Abstract
The Bridge Principle states that one shouldn’t assert a sentence that is indeterminate relative to possibilities that are still live options. This principle serves as a bridge between semantic and pragmatic presuppositions. I argue that, given the phenomenon of vagueness, the bridge principle cannot be true as formulated. An alternative formulation of the Bridge Principle is offered.
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Notes
Stalnaker (2014) claims that the notion of the pragmatic presupposition of a sentence is a derived one. However, that doesn’t prevent it from being theoretically useful.
Von Fintel (2008) claims that the source of pragmatic presuppositions is mostly conventional. In this paper I don’t need to take a stand on this issue.
To the best of my knowledge, Soames (1989) first pointed out that vagueness could be problematic for the Bridge Principle. This problem has also been discussed in Rayo (2008), Zehr (2013), and Spector (2016). At the end of the paper I offer some considerations to favor my solution to the problem over the solutions proposed by Rayo, Zehr, and Spector.
Of course, in a normal conversation we would presuppose that she isn’t a toddler, and that she isn’t two hundred years old either. Vagueness is lurking.
Thanks to an anonymous referee for helping me clarify this point.
Sometimes I think that when Stalnaker stated the Bridge Principle and its rationale he was idealizing vagueness away. Be that as it may, this principle has implications for vague assertions, and, as such, we should take them into account.
We can extract from Rayo (2008) an argument to the effect that there’s nothing wrong with principle (II). Rayo’s point is that in cases like Fodor’s Apartment interlocutors accommodate the context set by ruling out all those worlds where (FA) is indeterminate. Thus, after accommodation, (FA) is either true or false in every world in the resulting context set, securing compatibility with Stalnaker’s version of the Bridge Principle (II).
My problem with this strategy is that the only way in which worlds can be ruled out from the context set is by adding presuppositions to the common ground, and it isn’t clear at all which propositions can get the job done in this kind of case. So, in Fodor’s Apartment, accommodation must consist in the addition to the common ground of a proposition that rules out worlds from the context set where (FA) is indeterminate. However, it is far from clear which proposition could get the job done. It cannot be a vague one, because that would also violate principle (II). And it’s quite implausible to think that it is a precise proposition, because then it would be a mystery why a precise sentence wasn’t uttered instead of (FA) to begin with. I develop this objection in much more detail in (ms).
Of course, and Epistemicist would argue that I haven’t done such a thing. She would insist that at most my examples can be used to show that we are ignorant as to whether those worlds are in the context set, but that there’s always a fact of the matter as to whether a given world belongs to a set of worlds. That’s not an unreasonable proposal. However, in this paper I’m just going to assume, along with the majority, that vagueness is a semantic phenomenon.
Unless the semantic presuppositions of the relevant sentence are false at those worlds. I’ll say more about this bellow.
Supervaluationism faces some well known problems, as every other theory of vagueness does. Even though I am not convinced that Supervaluationism can solve its problems, it is of some theoretical value to see how this theory can help solving the problems that we face in this paper.
As we shall see, this way of thinking about things resembles a bit von Fintel and Gillies’ cloudy contextualism (Von Fintel and Gillies 2011).
By asserting a vague proposition one isn’t asserting all of the precisifications, rather it’s indeterminate which precisification one has asserted. Thanks to...for helping me clarify this point.
This rises an interesting question regarding the possibility of there being indeterminacy as to whether a sentence semantically presupposes a given proposition. The sentence “Mary knows that John is bald” presupposes that John is bald. But it also presupposes every admissible precisification of the vague proposition that John is bald: if one of those precisifications is not true, then the vague proposition would be indeterminate, at best. But now consider a proposition such that it is indeterminate whether it is an admissible precisification of the vague proposition that John is bald. It seems that it is indeterminate whether “Mary knows that John is bald” presupposes that proposition. Thanks to Martín Abreu for pointing this out. Now, this is an issue that comes up when we start thinking about higher-order vagueness. For the purposes of this paper I want to bracket all those issues.
Note that this is consistent with the knowledge norm of assertion. After the interlocutors accept a given assertion, it could be that it is indeterminate whether the actual world is in the context set. In a case like this, the speaker doesn’t know whether what she asserted is true: in this case the knowledge norm of assertion has been violated. This, however, isn’t a problem. Speakers sometimes violate that norm. Moreover, sometimes they violate that norm by asserting something that is false.
Fine (1975) is the first one to introduce the term “penumbral connection”.
It’s important not to confuse acceptability with admissibility. As we shall see briefly, acceptability is a constraint on intersection, whereas admissibility is a relation useful for defining the determinacy operator.
If the book I’m pointing at is borderline red and borderline orange, then the actual world is a member of a precisification of “this book is red” and of a precisification of “this book is orange”. Quite clearly these two precisification are not acceptable for intersection: if it were acceptable to intersect those precisification, the actual world would be a member of a precisification of “this book is both red and orange”. But this is absurd, so we need a constraint regarding which precisifications are admissible for intersection.
A way of formulating the principle that is perhaps closer to its intuitive version would be this: Only assert sentences S such that for every w in \({\cup}C\) there is a precisification of S that is either true or false relative to w. I prefer the formulation in the body of the text because it’s easier to explain instances of presupposition accommodation with it.
Zehr (2013) also has a nice paper arguing that an unified account of presupposition and vagueness requires more than three truth-values. That paper is concerned with truth-value judgments for vague and presuppositional sentences like it’s both false and not false. The data comes from the judgments of competent speakers. In this paper I’m not concerned with those kinds of judgments. However, my general attitude towards judgments like it’s both false and not false is to explain them away, rather than to take them at face value and making sure that our semantics captures them. This is not meant to be a refutation of Zehr (2013), I’m only flagging out that we may have a basic methodological disagreement.
To be more precise, in formulating the Bridge Principle I only appeal to the notion of a precisification of a sentence being true/false relative to a world. But, of course, the underlying logic is three-valued.
For many supervaluationists it is crucial that their logic is fully classical. Now, in the proposal I’m considering here, we can still reason in a classical way, so long as we are careful enough not to incur in instances of presupposition failure.
For their helpful comments, I'm grateful to Martín Abreu, Axel Barceló, Daniel Drucker, Andy Egan, Maite Ezcurdia, Katharina Felka, Eduardo García-Ramírez, Simon Goldstein, Andrea Iacona, Carlotta Pavese, Agustín Rayo, and Brian Weatherson.
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Mena, R. The Bridge Principle and Stigmatized Truth-Values. Topoi 40, 171–180 (2021). https://doi.org/10.1007/s11245-019-09649-2
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DOI: https://doi.org/10.1007/s11245-019-09649-2