Abstract
In this paper we argue for a unified semantics for hypothetical conditionals, hcs, e.g. if it rains, we’ll cancel the picnic, and biscuit conditionals, bcs, e.g., if you are hungry, there are biscuits on the sideboard. We side with recent literature in proposing that differences in the interpretation are related to (in)dependence between antecedent and consequent, but we move beyond current accounts in spelling out a characterization of independence that is actually predictive. We further establish a systematic link between if-constructions and discourse structure, providing a dynamic update model that integrates the QUD, and thus the intentional discourse-structure. We argue that in bcs the antecedent sets up the question that is addressed by the consequent, and show that rescuing (Gricean) relevance in face of independence gives rise to implicatures corresponding to the different flavors associated with bcs. Crucially, we argue, this is the same mechanism responsible for our understanding that in the hc above, for example, it is the rain that will cause the cancellation of the picnic. Along the way we notice how the phenomena observed in if-constructions are also replicated in other quantificational structures. Ultimately, there is not much that is biscuit-specific. Their interpretation is the result of a conspiracy among semantics, dynamic update and intentional discourse-structure.
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Notes
Austin’s (1956) original example was similar to (1) but with a final if-clause: There are biscuits on the sideboard, if you want them.
Through out this paper we make use of the gender unmarked singular they. See, e.g., Dictionary.com (https://bit.ly/2FUu6nw) for a non-specialist overview and, e.g., Konnelly and Cowper (2020) for a recent theoretical overview on the matter.
This is not as strong as saying that the addressee believes that the consequent is not true across the board, but includes these cases too.
Factual conditionals are if-constructions in which the antecedent is taken to be true by somebody other than the speaker (and possibly also the speaker) (see a.o. Iatridou,1991; Bhatt and Pancheva, 2006; Constant, 2014). See, e.g., (8) below. We take this label to be descriptive and not to affect the semantics of if-constructions.
Following Arregui (2011) we simplify Veltman’s original presentation, which targeted the context update of counterfactuals.
The label transcontextual is from Merin (2007).
See Franke (2009, def. 5.12). As Franke points out, this notion of independence captures the idea that two propositions are independent for an agent when learning the truth or falsity of a proposition doesn’t allow the agent to decide whether the other is true or false when the truth of such propositions was not decided before. As we argue below, this notion of independence doesn’t allow us to explain our intuitions about factual conditionals.
Franke calls this notion of independence epistemic independence. We thank Cleo Condoravdi for this alternative denomination.
See also Mandelkern and Rothschild (2019) for discussion on this problem and for a version of (7).
Though the bc-reading is also available and would be even more prominent with reversed temporal order, as in Grampa\(_2\): I can imagine! It’s been a long trip! If you are hungry, I just made some biscuits. They are on the sideboard.
This is illustrated by (4): Depending on discourse participants’ conceptualization of how the particular matters of fact in the situation referred to are or can be connected, i.e., on how they depend on one another, either an hc or a bc reading arises.
In Veltman’s (2005) propositional framework generalizations are encoded indirectly, first, because such generalizations involve some kind of quantification that is not available with respect to a propositional account and, second, because what is at issue are dependencies between particular matters of fact. Hence, factual dependencies are particular instantiations of such generalizations in specific circumstances. In previous work (Veltman, 1976), laws are prejudices in a morally neutral, theoretical way. In a way, they constitute the world view or the ideology (or, in Quine’s, 1960 terms, what is at the core of the web of beliefs).
As noted in Starr (2014a) what counts as a base (in the case of a causal model, what counts as salient variables) might be context dependent. For purposes of simplicity, we do not go into this issue.
Systems that do not make use of material implication do not face this problem, but are also formally more complicated and possibly not as general as Veltman (2005).
We thank an anonymous reviewer for this observation.
Our proposal does not predict that we automatically strengthen an update to learn a factual dependence from informational dependence. The Mirror Principle is not symmetric. The prediction is that informational dependence merely requires that factual dependence be possible. In fact, our characterization of the update by if-constructions in Sect. 3 will not make any predictions about when new factual dependencies are learned.
Merin (2007, p. 21): “Lexical and inflectional information, including indicators of tense, along with their respective semantic interpretations and convictions about the physical world make the assumptions of causal independence in [(1)] accessible to every linguistically competent listener. If any of these lexical or grammatical features are modified, the scope for consequential readings will usually increase.”
Swanson (2017) provides another example with presupposition triggers, in this case with too:
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(i)
If you want to go to the movies, Henry and Iris are going too.
Swanson’s concern, again, is that even though we take (i) to convey that Henry and Iris are going to the movies no matter what, the satisfaction of the presupposition triggered by too in the consequent depends on the truth of the antecedent. Notice, however, that the licensing conditions of too are of a different nature from our notion of independence: Too does not require that the antecedent be true (or false) depending on the truth of the prejacent ((ii) is adapted from Heim (1992, ex. (71)); the original example involves also):
-
(ii)
A: I am already in bed.
B: My parents think I am in bed too.
In (ii) A is in bed but B isn’t and yet, too is licensed. The proposal in this paper predicts that (i) is a bc because that you want to go to the movies and that Henry and Iris are going to the movies are presupposed to be independent (in the most obvious contexts of interpretation for (i)).
Notice also that the discussion regarding too also applies to other presupposition triggers such as possessives (see Heim, 1992, ex. (28)):
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(iii)
Patrick and Ann both dream of winning cellos. Ann would like one for her own use. Patrick wants to sell his cello for a profit.
The use of the possessives does not require that that Patrick or Ann won (and hence, actually have) a cello each. The anaphoric relation imposed by the possessive is of a different nature.
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(i)
Note that attempts to spell out (28) as a bc in contexts where the antecedent is accepted as true are not felicitous:
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(i)
# If you feel like having tapas right now, as you obviously do/must, because as we both realize this is a great tapas restaurant, this is a great tapas restaurant.
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(i)
There are also bc-questions: If I’m hungry, are there biscuits on the sideboard? The question is ultimately asking whether there are biscuits on the sideboard (independently of the hunger). See Sano and Hara (2014), who derive this result within Franke’s (2009) proposal of independence. Their result translates to the system presented here.
This is effectively the context change potential in Heim (1983):
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(i)
If-construction with matrix declarative update: Where \(M\backslash N =M\cap (W-N)\) \(c + \text {\textit{If }} p, q = c \setminus (c + p\setminus c + p + q)\), where p and q are declarative clauses.
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(i)
Isaacs and Rawlins (2008) point out that it is not always clear when assumptions are lifted: A: If it rains today, we cancel the picnic; B: And everybody stays home. In this example, B’s utterance still considers the assumption that it rains today. We do not dwell on this here and leave it for future research. Notice however that linguistic cues often help to identify whether assumptions are lifted. B’s utterance above is more natural with and, indicating that the proposition is to be understood in conjunction to the matrix clause in the previous utterance (we cancel the picnic and everybody stays home) and hence should be evaluated under the same assumptions.
It allows us to explain why there are if-constructions that we (intuitively) interpret as hcs that still trigger a global update (although, arguably, through a different route).
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(i)
This is the best book of the month if not of the year.
The regular update of if-constructions together with our assumptions that the best book of the year has to be the best book of the month it appears in is what derives the global update in this case. It is a different process than the one we saw in bcs.
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(i)
Given a stack s, push(s, x) delivers the stack resulting from adding x to the top of s. Conversely, pop(s) delivers a stack in which the top element of s has been removed. Finally, top(s) just establishes what’s the top element on the stack.
See Büring (2003) for a more relaxed notion of answerhood. The differences do not matter for our purposes.
In Rooth’s framework this focus presupposition is formalized by making use of the ‘\(\sim \)’ operator. We simplify here and do not introduce this additional formalism in an attempt to keep things as simple as possible. See Biezma (2020) for more details on the update process.
If-constructions are not different from other linguistic devices that serve such purpose. See for example Regarding the concern about adverse ecological impacts, AFCD advises that cropping activities could co-exist with conservation. Other similar cases include With respect to\(\ldots \), in relation to\(\ldots \), which serve a similar purpose.
The mechanisms at play are somewhat similar to those proposed in Roberts (1996), Büring (2003), Biezma and Rawlins (2012), where it is noted that a question may be followed up by a sub-question as a way of clarifying the speaker’s goal regarding the original question, e.g., How was your evening? Was dinner good? vs. How was your evening? Was your date attractive?. In the case of bcs, as well as hcs with the default mapping to discourse, it is the answer to the question that allows us to identify the QUD targeted by the speaker, not a subquestion.
That the if-construction form gives rise to the same inferences as the distributed fragments has already been observed in Starr (2014b, p. 18). There are, however, several differences between Starr’s (2014b) proposals and the one in this paper. Most importantly, Starr establishes in the semantics of the if-constructions that the antecedent signals the question being addressed. It is not clear to us whether his proposal can be modified to allow for the required flexibility in the mapping between if-constructions and discourse necessary to derive cases of classic conditional perfection à la von Fintel (2009) (see example (69) below).
See Biezma et al. (2012); Arregui and Biezma (2016) for a discussion on discourse manners and non-cancellable implicatures in if-constructions and Lauer (2014) for a discussion on “mandatory implicatures” in general and why they result in infelicity or oddness if the implicature is known to be false.
Notice that this is not always necessary. That is, bcs are not only uttered when relevance needs to be established:
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(i)
A: Oh look at the weather! It’s probably going to rain. Poor Alex is still out there. Alex
will get completely soaked.
B: Don’t worry. Alex has an umbrella.
A: But the poor child! This is terrible! Dreadful!
B: Stop exaggerating. If it rains, Alex has an umbrella.
B’s point in uttering the bc is to emphasize that Alex has an umbrella. Relevance was already established and the speaker could have uttered the declarative alone, but by uttering the if-construction the speaker further makes the point that the question ‘what if it rains?’ has already been fully answered by the statement that Alex has an umbrella and it’s now time to move on (the matrix clause is intended to convey an exhaustive answer).
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(i)
For approaches to indirect speech acts that make use of tools from decision theory (see van Rooy, 2003; Benz and van Rooij, 2007; Benz, 2006; and especially Stevens et al., 2014). According to these proposals indirect speech acts have to be considered as indirect answers that pertain to decision problems. The central insight is that preferences that are elements of agent’s goals are a central element in deriving the specific force of an utterance, which is e.g. implemented in Bledin and Rawlins (2019). In a slightly different setting, this insight is also used in Condoravdi and Lauer (2011, 2012, 2017) to derive the different forces of imperatives. In a dynamic setting, Murray and Starr (2018) have also pointed to the role of preferences in deriving force.
Ippolito (2016) also considers the mapping of bcs into discourse and their differences in interpretation with hcs in a short note on relevance conditionals, although her overall proposal is rather different. Ippolito (2016) proposes that if-constructions of the form if \(\phi \), \(\psi \) address a ‘conditional question’ of the form if \(\phi \), Q?, where \(\psi \) is a possible answer to Q. The bc in (1), for example, is taken to address an ongoing QUD that can be paraphrased by ‘If you are hungry, is there anything to eat?’. The bc addresses this question by offering the ‘premise’ in the consequent that, indirectly, answers it. It is not clear to us how this question is identified in Ippolito’s system, i.e., what are the conventional cues in the information structure of the utterance identifying that such is the inquiry being addressed, which is essential within the QUD model. In addition, given the arbitrary choice of question, it is not clear to us how this system would account for cases of ‘classic’ conditional perfection in hcs like (69), or cases of ‘biscuit perfection’ (see Biezma and Goebel, 2018), which are explained by assuming a mapping to discourse that does not involve conditional questions but a classic information-structural division of labor between antecedent and consequent like the one explained above and adopted in this paper. Indeed, as we will see, classic conditional perfection require the system to be flexible enough to allow the opposite mapping, one in which the consequent provides the QUD and the antecedent provides the answer. In addition, Ippolito (2016, p. 56) also aims to offer an explanation as to why some if-constructions have a ‘causal’ interpretations while others don’t: “The proposal that I would like to make is that the difference between causal and non causal counterfactuals lies in their relation to the [QUD]. A causal counterfactual answers the [QUD] directly, whereas a non-causal counterfactual answers de [QUD] indirectly by spelling out a premise assuming which the [QUD] is then answered.” In our system, causality is also an inference, but it does not result from the utterance providing a direct answer. In our account, that the hc is taken to provide a direct answer to a QUD is the byproduct of there being a dependence relation between antecedent and consequent.
Overall, Ippolito (2016) is not devoted to bcs but aims to explain how context dependence allows us to identify the premises relevant in the interpretation of counterfactuals. We leave for future research the investigation of her claims with the mapping between if-constructions and discourse proposed here.
Commands, suggestions or advises are proposals to update an element we have not introduced in the toy model used here: participants’ preferences (see e.g., Starr, 2020). Developing all the details here goes beyond the scope of this paper and is left here for future research. It suffices for us to encode the cs update triggered by the manifest event. We can accept both the information and the suggestion made, but things are more complicated. A full model for the dynamic update should be able to derive that while participants learn that a suggestion has been made (unless this is cancelled immediately), the suggestion itself can be rejected while the information that there are biscuits be accepted, (iB\(_1\)). We can also accept the suggestion to alleviate the hunger by eating biscuits while rejecting the information that there are biscuits on the sideboard, (i-B\(_2\)):
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(i)
A: If you are hungry, there are biscuits on the sideboard.
B\(_0\): Thanks! I really need to eat something.
B\(_1\): I saw them, but they are Morgan’s! They may be reserving them for something.
B\(_2\): Thanks for the suggestion, but they are not on the sideboard anymore. I’ll ask Morgan where they put them.
To build a model that predicts these possibilities would complicate matters greatly and goes beyond the scope of this paper.
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(i)
It is not clear to us why the default mapping is one in which the if-clause introduces the QUD. It may be due to the fact that the antecedent is the restrictor of the modal, and restricting the domain of quantification is usually thought as previously agreed upon. Alternatively, it may be the result of understanding the main clause as usually conveying the main-point of the utterance (the at-issue meaning), while adjuncts are more easily understood as constraining the main claim. What is important is that this is a tendency, not something that is conventionally indicated by the linguistic form, and hence it can be transgressed.
Given our view that discourse-driven effects can replicate across constructions, it is interesting to see that we find instances of ‘perfection’ in other types of quantificational statements (not only if-constructions). Consider (i) (from the movie Logan, 2017):
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(i)
A: Everyone I care about dies.
B: Well, then I should be perfectly safe.
In B’s response we understand that they have perfected A’s claim to understand that only the people A cares about dies.
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(i)
Notice that in a context in which the only thing that can be eaten to alleviate hunger are biscuits and that biscuits are always on the sideboard, A’s question in (70) can be taken to convey that the speaker is hungry and wants to address that issue. The bc is then a means to rephrase A’s question making clear that the question that is being addressed is what the selected worlds in which A is hungry look like. In this alternative scenario, the bc in (70) is expected to be felicitous. The prediction agrees with speakers’ intuitions.
EEH offer the following example of a bc question:
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(i)
If I may ask a stupid question, did Miles Davis ever play in a combo that was led by Thelonious Monk?
In justifying that (i) is a bc they argue that “the speaker is not just asking for the truth of the proposition Miles Davis played in a combo led by Thelonious Monk in the maximal plurality of worlds where she may ask a stupid question, but she performs this question unconditionally in the actual world.” Notice that this explanation has nothing to do with syntax or how the processor identifies that syntactically the if-construction is a bc. In fact, the speaker has no way of telling via the syntax whether the if-construction with a matrix interrogative is to be understood as a bc or a hc.
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(i)
Notice however that, even though EEH only treat then as a proform, they also make a connection between the presence of then and causality (see Ebert et al., 2014, p. 374). Nothing is said, however, about how the causal meaning is brought about. We address this below.
The hc interpretation could also be brought about with this utterance, namely that my thinking that you are making a mistake is the result of you wanting to know my opinion, and we can design contexts in which this is available, but the point here is that the most prominent reading in uttering these if-constructions with then is similar to what we obtain in the then-less utterance and we arrive at it by considering the propositional content in the antecedent and matrix clause and their dependence relation or lack of it.
McCready (2014) also argues that bcs and hcs have different semantics and that, unlike in hcs, in bcs the consequent is asserted. Support for this claim, McCready argues, comes from the contrast between (i) and (ii):
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(i)
If a farmer owns a big piece of property, he usually keeps a donkey. # It lives a free and easy life.
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(ii)
a. If you’re hungry, there are some\(_1\) cookies on the table. They\(_1\) are ginger snaps.
b. If you’re free, I’m going to a\(_1\) party tonight. It\(_1\) starts at midnight.
McCready argues that (i) illustrates that in hcs non-specific indefinites introduced in a conditional consequent cannot serve as antecedents for anaphora while the examples in (ii) show that in bcs this is possible.
There are several problems with this argument. First, (i) and (ii) are not a minimal pairs. In (i) the indefinite in the consequent covaries with farmer-owning-property cases (this reading is helped by the presence of usually) whereas the examples in (ii) do not run into such problems. Differences in judgments are due to this fact. Consider (iii) instead:
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(iii)
a. If the farmer sees the plowing is going slow, he buys a new donkey. It must be young so it can help the older ones.
b. Around here, if a fisherman wants to catch a chinook, he brings a red Marabou. He usually sticks it in his hatband.
The examples in (iii) are hcs and are good. The only problem is that the indefinites in the consequent in these examples do not receive a non-specific interpretation. However, notice that contrary to McCready’s claim, it doesn’t seem that the indefinites in the consequent in the bcs in (ii) or (iii) are non-specific either:
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(iv)
a. If you’re free, I’m going to a party tonight, either the one at Joe’s or the one at Sue’s. # It starts at midnight.
b. If you’re free Tuesday or Wednesday, I’m going to a party. # It starts at midnight.
If they were non-specific, we would expect the utterances of (iv) to be felicitous, but they are not. Hence, (iii) and (ii) form a minimal pair and both behave alike leaving us with no argument to support the hypothesis that they have different semantics (and hence with no argument supporting that in the case of bcs the consequent is asserted whereas in hcs it isn’t). For the sake of completeness consider (v), a variant of the hc in (i) in which the indefinite in the consequent doesn’t covary with farmer-owning-properties and is clearly specific.
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(v)
If a farmer owns a big piece of property, he usually feeds a donkey, Platero. It lives a free and easy life.
As expected, (v) is now fine. Thanks to Andreas Walker for discussion regarding this point.
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(i)
This is a possibility that Siegel had already dismissed, since (3) doesn’t behave like an imperative. In particular, the addressee cannot respond to (3) with No, I won’t! However, further considerations of the data led EEH to argue that Siegel’s data-point regarding the response patterns only shows that (3) does not provide an antecedent for VP ellipsis: No, I won’t say that is actually a possible response to (3). Notice however that EEH are careful to signal in fn. 8 that this is not sufficient to claim that the consequent performs a command speech act.
Indeed, if one were to adopt a speech act account of BCs, this would be a better approach. One of the main problems of this approach to bcs is how to constrain when speakers have to process one speech act or another, or how many different speech acts there are. For example, in order to explain bcs like if you want to hear a big fat lie, George W. and Condi Rice are secretly married (example from Siegel, 2006), EEH need to appeal to a speech act that is not “a run of the mill assertion”, it is a speech act that involves a ‘false assertion’. See also fn. 50 for further concerns.
This is because we eliminate all worlds in which the inspector asks (+A) and the addressee is not four (-4) because of the informational update of the if-constructions, and notice that we do not have +4+A or +4-A-worlds, since in cs all the worlds are -4-worlds. There would only be -A-4-worlds left.
The following is a similar example from Siegel (2006):
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(i)
If you want to hear a big fat lie, George W. and Condi Rice are secretly married.
Siegel used this example to argue against speech-act operator accounts arguing that the matrix clause in bcs was headed by an assertion operator. Certainly the speaker is not asserting the matrix clause, rather, the speaker is saying that the proposition denoted by the matrix clause is not true. That the matrix clause is a lie is derived in our system in the same way it is derived in (i) that the speaker is suggesting that the addressee lies. Notice that in this case there is a common denominator helping to trigger the inference: the if-clause has a verbum dicendi or refers in some way to an utterance. The matrix clause is easily interpreted as the response or the utterance being predicated about.
It has been claimed in the literature that these bcs, unlike other canonical bcs, cannot shift to the past (see Csipak, 2015):
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(ii)
a. If you are hungry, there is pizza in the fridge.
b. If you were hungry yesterday, there was pizza in the fridge.
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(iii)
a. If you ask me, Alex is getting ready to leave.
b. #If you asked me yesterday, Alex was getting ready to leave.
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(iv)
a. If I’m being frank, you look tired.
b. ?If I was being frank yesterday, you looked tired.
Notice however, that this observation is not quite right. The matrix clause is interpreted as the response to the antecedent, and hence it is anchored at the time of the utterance. When we cannot understand that the response provided in the matrix clause was what was provided at the time of the event in the antecedent, we get oddity. However, when the times match, we still can get a bc even if in the past:
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(v)
Everybody was very liberal and went to bars in those days. If they asked us how old we were, we were twenty one.
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(vi)
Sue was always complaining and saying that she was done with her partner. I was worried and,
a. if you asked me those days, she was ready to split.
b. when asked, if I was being frank, she was ready to split.
More research is needed to understand and formalize what is behind the contrast between the infelicitous (iiib) and (ivb) vs. the perfectly fine (v) and (vi). This is beyond the scope of this paper and we leave it here for future research.
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(i)
Notice that in this reasoning it is important that we consider that there are antecedent worlds in \( cs \): the ticket collector may certainly ask about the kid’s age. This assumption is what leads to look for a different interpretation for the update proposed by the matrix clause. However, in other contexts, we may conclude that the update proposed is in fact the literal update even though the resulting \( cs \) is one in which nor antecedent nor consequent is actually true! This is what we observe with extreme cases in which the update proposed is incompatible with what we accept to be the case (this kind of examples have been dubbed ‘Dracula conditionals’, see Akatsuka (1991), or ‘monkey’s uncle conditionals’, see Franke (2009)):
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(i)
If I pass the calculus exam tomorrow, elephants fly.
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(ii)
A: Why did she leave me? I’m such a good guy!
B: If you are a good guy, I’m Marilyn Monroe.
The consequent in both cases is incompatible with \( cs _c\), assuming that we all accept that elephants don’t fly or that the speaker is not Marilyn Monroe. The effect is similar to that triggered by examples of vacuous quantification utterances (e.g., all my Ferraris are in the garage uttered by someone who has no Ferraris). If we proceed with the regular update of the if-construction nevertheless, it leads to a \( cs \) in which the speaker does not pass the exam and elephants don’t fly or in which the the addressee is not a good guy and the speaker is not Marilyn Monroe either (just as in the ticket collector example in (3), see fn. 47). This is indeed what is intended in these cases (unlike in (3)). Again, in (i) and (ii) we do not obtain consequent entailment even though these if-constructions are bcs: the resulting \( cs \) doesn’t reflect an informational dependence running against the factual-dependence assumptions and, hence, no strengthening is necessary.
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(i)
In fact, speech act accounts like EEH’s would have to rely on those pragmatic mechanisms to explain why If you are hungry, there are biscuits on the sideboard is a suggestion/invitation to the addressee to eat the biscuits, not just an assertion of the presence of biscuits on the sideboard. Otherwise they would have to speculate that the interpretation involves simultaneously two speech act operators, one an ASSERTION operator and one a SUGGESTION operator.
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Acknowledgements
This paper has evolved over time thanks to the insights of our reviewers and the handling editor. Arno had to leave the project midway, but Sect. 2, which was his main focus, still has at its core the main ideas in Goebel (2017). Its shape and the formal apparatus presented, however, has changed to address the issues raised during the review process. All reminding errors in its current form are María’s. This paper would not have been possible without the comments and insights from three anonymous reviewers and the handling editor, Regine Eckardt. Ana Arregui also deserves immeasurable gratitude for her comments and encouragement throughout the development of this project. Thanks also to Justin Bledin, Eva Csipak, Sven Lauer, Kyle Rawlins, Maribel Romero, Wolfgang Spohn, Eric Swanson, Andreas Walker and the members of the DFG Research Unit Was wäre wenn. Research in this paper was partially funded by the project DFG 1836.1-1 awarded to María Biezma.
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Biezma, M., Goebel, A. Being pragmatic about biscuits. Linguist and Philos 46, 567–626 (2023). https://doi.org/10.1007/s10988-022-09368-9
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DOI: https://doi.org/10.1007/s10988-022-09368-9