Abstract
The last several decades of research on counterfactual conditionals in the fields of philosophy and linguistics have yielded a predominant paradigm according to which the notion of similarity plays the starring role. Roughly, a counterfactual of the form A > C (if A were the case, C would be the case) is true iff the closest A-worlds are all Cworlds, where the closeness of a world is a function of its similarity, in a certain sense, to the actual world. I argue that this is deeply misguided. In some cases we may only care about the closest A-worlds, but quite often we care about some broader variety of A-worlds varying in closeness. After presenting several problem cases for the similarity-based paradigm, some new and some known, I propose an alternative paradigm for the semantics of counterfactuals, which introduces the notion of Ascenarios, understood roughly as different ways of making A true. According to this view, A > C is true iff all the contextually relevant ways of making A true also make C true. I then more carefully spell out a working view that formalizes this idea with greater precision, and explore the consequences of that version of the view.
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Notes
See, e.g., Stalnaker (1968, 1981), Lewis (1973, 1986b), Kratzer (1986, 2012), and Bennett (2003). Von Fintel’s (2001) view agrees with these views in most ordinary cases, so my arguments apply to him; Gillies (2007) refines von Fintel’s view, but is reluctant to commit to a similarity-based ordering, though were he to do so, my arguments would apply to him too.
We precede a sample sentence with # to indicate that the sentence is intuitively false/infelicitous.
This example becomes a bit less forceful as US-Cuba relations thaw. Imagine it uttered in 1990.
It has been pointed out before that it may be possible to force a true (or at least better) reading of cases like USA, e.g.: “If I were in Miami or Havana, it would be Miami, not Havana; and then I’d be in the USA; so if I were in Miami or Havana, I’d be in the USA (rather than Cuba)”. I find such speeches quite awkward, but perhaps they do force true readings. But we can force the more natural false reading as well, e.g. by stressing or, and/or by adding either: “#If I were in either Miami or Havana, I would be in the USA”. I find it impossible to hear this as true. And anyway, all I need for my point is that there is some false reading not accounted for by the standard approach.
I borrow this case from Alan Hájek (ms); the following one is obviously derivative of it.
The later Lewis (1986b) further spelled out his account in an attempt to yield the result that similarity at or after the antecedent time—the time the antecedent is about – matters less than similarity before it, so one might think COAT has been adequately responded to, since the antecedent of COAT is about a particular time (last night). But it is doubtful he was successful (see Bennett 2003 and Elga 2001), and the result seems undesirable anyway for reasons unforeseen at the time (see Kment 2006). Anyway, it is easy to come up with temporal cases where the intuitively relevant antecedent-worlds differ before the antecedent time, e.g. THIEF below.
In fact, recently this sort of diagnosis has been developed further into a style of response that bears some similarities to mine, which we might call the Syntactic Solution. Due to the existence of cases like those discussed presently, which do not plausibly contain any syntactically idiosyncratic component, I find this style of response unpromising. But due to its prevalence in the recent literature, it is worth discussing in more detail, and distinguishing from my own proposal. (Thanks to an anonymous referee for this journal for pointing out this omission in a previous version of this paper.) To maintain the flow of the paper, I defer this discussion to Sect. 6, where I discuss two other alternative solutions as well.
I defend this claim more extensively in Sect. 6 as part of a discussion of two SFP-friendly alternative solutions that I reject, one of which appeals to the putative context-sensitivity of the closeness ordering, and one of which relaxes the closeness constraint to the sufficiently close A-worlds. I postpone this discussion so I can introduce my positive view.
Interestingly, Manley and Wasserman (pp. 69–70) discuss a case analogous to my comparative and interval cases, and assume as a premise in one of their arguments that the standard (Lewis–Stalnaker) account’s prediction about it is correct. They imagine that a concrete block built to withstand drops from up to 20 meters (but no more) is in fact suspended from more than 20 meters in the air. Observing that the closest worlds where the block is dropped are presumably ones where it is dropped from its current height, at which it breaks, they claim the counterfactual If the block were dropped from higher than one half meter, it would break is true, since its current height is higher than one half meter. This strikes me as the wrong judgment; rather, we should think this counterfactual false, and add this case to the list of counterexamples to the Similarity First Paradigm.
To clarify, there is a reading of the relevant worlds, meaning merely something like the operative worlds or the worlds that matter, according to which RFP-1 is more or less trivial. It would hardly be informative or controversial to claim that If A, then C is true iff C is true at all the A-worlds that matter for the truth conditions, beyond the presupposition that there is some such set of worlds. I mean something stronger: roughly, the relevant worlds are the ones made pertinent or germane by the context, including but not limited to speakers’ interests and the sorts of purposes typically served by counterfactual assertions. For comparison, it might turn out that the best theory of proper nominal reference appeals to relevance similarly construed, such that names like Jeff typically refer to whichever Jeff is most relevant given the contextual forces at play. Note that relevance is only partly determined by factors under speakers’ control. If we’re wrong about which Jeff is on the phone, we may be wrong about which Jeff we are referring to, and thus about which statements about Jeff are true. Similarly, if we are wrong about which cities have over a million Cubans, we may be wrong about which scenarios are relevant to counterfactuals like USA-any. The relevant worlds needn’t always be the worlds we have in mind.
Strictly speaking, a version of the RFP is compatible with the SFP, since in principle it could turn out that the relevant worlds are always the most similar ones. But this would be surprising, since the pragmatic factors that determine relevance, in the appropriate sense, are distinct from the factors generally taken to determine similarity.
Plenty of philosophers and linguists are skeptical towards possible-worlds-based analyses for various reasons. I am sympathetic, but for present purposes, given the familiarity of possible worlds and the precision and clarity they provide, I appeal to them in my analysis. I am not opposed to abandoning them if some other sort of analysis turns out to be better.
I intend the term scenario to be theory-neutral. Unlike the terms situation, state of affairs, or possible world, there are no widely established theoretical associations with the term scenario that I am aware of. I also expect the reader will find it intuitive; I have already used it several times.
I borrow this terminology from Stalnaker, but I do not mean it to come along with any of the attendant theoretical commitments of his theory, e.g. that the output of the function be a single world.
We represent a proposition set-theoretically as the set of worlds where it is true, so the union set of the Wi is a subset of C iff C is true at every member of that set.
Is it really plausible, though, that such multi-layered quantificational structure is involved in a fairly syntactically simple natural language construction such as an if… then… statement? Especially if this kind of quantification were only found to occur in this construction? As a matter of fact I believe there are analogous examples involving other kinds of quantification. Suppose we are at a chess tournament separated into different age groups, and I say “Only the best players get trophies”. Of course, the runner-up in the highest age bracket is likely to be a significantly better player than any of the winners of the younger groups, but they get trophies and he or she does not. Still, my statement seems true (or at least has an interpretation on which it is). So we must interpret it as quantifying over the best players in each group, not over the best players simpliciter. Here is another case: suppose my two or three favorite restaurants in the world are traditional old-world Italian restaurants, and I only like that kind of authentic Italian cuisine, like Grandma used to make. But when it comes to any other kind of restaurant, my tastes are more adventurous, and I almost always go for creative, innovative, experimental twists on traditional cuisines. So my other favorite restaurants include ones that are New American, Japanese fusion, molecular gastronomy, French-inspired soul food, avant-garde Mexican, etc. Now suppose I say “My favorite restaurants are traditional ones”. This seems false, at least on one very natural interpretation. But if only my very favorite restaurants were relevant, it would be true. It seems like we must consider a wider variety of my favorite restaurants from different categories.
These cases have a similar structure to the counterfactual ones, in that they involve some sort of maximal ordering—the best players, my favorite restaurants, the closest worlds—applied individually to a variety of subsets of the category under discussion. So perhaps something about these sorts of orderings, in combination with quantification over the elements ordered by them, yields an environment conducive to the kind of “grouping” structure I have proposed in the case of counterfactuals. Further exploration of this possibility will have to await further research.
One might wonder whether a partition on the set of all A-worlds might do the trick. It won’t. The cells of a partitions are by definition non-overlapping, since a partition of a set assigns each member of the set to exactly one of the subsets induced by the partition. But we want the sets of worlds representing the relevant scenarios to be able to overlap. For the antecedent If Sophie and Tina came to the party…, presumably the relevant A-scenarios are Sophie coming to the party and Tina coming to the party. But suppose Sophie and Tina have recently started dating, and are joined at the hip lately. Then the closest worlds where Sophie comes to the party are likely ones where Tina does too, and vice versa. So these worlds had better be in both the set of Sophie-worlds and the set of Tina-worlds.
In particular, see the sections below on might counterfactuals and the reordering approach.
It is worth noting that Lewis himself appeals in a similar way to a nebulous complex of contextual factors, which putatively determine the similarity facts: “the truth conditions for counterfactuals are fixed only within rough limits; …they are a highly volatile matter, varying with every shift of context and interest” (1973, p. 92). (See Sect. 6.2 below, on the “reordering solution”, for more on this.).
There may be independent motivation for such a constraint. We routinely make stand-alone would claims, like you would love Rome or I wouldn’t lie to you, which seem to be about a fairly wide variety of possibilities. One plausible account of this phenomenon is that the sorts of modal quantifications involved are typically implicitly restricted to something like the sufficiently close worlds, subject of course to contextual variation, so that any world too far-fetched is ignored. And Furthermore, von Fintel (2001) appeals to a similar notion, which he calls the modal horizon. I discuss this in Nichols (2017).
Though it’s not obvious we will entirely. There are uncountably many moments at which I could’ve struck the match, uncountably many angles at which I could’ve held it, etc. Unless there are uncountably many relevant scenarios, some of these combinations of moments and angles will be ruled out as counterfactual possibilities. Whether this yields acceptable results will depend on the details, and may vary from case to case. But if it requires uncountably many relevant scenarios, the appeal to scenarios in addition to worlds may seem less plausible.
UA is often discussed alongside another principle called the Limit Assumption (LA), which is the assumption that there is always at least one closest A-world. Stalnaker accepts LA, but Lewis rejects it. He worries in some cases there may turn out to be an infinite series of closer and closer worlds, e.g. if there is a line that is actually one inch long and a series of worlds where it is longer than one inch but closer and closer to its actual length (Lewis 1973, pp. 19–21). Lewis complicates his semantics to accommodate such cases, so that A > C is true iff some (A&C)-world is closer than any (A&¬C)-world, i.e. iff, when examining closer and closer A-worlds, so to speak, we reach a point at which all the remaining A-worlds in the ordering are C-worlds. I could, if I wanted, easily amend my view analogously, so that A > C is true iff, for each scenario, some (A&C)-world witnessing that scenario is closer than any (A&¬C)-world witnessing it.
An anonymous referee astutely noted that such an analysis of might counterfactuals breaks the might-would duality. If KLAUS is false in this case, then its negation is true: “it’s not the case that if I were in Miami or Havana I would run into Klaus”. But then, taken at face value, the might-would duality predicts the truth of the corresponding would counterfactual with the negated consequent: “If I were in Miami or Havana, I wouldn’t run into Klaus”. But, as the case was described, this is false, because I might run into him in Miami. I’m not sure what to say about this at this moment.
To be clear, this is not to suggest that no semantics formulated in terms of a set of relevant worlds can be adequate. Indeed, my initial, coarse-grained formulation of the Relevance First Paradigm was stated this way. And Lewis (2016, 2017) also defends a relevance-based view, according to which closeness is understood as a function of both similarity and relevance. As far as I can see, nothing about her conception of relevance rules out spelling it out in terms of scenarios, in which case our views could be compatible.
Von Fintel’s view is an exception, strictly speaking, because in certain cases counterfactuals quantify over a domain including not only the closest A-worlds but others as well. But in ordinary cases his view predicts the same truth conditions as other similarity-based views, so in these cases the entailment would hold. (And in ordinary settings my problem cases would apply to him as well.).
We could still preserve TAP, if we wanted, by embracing a principle about scenarios analogous to SC, to the effect that whenever an antecedent-scenario is witnessed by the actual world no non-actual scenarios are relevant. Call this Strong Scenario Centering (SSC). The combination of SSC and SC would entail TAP: by SSC, whenever some scenario s is actual, no non-actual scenarios are relevant; by SC, the actual world @ is the unique closest world where s obtains; by my semantics, f will map s onto @, and @ will be the only relevant A-world; in this case A > C will be true iff C is true at @.
I discuss an exactly analogous case in my [citation redacted] as a counterexample to the dynamic strict conditional view defended by von Fintel (2001) and Gillies (2007), since the domain expansions postulated by these views are structurally analogous to the expansion of the antecedent domain to include the “close-enough” worlds.
This is not to be confused with indeterminacy regarding which is more similar. It’s easy to imagine, in the absence of some specific set of criteria, denying that there is a determinate fact of the matter whether Philadelphia or Los Angeles is more similar to New York. It’s harder to imagine spelling out some specific, non-arbitrary criteria for comparison and finding that the two cities are exactly tied.
The case is even stronger if we add on more scenarios. Suppose I say “If I were in Miami or Havana or Tampa or New York City or anywhere else where I could find good Cuban food, I would get some Cuban food”. The more scenarios are relevant, the more worlds we have to treat as equally close that we normally would not, and the more aspects of similarity we have to assign low or zero weight, so the more likely we are to count other, intuitively irrelevant worlds as equally close too.
Of course, in response, one could in principle part with Lewis here by denying that the operative world-ordering appealed to by the theory ought to be grounded in similarity. Aside from the fact that this constitutes abandonment of the similarity-based approach – which is exactly what I am advocating for!—we would then be owed an explanation of what generates the ordering instead, i.e. what unifies all the worlds ranked highest on the ordering. It’s no help anymore to say they are the “closest” worlds, for this term was meant to invoke a connection to similarity. We might as well call them the “special” worlds, and then ask: What makes them special? I say it’s relevance.
More formally: suppose there are three relevant scenarios, s1, s2, and s3, and a different similarity ordering appropriate for each one, ≤ 1, ≤ 2, and ≤ 3, respectively. Then f would take as its input not just scenarios but scenario-ordering pairs, and map each scenario onto the set of worlds that are closest according to that scenario’s associated ordering, i.e. s1 onto the ≤ 1-closest worlds, s2 onto the ≤ 2-closest worlds, and s3 onto the ≤ 3-closest worlds.
“Alternative semantics” is actually standard, but since this phrase can also be interpreted as referring to a semantic account which is an alternative to some more established analysis—which is what this whole paper is about!—I will use the term “alternatives-based semantics” to avoid confusion.
For instance, the statement “Every student read War and Peace or Anna Karenina” is intuitively true if some of the students read the former and the rest read the latter (amongst other possibilities). But, according to Santorio, Alonso-Ovalle’s account can’t capture this reading, since according to his account the disjunction simply contributes the set containing each of the disjuncts, in this case {every student read War and Peace, every student read Anna Karenina}. Santorio’s account allows for the more complex quantificational structure required for the above reading. This interpretation can then be applied to counterfactuals with antecedents containing disjunctions requiring the same sort of reading, e.g. “If every student read War and Peace or Anna Karenina, the world would be a better place”.
I do beg to differ, however, with one claim made by an anonymous reviewer: the reviewer speaks as though my account just is a type of alternatives-based semantics, full stop. But I am inclined to disagree. See below for a discussion of this.
Fine’s notion of relevance is not the same as mine. His is a notion of truthmaking or grounding relevance, while mine is a linguistic/contextual notion of relevance. For example, the state of there being rain is wholly relevant to the fact that it is raining, but the state of there being rain and wind is not wholly relevant to the fact that it is raining, since part of that state—namely, there being wind—is not part of what makes it true that it is raining, and is thus not relevant. This is very different from my notion of relevance, which amounts to contextual factors, primarily linguistic, which help determine which sets of entities of various kinds will be most appropriate to serve as theoretical stand-ins for various linguistic parameters.
I am ignoring the syntactic difference between the Kratzer-style conditional semantics and the Lewis/Stalnaker-style, which is irrelevant here.
I take it something analogous to this is, however, implicit in discussions of the alternatives-based views, since the alternatives are clearly individuated and the conditional must be evaluated against each alternative individually. Though I suppose this is a sociological matter about alternatives-based semanticists, and could be settled more conclusively by asking them how they conceive of their own theories.
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Nichols, C. Relevance first: relocating similarity in counterfactual semantics. Synthese 198, 10529–10564 (2021). https://doi.org/10.1007/s11229-020-02735-8
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DOI: https://doi.org/10.1007/s11229-020-02735-8