On Presuppositional Implicatures


Scalar implicatures arise when a speaker uses a logically weak alternative in a context where a logically stronger alternative was available. Presuppositional implicatures, as I call them, arise when a speaker uses a presuppositionally weak alternative when a presuppositionally stronger alternative was available. My goal is to give a detailed, working theory of presuppositional implicatures, and show that they are a special case of scalar implicatures. In doing so, I carefully contrast presuppositional implicatures with antipresuppositions. These two phenomena have been treated as closely related in the literature, but some differences have not been adequately appreciated. Antipresuppositions are observed when a presuppositionally weak alternative is infelicitously used in a context that satisfies the presupposition of a presuppositionally stronger alternative. Presuppositional implicatures arise when a presuppositionally weak alternative is felicitously used in a context that does not satisfy the presupposition of a presuppositionally stronger alternative, but where that stronger presupposition would have been accommodated. Attention to this difference reveals a shortcoming in Schlenker’s (Nat Lang Semant 20:391–429, 2012) theory of presuppositional implicature. This paper both identifies and remedies that shortcoming.

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  1. 1.

    My reservations about this model are apparent in, for example, (Leahy 2014). However, the alternative to the Stalnakerian framework I prefer is not yet sufficiently developed to motivate the position I take in this paper; consequently I adopt Stalnaker's framework to make my position clear.

  2. 2.

    He notes that he first heard the term from von Fintel.

  3. 3.

    I suspect that some philosophers will object to this example, since the assertive contents of (3a) and (3b) may not be equivalent; (3b) may also assert that John meets some kind of justification condition. I am sympathetic to this objection, and so I also provide example (4). For more discussion, see footnote 6.

  4. 4.

    I am ignoring here the non-vacuity presupposition of quantified sentences, described in (von Fintel 1998: 30), since it is shared by both (4a) and (4b). Similarly, following (Musan 1997), (3a) and (3b) both presuppose that John is alive; this presupposition can be safely ignored when our goal is to compare the relative logical strength of the presuppositions of alternatives.

  5. 5.

    A referee offered an alternative definition of contextual equivalence, which differs both from mine (V) and Schlenker’s (III). Call the referee’s proposal Invariant Contextual Equivalence:

    (ICE) Invariant Contextual Equivalence

    If F and F′ are sentences, and for every context C that satisfies the presuppositions of both,

    {w∈C: F is trueC in w} = {w∈C: F′ is trueC in w},

    then F and F′ are invariant contextual equivalents.

    The referee correctly notes that this definition of contextual equivalence (with appropriate adjustments to (MP)) accounts for most of the presuppositional implicature data described in this paper. However, I wish to leave open the possibility that presuppositional implicatures arise between competing alternatives that are not invariant contextual equivalents when contextual factors conspire to render the asserted contents of alternatives (potentially) equivalent in that context.

    For example, on some views, ‘X knows p’ presupposes that p and asserts that X believes p and X has a good/justifying reason for believing that p. Then consider an utterance of (i-a):

    1. a.

      John believes that Bill is sad.

      • Presupposition: ∅

      • Assertion: John believes that Bill is sad.

    2. b.

      John knows that Bill is sad.

      • Presupposition: Bill is sad.

      • Assertion: John believes that Bill is sad and John’s belief is justified.

    The assertion of (i-b) is strictly logically stronger than that of (i-a) (on the view at hand), as is the presupposition. If we adopt this view of knowledge claims, then a theory of presuppositional implicatures that appeals to potential contextual equivalence (V) predicts antipresuppositions that a theory that appeals to ICE does not predict. For (i-a) and (i-b) are not ICE, and so will not be compared by the resulting version of MP. (i-a) and (i-b) are potential contextual equivalents in contexts that entail, for example, that all of John’s beliefs are justified, or that if John believes that Bill is sad, then John’s belief is justified. An assertion of (i-a), in such a context and on my theory of presuppositional implicature, predicts the implicature that Bill is not sad. I take this to be a desirable consequence.

  6. 6.

    A referee objected to my habit of calling (4a) ‘presuppositionally weak’ instead of ‘nonpresuppositional’. Note that if an utterance is nonpresuppositional, it is presuppositionally weak, but not vice versa. (MP-PI), like all other versions of (MP), says that speakers should prefer presuppositionally strong alternatives over all weaker alternatives, not just nonpresuppositional alternatives. So ‘presuppositionally weak’ cannot in full generality be replaced with ‘nonpresuppositional’. This is especially clear in the light of footnote 5, which points out that (4a) is not in fact nonpresuppositional; however, we have ignored the presuppositions that (4a) shares with (4b) in the name of simplification.

  7. 7.

    A referee asked me to comment on Schlenker’s theory of antipresuppositions. Very briefly and very roughly, Schlenker extends his proposal for presuppositional implicatures to antipresuppositions by arguing that even if a proposition is entailed by the common ground, there is always a nonzero chance that an addressee has forgotten (or isn’t adequately attending to) this fact. This is called the principle of Fallibility. Consequently, there is some expected value in reintroducing this fact into the conversation. So it is rational for speakers to reintroduce this fact into the conversation.

    Schlenker provides the example in (iv). In a context where it is obviously raining, (iv a) is pragmatically infelicitous, although in this context it has exactly the same informational content as (iv b). There is a nonzero probability that the addressee has forgotten the rain, and so there is nonzero probability that marking that information by choosing (vi b) over (iv a) increases informativeness.

    1. a.

      John believes that it is raining.

    2. b.

      John knows that it is raining.

    Schlenker notes that while the motivation for Fallibility is largely theory-internal, there is some independent motivation. He argues that the expected payoff of choosing the presuppositionally stronger alternative is always slightly higher than choosing the presuppositionally weaker alternative. For there is no extra cost associated with the stronger alternative and there is some additional expected payoff, since there is nonzero probability that the audience has forgotten (or isn’t adequately attending to) the additional presupposition. While I do not have a worked-out critique, I do have the following concern. Schlenker asserts but does not argue that there is no extra cost associated with the stronger alternative. But this needn’t be the case, for example, if the stronger alternative takes longer to produce. Of course, this extra cost may be very small, but then, so is the extra payoff produced by choosing this alternative when the probability of forgetting is very small.

    So the motivation for Fallibility is, indeed, largely theory-internal. As far as I can tell, my proposal for presuppositional implicatures could be extended to antipresuppositions using the same tools. However, I choose to be conservative for the moment, and remain agnostic regarding how we should account for antipresuppositions.


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I thank Maribel Romero and the Linguistics community at University of Konstanz for feedback on this project during its development. Filippo Domaneschi and two referees provided useful and supportive feedback. Research for this paper was supported by Deutsche Forschungsgemeinschaft Research Group 1614 “What if: On the meaning, relevance, and epistemology of counterfactual claims and thought experiments”.

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Leahy, B. On Presuppositional Implicatures. Topoi 35, 83–91 (2016). https://doi.org/10.1007/s11245-014-9281-4

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  • Antipresupposition
  • Presuppositional implicature
  • Philippe Schlenker
  • Presupposition accommodation