vagueness on which we are speaking many precise languages simultaneously but the view is not given an extended treatment. In his (2014, §3.4 (esp. fn. 13)), Dorr voices his endorsement of the view—although it is not defended. See also Varzi (2007) who delineates a view on which precisifications are treated as precise Lewisian languages. It’s not clear, however, whether the view he outlines is meant to include the claims Assertive Pluralism or Many Languages below.
Thanks to an anonymous referee for encouraging me to get clearer on the relationship between supersententialism and plurivaluationism.
A sentence of the vague language is true on a precisification when, roughly, the sentence of the language that would result from that way of making the vague language precise is true when evaluated at the actual world.
A more powerful model theory would more closely resemble the model theory of quantified modal logic (without a world designated as actual), thus allowing us to assign meanings to a richer uninterpreted language that contains a determinacy operator. The simpler model theory, however, suffices to illustrate the main points of this paper.
cf. Smith (2008, pp. 31–32). I offer a slightly revised definition in fn. 36.
I am ignoring higher-order vagueness here. With higher-order vagueness, the point is simply that (6) does not adopt the first-order vagueness of (1).
Keefe (2000) tries to lessen the incredulity of the supervaluationist position by pointing out that they can accept that the right and left hand side of instances of the T-schema are mutually entailing. This, however, is only the case on a impoverished view of supervaluationist entailment that is objectionable for other reasons. The problem re-arises for more sophisticated views (cf. Williams (2008)).
The conclusion also follows by similar reasoning from the revised definition of an intended model I give in fn. 36.
I take Smith to be talking about propositions by ‘claims’ (rather than sentences) for he takes claims to be true or false, but Thesis 1 denies that the notion of truth (simpliciter) applies to sentences.
This is not a criticism of Smith: his primary goal is to delineate supervaluationism and plurivaluationism.
Thanks to an anonymous referee for pressing me to discuss this alternative.
I am ignoring context sensitivity and disputes about the existence of propositions.
Cf. Andjelković and Williamson (2000). Although I won’t discuss it here, several authors have (i) suggested that the principle of uniformity indicates that (T*) is not definitional of truth and (ii) have explored whether to accept the principle of uniformity. See Dutilh Novaes (2008) for helpful discussion and references. Thanks to Catarina Dutilh Novaes for discussion.
Proof: Suppose for reductio that S says propositions \(q_1\) and \(q_2\), and \(q_1\) is a true proposition, but \(q_2\) is not a true proposition. Then one instance of (T*) implies that S is true, and another instance of (T*) implies that S is not true. Contradiction.
Faced with this difficulty, might we continue to hold that the truth predicate is vague but simply give up Assertive Pluralism? We might instead claim that in a given utterance, we assert just one precise proposition, but it’s vague which precise proposition is the one we assert. Because this position gives up Assertive Pluralism, it is no longer a plurivaluationist position (according to the envisaged theory one model is intended, but it’s vague which model that is) and cannot help itself to the plurivaluationist’s explanation for the unassertibility of borderline sentences. Instead the position becomes a form of what’s know as non-standard supervaluationism (cf. the position in Field (1994)) according to which our bivalent sentences have a single precise meaning but it’s indeterminate which meaning it has. Although I won’t discuss non-standard supervaluationism here, see Williamson (1994b, p. 164) for a criticism (He argues that the non-standard supervaluationist fails to give a non-circular account of the ‘philosophical significance’ of indeterminacy.)
Thanks to an anonymous referee for emphasizing this advantage of my proposal.
At least vague in the same way that the vagueness-philosopher claims—the plenitudinous-philosopher might admit vagueness as to which plurality of cat-candidates count as the many cats on the mat.
We might further require that the assignments conform to compositionality requirements so that the semantic value of a composite expression in the uninterpreted language is composed of the semantic values assigned to the parts of that expression. Languages are thus the functions generated by what Lewis calls ‘grammars’ on p. 175 of his (1975).
cf. fn. 36.
This would be akin to a sort of non-standard supervaluationism, according to which the meaning of our language is given by one classical model but it is indeterminate which that is. As Williamson (1994b, p. 164) correctly points out, this suggestion does not give a non-circular account of the ‘philosophical significance’ of indeterminacy.
Cf. Keefe (1998). Lewis writes “we are free to settle these indeterminacies however we like” (1975, p. 188) and “the different languages of the cluster...may be differently suited for individual opinions, tastes, and conversational purposes. If everyone can pick from the cluster, incompatible preferences among languages may all be satisfied” (1969, p. 202). (In other places, it should be noted, Lewis suggests a non-pragmatic treatment of vagueness more akin to supervaluationism.) Linda Burns (1991, p. 182), in developing Lewis’s pragmatism, makes similar statements such as “where there is vagueness speakers must be represented as alternating between members of a range of such languages” (182) and “speakers may adopt different languages from one another and shift from one language to another at different times” (186). Neither Lewis nor Burns make the claim of Assertive Pluralism or use it to explain why we do not assert borderline sentences.
Smith (2008) writes “Pragmatism, then, is simply a stylistic variant of plurivaluationism”. As should be clear by now, I disagree on two fronts. First, pragmatism can be developed in ways that are not plurivaluationist. Second, the pragmatic treatment of vagueness makes claims about the ontology of languages that are not part of the Central Claim of plurivaluationism. Part of the work of this paper is to show that those claims can form part of a talk-of-language account that can be leveraged to great effect.
Thanks to Chip Sebens for suggesting this example.
This appears to be Lewis’s view. See his (1975, p. 163). I suspect this is the more popular view, and may have been Smith’s view when he gave his talk-of-language account.
For instance, I could imagine someone saying that truth simpliciter is predicated of a plenitude of occurrences rather than a plenitude of sentences, where a given uninterpreted sentence can figure in many occurrences by occurring in different languages. Much of what I say below regarding a plenitude of sentences might be parroted for a plenitude of occurrences.
Of course the relevant notion of overlap used to define almost*-identity is not the mereological notion Lewis used to define almost-identity, but I take it that the notion is obvious enough. For example, take some suitable measure m. Two intentions \(i_1\) and \(i_2\) massively overlap if for all w in the domain of both \(i_1\) and \(i_2\), \(m(i_{1}(w) \cap i_{2}(w))\) is very close to \(m(i_{1}(w))\) and very close to \(m(i_{2}(w))\).
For more on the parallel between counting the many cats and the many languages, including how we react when the differences between the cats and languages are made salient or are relevant to our interests, see Reply 3 in Sect. 8.3.
This point is from MacFarlane (2014, §3.1.2)
Denying that expressions in an uninterpreted language have meanings requires a revision of the definitions of intended model and speaking a language that I gave in Sects. 1 and 6. A more careful definition of intended model is: a model for an uninterpreted language \(\mathcal {L}\) is intended for a community C when the model assigns to the parts of the uninterpreted language \(\mathcal {L}\) those meanings had by those parts on one of the languages spoken by C. We can similarly revise the minimal claim of what it means to say a community uses a language: a community uses a language \(\mathcal {L}\) when the language assigns to each expression of the uninterpreted language a meaning had by an expression that is co-tokened with the expression of the uninterpreted language.
The dialectic is more complicated than I am reproducing here. Schiffer also thinks that positing vague propositions cannot explain de re indirect speech reports in which singular terms scope over the that-clause. Much of García-Carpintero (2000, 2009) is dedicated to rebutting this claim. An alternative solution, given by Weatherson (2003) and Keefe (2009), posits a penumbral connection between the sentence (1) uttered by Hsiao and the that-clause in (17) such that, although determinately there is a unique precise proposition that is both expressed by Hsiao’s utterance of (1) and subsequently picked out by the that-clause in the indirect speech report, it is indeterminate which. That approach (i) cannot explain the assertibility of the negations of (13a)–(13c) and (ii) is effectively criticized by Rohrs (2017) for conflicting with the truism that a sentence adopts the truth-value of the proposition it expresses.
See Keefe (2000, Chapter 8) for this response.
This includes the main objection that is raised by Smith (2008) against classical plurivaluationism—that it violates the thesis he calls Closeness. As he argues, this complaint also applies to supervaluationism.
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Acknowledgements
Thanks to Mercedes Maria Corredor, Daniel Drucker, Jim Joyce, Jeremy Lent, Chip Sebens, Ted Sider, Eric Swanson, three anonymous referees and, especially, David Manley and Brian Weatherson for helpful conversations and comments. Thanks also to audiences at the University of Michigan, the University of San Diego, Colgate University, the 10th Annual Mark L. Shapiro Graduate Philosophy Conference (and my commentators Geoffrey Grossman and Yongming Han), and the 2018 Eastern APA (and my commentator Catarina Dutilh Novaes).
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Sud, R. Plurivaluationism, supersententialism and the problem of the many languages. Synthese 197, 1697–1723 (2020). https://doi.org/10.1007/s11229-018-1764-1
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DOI: https://doi.org/10.1007/s11229-018-1764-1