Introduction

This note presents challenge cases for prominent pragmatic responses to the proviso problem. The proviso problem (Geurts 1996, 1999) is the problem for many theories of presupposition of explaining why sentences predicted to semantically presuppose ψP seem in certain uses to commit the speaker to an unconditional presupposition P — for instance, why a use of (1) would typically commit the speaker not merely to (1a) but to the logically stronger (1b).

  1. (1)

    If Alice wants to impress us, she will bring her wetsuit.

    1. a.

      Alice wants to impress us ⊃ she has a wetsuit

    2. b.

      Alice has a wetsuit

I focus primarily on speaker-based responses that attempt to derive the apparent unconditional presuppositions from an assumption of independence between ψ and P (van Rooij 2007, Schlenker 2011, Lassiter 2012); non-speaker-based responses invoking a mechanism of context repair are briefly considered (Heim 1992, 2006). I offer examples of uses of conditionals if\(\psi,\,\phi_{P}\) that seem to commit the speaker unconditionally to the presupposition P of the consequent clause ϕ even though independence between ψ and P isn’t antecedently assumed (contrary to independence-driven accounts) and the sentence’s predicted semantic presupposition ψP is antecedently satisfied (contrary to context-repair accounts).

The paper proceeds as follows. Section 2 introduces the proviso problem and the types of pragmatic accounts at issue. Section 3 presents the main challenge cases. Section 4 argues that the examples from Section 3 avoid problems with other examples from the literature used against pragmatic accounts. Section 5 takes stock.

Background

Satisfaction theories and the proviso problem

Uttering (2) would typically commit one to an assumption that Alice has a wetsuit. This commitment, unlike the commitment that Alice will bring the wetsuit she has, typically remains even when (2) is embedded in entailment-cancelling environments such as those in (3). In light of such behavior it is common to treat the implication that Alice has a wetsuit as a semantic presupposition of (2).Footnote 1

  1. (2)

    Alicei will bring heri wetsuit.

  1. (3)
    1. a.

      It’s not the case that Alice will bring her wetsuit.

    2. b.

      Will Alice bring her wetsuit?

    3. c.

      Perhaps Alice will bring her wetsuit.

Many theories of presupposition predict that if a sentence ϕ semantically presupposes P (written \(\phi_{P}\)), the presupposition of a conditional if\(\psi,\,\phi_{P}\) is the material conditional ψP. To fix ideas I focus on satisfaction theories (Heim 1983; Beaver 2001; cf. Klinedinst and Rothschild 2012).Footnote 2

Satisfaction theories aim to derive a sentence’s semantic presuppositions from its meaning — in dynamic semantics, its context change potential (CCP) — and a principle of context satisfaction. The semantic presuppositions of a sentence are represented as definedness conditions on the sentence’s CCP. If a sentence ϕ presupposes P, the CCP of ϕ is defined only on contexts that entail, or satisfy, P. The CCP is a partial function [ϕ] from contexts c that satisfy P, cP, to contexts in which ϕ is accepted. (I simplify by representing contexts as sets of worlds.) For instance, the CCP of (2) would be a partial function that (i) is defined only on contexts which entail that Alice has a wetsuit, i.e. contexts c such that [Alice has a wetsuit](c)=c, and (ii) maps any such c to the set of worlds in c where Alice brings her wetsuit:

  1. (4)

    [(2)](c)={wc:Alice brings the wetsuit that she has in w} if \(c \subseteq \{w'\colon \text{Alice has a wetsuit in }w'\}\), undefined otherwise

A sentence ϕ presupposes P iff for any context c, [ϕ](c) is defined only if c entails P.

Although every sentence is interpreted in a context with respect to a body of information, embedding environments may modify the information with respect to which embedded sentences are interpreted. The presupposition of a complex sentence is derived by ensuring that the presuppositions of its constituents are locally satisfied — satisfied in the (local) context in which the constituent is interpreted:

  1. (5)

    Local context satisfaction:

    For any sentence ϕ, the semantic presupposition of ϕ is the minimal condition ensuring that, for any constituent \(\psi_{P}\) of ϕ, the local context of ψ entails P.

The local satisfaction requirement generates a condition on the discourse context corresponding to the semantic presupposition of the sentence. Consider, for instance, the following CCP from Heim (1982, 1983):

  1. (6)

    \(c + \textit{if}\ \psi,\phi_{P} = c \backslash ((c + \psi) \backslash (c + \psi + \phi_{P}))\)

In order for the local update of \({c' = c+\psi}\) with \(\phi_{P}\) to be defined, \(c'\) must entail P; so, in order for the update as a whole to be defined, c must entail ψP. Given the local satisfaction principle in (5), the predicted semantic presupposition of if \(\psi,\,\phi_{P}\) is thus the material implication ψP.Footnote 3

The previous prediction is supported by examples such as (7) (cf. Soames 1982, Geurts 1996, Beaver 2001). Although (2) presupposes that Alice has a wetsuit, one would typically take a speaker of (7) to be committed only to the conditional that if Alice is a scuba diver, she has a wetsuit.

  1. (7)
    figure a

The “proviso problem” (Geurts 1996, 1999) is the problem of explaining why some uses of if\(\psi,\,\phi_{P}\) seem to presuppose not simply ψP, but P.Footnote 4 One would typically take a speaker of (8) — which has the same consequent \(\phi_{P}\) as (7) — to be committed to the stronger unconditional implication that Alice has a wetsuit.

  1. (8)
    figure b

Call the apparent implications P in certain uses of if\(\psi,\,\phi_{P}\) “unconditional P-implications.” The challenge for theories such as satisfaction theories is to explain what triggers unconditional P-implications and to delineate the uses in which they will (and will not) arise.

Pragmatic responses: Independence and context repair

A sentence’s semantic presupposition provides a minimal condition that a context must satisfy in order for the sentence to be felicitously used (accommodation notwithstanding; cf. Stalnaker 1974, Soames 1982, Beaver 1999, 2001, van Rooij 2007, von Fintel 2008). The principle in (9) relates the notion of semantic presupposition with conditions on felicitous use in this way.

  1. (9)

    Semantic presupposition and felicitous use:

    If a sentence ϕ presupposes P in c, then ϕ may be felicitously used in c only if c entails P.

A common approach to the proviso problem is to treat unconditional P-implications as pragmatic strengthenings of the sentence’s semantic (conventionally encoded) presupposition. On context-repair accounts, the strengthened P-implications are understood as inferences drawn in response to violations of (9) (cf. Heim 1992, 2006). The contexts in which unconditional P-implications arise are contexts in which the semantic presupposition ψP isn’t antecedently satisfied and (for reasons to be specified) the preferred means of repairing the context is to accommodate P. On speaker-based accounts, the strengthened P-implications are understood as inferences about what the speaker is presupposing, given her performance of an act which conventionally presupposes ψP (cf. Beaver 1999, 2001, von Fintel 2008). Prominent are independence-driven speaker-based accounts, which attempt to derive the unconditional inference P via pragmatic reasoning from the felicitous use of if\(\psi,\,\phi_{P}\) and an assumption of independence (in a sense to be made precise) between ψ and P (van Rooij 2007, Pérez Carballo 2009, Schlenker 2011, Lassiter 2012). The contexts in which unconditional P-implications arise are contexts in which ψ and P are assumed to be independent.

Section 3 offers challenge cases for certain prominent pragmatic responses to the proviso problem. I focus first on independence-driven speaker-based accounts using a non-probabilistic notion of independence. Accounts invoking an assumption of probabilistic independence or a mechanism of context repair are briefly considered.

Challenges for independence and context repair

Independent-driven accounts understand unconditional P-implications as inferences about the speaker’s presuppositions given her felicitous use of if\(\psi,\,\phi_{P}\), the sentence’s conventional meaning, and an assumption of independence between ψ and P. Adapting Lewis’s (1988) notion of orthogonal questions, van Rooij (2007) formalizes the relevant relation of independence as in (10), where \({\Diamond_{c}\phi\ \mathrm{iff_{def}}\ [\phi](c) \neq \emptyset}\). Roughly put, ϕ and ψ are independent in a context c iff committing to an answer on whether ϕ is true needn’t commit one to an answer on whether ψ is true, given the information in c. The unconditional P-implication is derived from a felicitous use of if\(\psi,\,\phi_{P}\) as in (11).

  1. (10)
    figure c
  1. (11)
    1. a.

      ψ and P are independent in c.   (assumption)

    2. b.

      \(\Diamond_{c} \psi\).   (felicity condition for indicative conditionals)

    3. c.

      c entails ψP.   (from semantic presupposition and (9))

    4. d.

      So, if \({\Diamond_{c}\psi \wedge \Diamond_{c}\neg P}\), then \({\Diamond_{c}(\psi \wedge \neg P)}\).   (from (a))

    5. e.

      So, \({\neg\Diamond_{c}\psi \vee \neg\Diamond_{c}\neg P}\).   (from (c), (d))

    6. f.

      So, \(\neg\Diamond_{c}\neg P\).   (from (b), (e))

    7. g.

      So, \(\Box_{c}{P}\).   (from (f))

This says that if a context c is compatible with ψ, and ψ and P are independent in c, then c entails the material conditional ψP only if c entails P unconditionally. Suppose the speaker felicitously utters if\(\psi,\,\phi_{P}\). Given the bridge principle in (9), we can infer that c entails the sentence’s semantic presupposition ψP, thus that c excludes ψ∧¬P, i.e. \(\neg\Diamond_{c}(\psi \wedge \neg P)\). So, insofar as ψ and P are assumed to be independent, either \(\neg\Diamond_{c}\psi\) or \(\neg\Diamond_{c}\neg P\) must be the case. But uttering an indicative conditional ifψ, ϕ is appropriate only if ψ is regarded as possible, i.e. \(\Diamond_{c}\psi\). So \(\neg\Diamond_{c}\neg P\), which is equivalent to \(\Box_{c} P\), must be the case, i.e. c entails P.

For example, whether someone has a wetsuit is typically independent of whether they want to impress us, though plausibly dependent on whether they are a scuba diver — hence the apparent unconditional implication in (8) and not in (7). As van Rooij puts it: upon hearing an utterance of if\(\psi,\,\phi_{P}\), “we either assume that [ψ] and [P] are independent, or not. If independence is more plausible,” as in (8), “the unconditional presupposition follows”; in (7), however, “it is [...] natural to assume that the independence assumption between [ψ] and [P] is not satisfied, and thus the conditional presupposition [ψP] cannot be strengthened to [P]” (van Rooij 2007: 298; cf. 303).

Problematic for this view would be uses of if\(\psi,\,\phi_{P}\) which intuitively imply P although a premise that ψ and P are independent cannot plausibly be assumed. The reasoning in (11) couldn’t get off the ground. Several examples are as follows.

Wintry weather is nigh. Whether one’s street gets plowed typically depends on whether it snows. It’s possible that the street will get plowed (◊plow), and it’s possible that it won’t snow (◊¬snow); but it isn’t possible that the street will get plowed without it snowing (¬◊(plow∧¬snow)). And yet you are incensed when your local government official tells you:

  1. (12)

    If it snows, I regret/know that your street won’t get plowed.

That is, it is “natural to assume that the independence assumption between [snow and ¬plow] is not satisfied” (van Rooij 2007: 298). And yet you draw the unconditional inference that your street won’t get plowed.

Or suppose NASA has been seeking recruits for a trial teleportation mission. The mission is, well, fraught, so only those in top physical condition will be chosen. You are acquainted with Alice, though you don’t know what she has been up to lately. Perhaps Alice will be teleported (◊teleport), and perhaps she hasn’t been training (◊¬training); but it couldn’t be that Alice is teleported and didn’t train every day (¬◊(teleport∧¬training)). I, who am better friends with Alice, say (13). You might assume that I must be more familiar with Alice’s routine, and respond as in (14).

  1. (13)

    If Alice gets teleported, she will be glad she has been training every day.

  1. (14)
    figure d

The strengthened inference that Alice has been training may be drawn although condition (ii) in (10) is violated.

The previous examples used factive attitude verbs. Examples with other types of presupposition triggers are also possible, as with the definite noun phrases and aspectual verbs in (15)–(16). One can imagine a context in which there is a music competition, and no one could make it to the finals without rigorous preparation.

  1. (15)

    If Sharon makes it to the finals,

    1. a.

      she will be glad she has been practicing every day.

    2. b.

      she will continue practicing every day.

    3. c.

      all the practicing she has been doing will be clear to the judges.

  1. (16)

    If Julian doesn’t make it to the finals,

    1. a.

      he will regret that he didn’t practice every day.

    2. b.

      he will start practicing every day.

    3. c.

      his lack of practice will have cost him a chance at a scholarship.

Upon hearing (15)–(16) one might infer that Sharon, unlike Julian, has been duly practicing.

The previous data are supported by results from an acceptability judgment task conducted via Amazon Mechanical Turk. Participants were 28 self-reported native English speakers, filtered to “Mechanical Turk Masters” with IP addresses from the US or Canada. Participants were presented with discourses including a target sentence if\(\psi,\,\phi_{P}\), followed by a “Hey wait a minute”-style (HWAM) reply echoing P (Shanon 1976, von Fintel 2004), like in (17).

  1. (17)
    figure e

Participants were asked how natural they found the replies on a scale from 1 (“completely unnatural”) to 7 (“completely natural”). The participants’ responses confirmed the availability of the strengthened P-implication readings, such as by finding the HWAM reply relatively natural or finding a counter-reply that denies the unconditional commitment (“I didn’t say P; (maybe) ¬P”) relatively unnatural. For instance, for (12), the average rating for the HWAM reply was 6.3 (SEM = .19); for (13), the average rating for the HWAM reply was 5.8 (SEM = .23); and for (15c), the average rating for the HWAM reply was 5.4 (SEM = .29). (See Appendix.)

Motivations for using HWAM replies were twofold. First, the HWAM diagnostic is widely acknowledged to be among the best ways of directly testing for a speaker’s pragmatic presuppositions in a particular utterance (von Fintel 2004, von Fintel and Matthewson 2008, Tonhauser et al. 2013). Second, what is important for present purposes is whether there is a plausible use of the target sentences which seems to imply P. Non-strengthened readings may also be possible. Soliciting judgments about HWAM replies extracts intuitions about the availability of strengthened readings while bracketing alternative ways of reconstructing the context.

The independence-driven account from van Rooij (2007) uses a non-probabilistic notion of independence. Examples such as (12)–(16) are also problematic for accounts such as Schlenker’s (2011) which treat unconditional P-implications as arising in contexts where the consequent presupposition P is regarded as probabilistically independent of the antecedent ψ, per (18). (Pr(p | q) is the conditional probability of p given q.)

  1. (18)

    p and q are probabilistically independent iff Pr(p)=Pr(p | q)

Probabilistic independence of ψ and P needn’t be assumed in (12)–(16) as a premise in one’s pragmatic reasoning. Typically the fact that it snows makes it more likely that your street will get plowed — hence your outrage upon receiving the official’s news in (12). The conditional probability of P given ψ here is plausibly less than the unconditional probability of P, i.e. Pr(P | ψ)<Pr(P). In (13)–(16), ψ and P cannot be assumed to be probabilistically independent for the opposite reason: Pr(P | ψ)>Pr(P). ψP is presupposed, and Pr(P | ψ) is (close to) 1. Yet P hasn’t been settled, and you aren’t independently au fait with Alice’s, Sharon’s, or Julian’s daily activities. So, the conditional probability is significantly greater than the unconditional probability of P.

Lassiter (2012) develops a sophisticated probabilistic account which he argues improves on Schlenker’s. In contexts where ψ can be assumed to be probabilistically independent of P or to lower the probability of P, the unconditional P-implication is derived via the argument in (19). (‘Pr(p)≥θ’ means that the probability of p is sufficiently high for p to count as taken for granted in the context, where θ is the threshold of probability sufficient for acceptance. Premise (a) is Lassiter’s posited felicity condition for the conditional sentence.)

  1. (19)
    1. a.

      Pr(P | ψ)≥θ

    2. b.

      Pr(P)≥Pr(P | ψ)

    3. c.

      So, Pr(P)≥θ

In (12), Pr(P)>Pr(P | ψ), per (19b). However, the availability of strengthened inferences in (13)–(16), where the conditional probability Pr(P | ψ) is assumed to be greater than the unconditional probability Pr(P), remains unexplained. (19b) cannot be assumed as a premise to derive the unconditional implications that Alice has been training every day, that Sharon has been practicing every day, etc.

Independence-driven accounts follow a speaker-based approach to the proviso problem, which treats unconditional P-implications as pragmatically derived inferences about what the speaker is presupposing. Examples such as (13)–(16) are also problematic for context-repair accounts (Section 2.2). Context-repair accounts claim that inferences P in response to a use of if\(\psi,\,\phi_{P}\) are responses to violations of the felicity condition in (9). Unconditional P-implications are predicted not to arise in contexts where the semantic presupposition ψP is already satisfied, as in (20).

  1. (20)

    If Lyle flies to Toronto, he has a sister. Moreover, if he flies to Toronto, his sister will pick him up from the airport.   (Katzir and Singh 2013: ex. 8a)

In (13)–(16) the strengthened inference may be drawn although the semantic presupposition is satisfied. In (13) the conditional presupposition teleporttraining follows from our background assumption that anyone chosen for the mission must be in peak physical condition. The posited mechanism for triggering unconditional P-implications is unavailable.

Literature comparison

This section compares the examples from Section 3 with a class of examples from Mandelkern (2016a,b) used in arguing against pragmatic accounts of the proviso problem.Footnote 5 Mandelkern reasons as follows: Pragmatic responses treat unconditional P-implications as conversationally derived implicatures. As such, we would expect the implications to be cancelled in contexts where there are reasons against inferring P or inferring that the speaker presupposes P. Mandelkern offers examples such as (21) as evidence that this prediction is not borne out.

  1. (21)

    ?? John was limping earlier; I don’t know why. Maybe he has a stress fracture. I don’t know if he plays any sports, but if he has a stress fracture, then he’ll stop running cross-country now.

      (Mandelkern 2016a: ex. 14; cf. 2016b: exs. 29b, 34b-ii)

Mandelkern diagnoses the oddity of (21) as due to the fact that the speaker professes ignorance about whether John plays any sports yet then seems to imply with the underlined sentence that John ran cross-country. The objection is that if unconditional P-implications were pragmatically derived, they shouldn’t arise in contexts such as (21) where deriving them would lead to infelicity. So (21) should be felicitous, contrary to fact:

[I]t is only because of this strengthening that [(21)] strikes us as infelicitous. If strengthening were indeed a pragmatic process, then we would expect it to be blocked in cases like this, where there is strong pragmatic pressure against strengthening. (Mandelkern 2016a: 397; cf. 2016b: 13, 15)

Both of Mandelkern’s points are questionable — that the oddity of (21) must be due to an unconditional P-implication that conflicts with contextual information; and that if a potential implication is pragmatic, it won’t be derived if deriving it would lead to infelicity.

Take the latter point first. Mandelkern’s assumptions about pragmatic reasoning are in tension with work on mandatory (uncancelable) implicatures. Various Gricean and optimization-based formal pragmatics make perspicuous how certain implicatures can arise even if they render the utterance infelicitous (Franke 2009, Magri 2011, Lauer 2013, 2014). Here are two examples from Magri:

  1. (22)

    # Some Italians come from a warm country.

  1. (23)

    # John is sometimes tall.   (Magri 2009: exs. 2–3)

In (22) the use of some implicates that, for all one knows, not all Italians come from a warm country. This implication is in tension with the background assumption that all Italians come from the same country. So, by Mandelkern’s assumptions, we should expect the implication not to arise. But it does, rendering (22) infelicitous. In Magri 2011 such infelicities are even used as a diagnostic for implicatures.

Of course, it doesn’t follow from the point that some implicatures might be mandatory that pragmatic strengthenings of conditional presuppositions are mandatory. Even if a strengthened P-implication doesn’t arise in (21) for conversational reasons, there are other grounds for the oddity of the example. Addressing a question with a projective content is typically infelicitous, as with B’s answers with the definite description and factive verb in (24)–(25) (adapted from Simons et al. 2010: 319; cf. Roberts 2011: 7).

  1. (24)
    figure f
  1. (25)
    figure g

In (21) a plausible QUD might be why John is limping, which could be addressed by answering the subquestion of whether John has played any sports. The conditional presupposition John has a stress fractureJohn used to run cross-country provides a partial answer (cf. Roberts 2012). Whether John wouldn’t do cross-country (given a stress fracture), in contrast, doesn’t directly address the QUD. This may be part of why the example improves if the conditional presupposition is asserted; as Mandelkern observes, (26) is felicitous.

  1. (26)

    I’m not sure why he was limping. Maybe he has a stress fracture. I don’t know if he plays any sports, but if he has a stress fracture then he used to run cross-country, but he’ll stop now.

      (Mandelkern 2016a: ex. 16; cf. 2016b: exs. 29a, 34b-i)

The oddity of (21) may thus be due not to an unconditional P-implication that conflicts with contextual information, but to the fact that it backgrounds the implication that directly addresses the QUD.

Unlike Mandelkern, I am not arguing against pragmatic responses to the proviso problem in general. The examples from Section 3 don’t show that no unconditional P-implications are derived from a prior assumption of independence between ψ and P, or derived in response to a mismatch between the sentence’s semantic presupposition and conditions on felicitous use. While (13)–(16) are evidently problematic for context-repair accounts, I haven’t argued that an alternative speaker-based account or hybrid account cannot succeed.

Recap

Satisfaction theories of presupposition predict that conditional sentences if\(\psi,\,\phi_{P}\) semantically presuppose the material conditional ψP. The proviso problem challenges such theories to explain why certain uses of conditionals if\(\psi,\,\phi_{P}\) seem to carry a stronger unconditional implication P. A prominent approach is to treat the apparent unconditional P-implications as pragmatic strengthenings of the sentence’s semantic presupposition. Examples such as (13)–(16) show that unconditional P-implications can arise in contexts where the sentence’s semantic presupposition ψP is satisfied, contrary to context-repair accounts, and in contexts where ψ isn’t antecedently assumed to be independent of P or to lower the probability of P, contrary to previous independence-driven speaker-based accounts. In (14), for instance, one may infer that Alice has been training daily, even if it is assumed that NASA would only accept peak physical specimens for the mission.

One response would be to reject pragmatic accounts of the proviso problem. One might instead pursue a theory such as DRT which predicts a general preference for global accommodation of presuppositions (van der Sandt 1992, Geurts 1996, 1999). Such a response needn’t be inevitable. An aim of utterance interpretation is to winnow down possible hypotheses for what the speaker’s state of mind is like given her performance of a certain (linguistic) act. One might expect there to be various pragmatic mechanisms and assumptions about a speaker’s state of mind such that the best ways of making sense of her utterance of if\(\psi,\,\phi_{P}\) involve attributing to her a presupposition P. I leave the matter unresolved as a challenge for satisfaction theories.