Complex Sentential Operators Refute Unrestricted Simplification Of

Semantics & Pragmatics Volume 11, Article 9, 2018 https://doi.org/10.3765/sp.11.9

This is an early access version of

Lassiter, Daniel. 2018. Complex sentential operators refute unrestricted Sim- pliﬁcation of Disjunctive Antecedents. Semantics and Pragmatics 11(9). https://doi.org/10.3765/sp.11.9.

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Complex sentential operators refute unrestricted Simpliﬁcation of Disjunctive Antecedents*

Daniel Lassiter Stanford University

Abstract There is a longstanding debate about the status of the principle Simpli- ﬁcation of Disjunctive Antecedents (SDA), according to which a counterfactual with a syntactically disjunctive antecedent [(φ ∨ ψ) > χ] entails a conjunction of counterfactuals [(φ > χ) ∧ (ψ > χ)]. This principle is highly intuitive for most examples that have been considered, but it has also been claimed to be subject to empirical counter-examples. However, there are promising pragmatic explanations for the currently known counter-examples, which have led several authors to argue in recent work that SDA is unrestrictedly valid after all. This short piece introduces new data involving sentential operators that impose both upper and lower bounds on conﬁdence, frequency, etc., such as likely but not certain, there is an exactly n% probability, and usually but not always. These examples show clearly that SDA is not valid tout court. While SDA-supporting interpretations do exist and require an explanation, every theory of counterfactuals also requires an explanation of examples that can only be read in a way that does not support SDA.

Keywords: counterfactuals, conditionals, disjunction, pragmatics

1 Simpliﬁcation of Disjunctive Antecedents: Detractors and defenders

Lewis’s (1973) semantics for counterfactuals does not validate the principle that Nute(1975) labels ‘Simplification of Disjunctive Antecedents’ (SDA). Using > to represent the counterfactual connective, I will define SDA as the claim that counterfactuals with the form of (1a) entail (1b).1 (1) a. (φ ∨ ψ) > χ b. (φ > χ) ∧ (ψ > χ) Nute(1975) and Fine(1975) object to Lewis’ semantics that SDA is intuitively valid in examples like (2) (slightly modified from Nute).

* Many thanks to Josh Dever and three anonymous reviewers for extremely helpful comments that helped me to improve and streamline this squib. 1 Note that the principle is sometimes given a stronger formulation according to which (1a) is equivalent to (1b). I will only be concerned with the weaker version, which is enough to generate the problems I will discuss. early access 2 2017. Santorio 2006, Rooij van 2003, Bennett 1984, em ob ruln entailment. troubling a be to seems (5b) harmless, is (5a) While hte oueasnl-o obymdlzditrrtto.Iwl o otruhtevrosoptions various the through go not will I interpretation. doubly-modalized or singly- a use to whether Op eatc,teeifrne ol o otruhfrsnecswt ooetoeao fthe if operator overt no with sentences for through go not would inferences these semantics, (1991b) gv the give Inwagen van & McKay valid. not is SDA that argue 1977) ( Inwagen van a. 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Willer 2014, Starr 2012, Fine 1981, od ¯ ( φ ∨ ψ ) Op > φ Kratzer’s in example, For modeled. is restriction how and must where , oee,oecudesl eieavrato the of variant a devise easily could one However, . 2 φ and Op ψ r noptbe r frequently are incompatible, are [ φ e se per ∨ ψ ][ nta ae ejs edto need just we case, that In . χ ] nal etne ihLFs with sentences entails 2 ailLassiter Daniel early access is not relevantly possible. Suppose also, 3 is not relevantly possible — that is, that (6) is false. Spain fights with the Allies ¯ od , 1981 Starr 2014, Willer ;2017 see also Fine 2012 for a related diagnosis). Ambiguity theories have the additional burden of explaining why the crop At this point, adopting a theory that validates SDA globally seems very attractive. In sum, McKay & van’s Inwagen ) (1977 purported counter-examples to SDA However, there is a very promising explanation for this apparent failure of example (2) and similar sentences are felt to be false. For them, (2) has two readings: case, the net resultinterpretation is that that sentences generates like onlysupporting (2) the interpretation are reasonable that ambiguous also inference between generates incall the a (3a), theories bizarre non-SDA in (3b). and this For an general a SDA- class brief “ambiguity label, theories”. I will readings arise. Some theories invokesupporting optional disjunctive covert antecedents operators into that ones thatthat convert receive SDA- does a not classical support interpretation SDA2017). (e.g., Others Alonso-Ovalle have2009, positedCiardelli more etreadings or al. less from2018 , complicatedSantorio a pragmatic theory derivations that, ofinterpretation SDA like (e.g., Loewer Lewis’,1976, doesNute not1980, supportBennett it2003, semantically Franke 2011). on In any either room for theories of counterfactuals that do validate SDA. Such a theory would explainother why examples SDA in readings a are very prominent straightforward inmore way. Theories (2) work that to and do do. so not First, many validate SDA they have must explain how both SDA-supporting and classical Example (4) conveys exactly what weand would (b) expect counterfactuals it with to impossible convey, antecedents if are (a) trivially SDA true. is valid, are often cited as showingfact that provide the an principle airtight is case not for this valid. conclusion, However, they and do the not empirical in situation leaves Likewise, someone who had little backgroundjustified knowledge in about inferring the from war (4) would that be 7) ( (7) is true. SpainFar would from never being have a fought refutation with of the SDA, Allies. then, McKay & van’s Inwagen 1977) ( example is presumably aware ofrender Spain’s the fascist possibility leanings of during alliance with the the WWII Allies period, against which Hitler exceedingly remote. Suppose that are vacuously true. Insince that both case, are both trivially true. counterfactuals So, in if (5) SDA is are valid unobjectionable, then (4)(6) should simply imply that Spain might have fought with the Allies. Complex sentential operators refute unrestricted SDA SDA, which has led some authors to argue that SDA is unrestrictedly valid after all Spain fights with the Allies This prediction appears to be correct. Someone whose knowledge supports (4) (4) is beginning to look like surprising confirmation of this principle’s validity. (Warmbr with (1973)Lewis and many others, that counterfactuals with impossible antecedents early access r rval as.So, false. trivially are (9) in entailments purported the of both but sensible, is (8) a. 9). 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If — a but classical musician switched to playingnot hip-hop necessarily she — would switch normally to — but playing jazz. If Jim had bet onbet 1 on there 3. is an exactly 50%If probability Jim that had he bet would on have bet 3 on there 3. is an exactly 50% probability that he would have If it were to rain in NewIf Mexico, it it were would to usually snow — in but New not Mexico, it always — would rain. usually — but not always — rain. tain — that it rained. If a person isally — driven but not by always — starvation choose to to eat eat insects. either dirt or insects, they usu- [Jim likes odd numbers, but ishe indifferent bet.] among them. We don’tIf know Jim how bet on 1 or 3 there isIf an it exactly rained 50% probability or that snowed he in bet New on Mexico 3. last week, it’s likely — but not cer- a. If a classical musician switchedmally — to but not playing necessarily jazz — switch or to hip-hop playinga. she jazz. would nor- b. a. b. If it were to rain or snow in New Mexico, it would usually —b. but not always — rain. The same problems apply to the These observations refute theories on which SDA is unrestrictedly valid. They implicature-based account. (16) Indicative conditionals may alsoHowever, this default is to apparently due an to interpretation semantic ambiguity that or licenses pragmatic enrichment, SDA. as intuitive interpretation of (13), none of16) (14)-( SDA entail would the assign conditionals them. that indicative (13) If you eat sea(14) cucumber or dung beetles you’ll get a stomachache. (15) are consistent with ambiguitydisjunctive theories, antecedents where are counterfactuals semantically withreading or syntactically which pragmatically validates SDA ambiguous and between one which a does not. to indicative conditionals. While indicative SDA would correctly characterize the (12) (11) Complex sentential operators refute unrestricted SDA we would expect (for example) from Alternative/Inquisitive Semantics or from an early access miut hoisoeadtie xlnto fwa rcsl swrong. is precisely what of explanation detailed a owe pragmatically theories something Ambiguity be also must there suggest, (1980) Nute (1976), Loewer As con- interpretation sensible a has that (2)/(17) like sentence a with presented when okwl enee odfn uhapamtcacuti ealadt ofotit confront to and detail in examples. account of pragmatic range a wider such a defend with to needed be will work idct hteeyter fcutratasms eable be must counterfactuals of theory every that indicate 2 Section in data The a. (18) over theories ambiguity for lower-bounding and SDA support upper- validate compelling of that sense theories provides make result to able This is that operators. that and antecedents SDA disjunctive support with not counterfactuals does for interpretation an generate to Conclusion 3 irel,Iao imnZag&LcsCaplin 08 w wthsi the in switches Two 2018. Champollion. Lucas & Zhang Linmin Ivano, Ciardelli, 2003. Francis. Jonathan Bennett, disjunction. and correlatives, Counterfactuals, 2009. Luis. Alonso-Ovalle, References more However, Quality. by ( 18b) and by Manner, (17) by of out would ruled interpretations bizarreness is its the (18a) of explain infelicitous: both can be why reasons we motivated out, independently works to explanation appealing of style this If (19) cold? growing the sun’s simpler, without the a content about is this (to detour conveys there pointless why that when — (18a), (17) (19) — in in available rigamarole expression meaning the unambiguous the choose she communicate would to Grice) intended paraphrase speaker the If Manner. (18a). interpretation sensible the convey to (17) sentence of use the about defective (17) interpreter an interpretation? would bizarre (18b), the interpretation on bizarre fixate a and (18a) to equivalent textually oapa in appear To hoyo onefcul:Asuyo rt odtoaiyadmnmlchange. minimal and conditionality truth of study A counterfactuals: of theory Oxford. 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