Abstract
This paper investigates propositional hyperintensionality in counterfactuals. It starts with a scenario describing two children playing on a seesaw and studies the truth-value predictions for counterfactuals by four different semantic theories. The theories in question are Kit Fine’s truthmaker semantics, Luis Alonso-Ovalle’s alternative semantics, inquisitive semantics and Paolo Santorio’s syntactic truthmaker semantics. These predictions suggest that the theories that distinguish more of a given set of intensionally equivalent sentences (Fine and Alonso-Ovalle’s) fare better than those that do not (inquisitive semantics and Santorio’s). Then we investigate how inquisitive semantics and Santorio can respond to these results. They can respond to them by helping themselves to considerations from Hurford disjunctions, disjunctions whose disjuncts stand in an entailment relation to one another. I argue that considerations from Hurford disjunctions are ad hoc modifications to less fine-grained theories to predict the expected results and they are not independently motivated. I conclude that the scenarios suggest a need for more fine-grained theories of sentential meaning in general.
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Notes
As I will use it, an intensional semantic theory is one that takes the meaning of sentences to be sets of possible worlds where the proposition expressed by the sentence in question is true.
SDA lets one infer if it had rained, the picnic would have been canceled and if it had snowed, the picnic would have been canceled from if it had rained or snowed, the picnic would have been canceled. See Alonso-Ovalle (2009), Fine (2012), Santorio (2018 ) and Ciardelli et al. (2018b) for defense of SDA. Also for a partial defense, see Khoo (2018).
This route is suggested to me by Paolo Santorio (p.c.).
This suggestion is made by Ivano Ciardelli and Floris Roelofsen (p.c.).
I will add the surface logical forms of the examples right after the example to keep track of equivalence among them.
The intuitive truth-value judgments throughout the paper are confirmed by the audiences at various presentations of this material as well as my editor and two reviewers for this journal. Furthermore, my editor reports that he ran the cases by some of his interlocutors and they also confirmed the intuitive judgments reported here.
A reviewer helpfully notes that the fate of these theories might not be decided as fast as I make it sound here. See footnote 28 for further discussion.
I use the conventional double-bracket notation \([\![\cdot ]\!]_X\) for the semantic value function with a subscript denoting the semantic framework; italic uppercase letters for sentences. I will suppress indices of evaluation for the semantic value function. In the course of the discussion, I will sometimes use sentences to stand for the things they mean, but the context should not cause any confusion about this.
I will assume for the rest of the paper that Blue is on the right is the negation of Blue is on the left (similarly for Red) and ignore the possibility that one of the children might not be sitting on either side.
Formally, this would correspond to the least upper bound of the subset of truthmakers for \(Blue_{left}\) and \(Red_{left}\).
I write \(|\alpha |\) to denote the intensional proposition expressed by \(\alpha \).
This presentation slightly distorts the formulation of inquisitive semantics, but not in a way that matters for the issues under investigation in this paper. What I call sentential meaning here is actually the set of alternatives associated with a sentence or the inquisitive proposition expressed by the sentence in inquisitive semantics (Ciardelli et al., 2018a, §2.4.2). I take this set of alternatives to be the meaning of a sentence. This assumption is harmless in this paper, because we will be working with antecedents of conditionals and these are alternative-sensitive environments (Ciardelli et al., 2018b, §3.1).
See Santorio (2018, §4), Ciardelli et al. (2018b, §3.2), Alonso-Ovalle (2009, §2) and Fine (2012, p. 237). The differences between these theories do not matter for our purposes. Ciardelli et al. use background semantics, which makes different predictions for cases involving negations taking scope over conjunctions, but our cases do not fall into that category. Fine employs a transition relation that represents causal outcomes of imposing changes as demanded by counterfactual antecedents. Here this relation can be interpreted as putting out the closest worlds where the truthmakers for the antecedent hold (Fine, 2012, p. 241). What matters for our purposes is the double universal quantification in \((>)\) that requires universal quantification not only on all the closest worlds for one of the semantic values for the antecedents, but also over all of the semantic values for the antecedent. This allows these theories to validate the inference pattern called Simplification of Disjunctive Antecedents (SDA), which lets one infer if it had rained, the party would have been ruined and if it had snowed, the party would have been ruined from if it had rained or snowed, the party would have been ruined. The validation of this inference pattern is essential for the expected judgments for the counterfactuals in question here.
Thanks to Paolo Santorio (p.c.) for suggesting this.
See Horn (1972), Simons (2001) and Sauerland (2004) for global-pragmatic approach. Global approach does not impose any LF change on the sentence in question. One reason why I prefer the local approach is because the change in LF seems required to get the desired truth-value predictions for our cases. Another reason is because there is independent evidence that global approach may not be able to explain embedded exhaustification operators (Chierchia et al., 2009). Ultimately, exhaustification operators required for our purposes have to be doubly embedded. Not only they are embedded in a disjunction, but the disjunction itself is embedded in the antecedent of a conditional.
For motivation and further discussion, see Fox (2007, §6.1).
The elements of this set is to be taken as a set of sentences for Santorio and set of sets of possible worlds for inquisitive semantics.
Even though more fine-grained theories need not appeal to Hurford-type explanations, could they, if they wanted to? This is not totally clear. Ciardelli and Roelofsen (2017) argue that more fine-grained theories are unable to predict the semantic redundancy in Hurford disjunctions, since in more fine-grained theories the meaning of Hurford disjunctions is not equivalent to one of their disjuncts. However, there might be other ways for these theories to explain why Hurford disjunctions sound bad without sacrificing their extra propositional grain. For instance, Fine might be able to say that the infelicitous Hurford disjunctions such as (5-a) and (5-b) sound bad because one of the disjuncts is a disjunctive part of the other (Fine, 2017, p. 565). For (5-a), this means that being Californian is a disjunctive part of being American, since being American is plausibly a covert disjunction of being Californian, being Texan, being Alaskan et cetera. On the other hand, felicitous Hurford disjunctions such as (6-a) and (6-b) sound fine, because one of the disjuncts is a conjunctive part of the other. If we couple this story with a truthmaker dynamics where an update with a context is by way of adding or fusing truthmakers of the assertions, then a context updated with an infelicitous Hurford disjunction is the same context as a context updated with the weaker disjunct of the same infelicitous Hurford disjunction. However, a context updated with a felicitous Hurford disjunction is not the same as a context updated with either disjunct of a felicitous Hurford disjunction. Thus, infelicitous Hurford disjunctions make the same contribution to the context as one of their disjuncts, whereas felicitous Hurford disjunctions make a different contribution to the context from either of its disjuncts does. One advantage of this explanation is that it does not require any covert exhaustification to block entailment between disjuncts, since the prediction of felicity/infelicity is made through the type of entailment between the disjuncts. There is much to say about such a pragmatic story in truthmaker semantics, but I aim to pursue it elsewhere.
A reviewer notes that less fine-grained theories at this point can point out that exhaustification is an optional phenomenon and so perhaps less fine-grained theories can take exhaustification on board for (3-a), but leave it out for (9-a). However, the reviewer also correctly comments that this behooves less fine-grained theories to explain what forces the insertion of exhaustification in (3-a) while leaving it out for (9-a), since both of their antecedents share the exact same logical form. Without this further explanation the optionality of exhaustification does not help with our cases.
Thanks to a reviewer for providing this informal gloss. Also an editor of this journal helpfully points out that the arbitrariness of when to exhaustify might be an independent challenge for those who already favor less fine-grained theories for independent reasons and is otherwise unfazed by our argument in the paper. The editor also conjectures that interactions with focus might be relevant here. I leave this investigation to future work.
Thanks to Ivano Ciardelli and Floris Roelofsen (p.c.) for proposing this defense on behalf of less fine-grained theories and a reviewer for bolstering it further.
It is also important to note that this story may help intensional theories as well, since a different set of non-trivial changes to the LF’s of our cases due to exhaustification on different QUD’s may break the intensional equivalence of these antecedents. This might help intensional theories pry apart the truth-value predictions for (9-a)–(10-b) in principle. However, it also requires a more radical departure from the story told in Sect. 6, because the exhaustification story in Sect. 6 preserves intensional equivalence of the antecedents of (9-a), (10-a) and (10-b). Intensional theories need break the intensional equivalence especially between (9-a)/(10-a) and (10-b) to predict (10-b) not true. Otherwise, even if they can get (9-a) and (10-a) right for Scenario 2, they cannot still get (10-b) right, since the antecedent of (10-b) would still only be true in worlds where Blue switches to the right and seesaw becomes unbalanced, even though the antecedent of (10-b) explicitly instructs us to consider the possibility where Blue switches to right, Red switches to left and seesaw consequently becomes balanced. Without breaking intensional equivalence of these antecedents intensional theories cannot generate the intuitive reading of (10-b), e.g. not true. Thanks to a reviewer for discussion here.
Singh argues (2008, p. 255) that strengthening the weaker disjunct should make it inconsistent with the stronger disjunct. Here I help myself only to the weaker case that the strengthening should break the entailment among the disjuncts.
Thanks here to two reviewers and the editor for pressing me to clarify what this objection exactly means for the less fine-grained theories and making me see in the process that two objections I have in this section are indeed related to each other.
Thanks here to the editor who is drawing my attention to the nonexistence of such a reading and the importance thereof to our argument.
For instance, the editor and reviewers attest to it along with many others to whom I presented this material.
Thanks to a reviewer for providing this line of defense on behalf of less fine-grained theories.
For a discussion of true-antecedent counterfactuals, see Lewis (1973, §1.7).
One test case for this explanation is the felicitous use of true-antecedent counterfactuals as investigated by Anderson (1951). Anderson uses an example like If Jones had taken arsenic, he would have shown just exactly those symptoms which he does in fact show to show that sometimes a counterfactual is perfectly fine when its antecedent is true. If the story we have told was correct, then we should have expected this counterfactual to sound bad, since the actual scenario is identical to the one invoked by the counterfactual. But this charge ignores the conditions under which true-antecedent counterfactuals are felicitous. Most notable analyses of felicitous true-antecedent counterfactuals argue that the felicitous use of those counterfactuals involve making an argument for their antecedent, e.g. the fact that Jones has taken the arsenic above (see Anderson, 1951; Mandelkern, 2020, §4). The question is: why make an argument? One reason is that some of the interlocutors are not aware that the actual situation is identical to the hypothetical situation for the counterfactual. Our pragmatic explanation anticipates this. In a context where a true-antecedent counterfactual is felicitous the actual and hypothetical situations are not known to be identical by at least some of the interlocutors. But this means that the counterfactual invokes a hypothetical scenario that is not accepted to be identical to the actual scenario at least by some interlocutors. This ensures that the assertion of the true-antecedent counterfactual is not redundant. This seems right, especially because the counterfactual would again feel odd if everyone accepted that John took the arsenic. Our pragmatic explanation paves the way for a non-trivial prediction for the use of true-antecedent counterfactuals, namely that true-antecedent counterfactuals will be felicitous only when the identity of the actual and hypothetical situation is not shared by the interlocutors.
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Acknowledgements
This paper has been developed as a third-year paper during my Ph.D. training at Johns Hopkins University. I have benefited from extensive discussions with many people along the way. First and foremost, thanks to Justin Bledin and Kyle Rawlins who supervised the project closely and shared insightful feedback. I also thank two extremely helpful reviewers and my editor of Linguistics and Philosophy who provided in-depth comments that led to many crucial improvements. Thanks also to Lucas Champollion, Ivano Ciardelli, Justin Khoo, Dean McHugh, Sonya Ringer, Floris Roelofsen, Jacopo Romoli, Paolo Santorio and Yasu Sudo for their comments and encouragement. I also benefited from many discussions when I presented this material at UCL Semantics Research Seminar, UC San Diego SemanticsBabble group weekly meeting, JHU Hammond Society weekly meeting, Justin Bledin’s Truthmakers seminar in Fall 2020 at JHU and Matt Mandelkern’s Modals and Conditionals seminar in Spring 2021 at NYU. As would be on-brand for this paper, the preceding acknowledgements have at least one instance of redundancy.
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Güngör, H. Counterfactuals, hyperintensionality and Hurford disjunctions. Linguist and Philos 46, 169–195 (2023). https://doi.org/10.1007/s10988-022-09360-3
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DOI: https://doi.org/10.1007/s10988-022-09360-3