Abstract
Free-choice disjunction manifests itself in complements of comparatives, existential modals, and related contexts. For example, “Socrates is older than Plato or Aristotle” is usually understood to mean “older than each”, not “older than at least one”. Normally, to get an “at least one” reading, a wh-rider has to be appended, e.g., “whichever is younger” or “but I don’t remember which”. Similarly, “Socrates could have been a lawyer or a banker” usually means “Socrates could have been a lawyer and ( not “or”) could have been a banker”. And “Socrates needs an umbrella or a raincoat” is normally understood in a way that isn’t synonymous with “Socrates needs an umbrella or Socrates needs a raincoat”. Roughly, the reading is “getting a satisfactory umbrella would meet his need and getting a satisfactory raincoat would meet his need”.
These examples all have “conjunctive force” and the question I address is whether there’s a satisfactory pragmatic account of why the force is with them. I present a simple Gricean argument that the “co-operative speaker” assumption, added to a disjunctive literal meaning, produces conjunctive force for epistemic modals. This argument may work for some other cases, but I express some pessimism about covering the full range of modals.
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- 1.
Note that analogous reasoning for ‘after’ is incorrect – arriving after the earlier of you did doesn’t imply arriving after both of you did, and consonant with this, the ‘after’ variant of (1c) has no cf reading. There are complications – (see Forbes 2014:178–9) – but this does seem to explain the main differences between ‘before’ and ‘after’ noted in (Larson 1988).
- 2.
The main ‘cue to the contrary’ is the appearance of a wh-rider; for example, cf in (2a) vanishes if we append whomever is younger or but I forget which one.
- 3.
Instances of cf which I do not discuss in this paper include dogs or cats make good pets, he’ll like the red one or the blue one, and you need an umbrella or a raincoat (which is not normally understood in a way that makes it a consequence of you need an umbrella – see Forbes 2006:118–21).
- 4.
- 5.
- 6.
van Rooij (2010:11) endorses a similar transparency principle.
- 7.
It is equally natural to understand Lestrade’s No, he can’t be as an expression of causal impossibility, though this still leaves work to explain how Lestrade is contradicting Watson. However, No, that’s not true would be a relatively unambiguous contradicting of Watson, since it is difficult to hear that as referring to the embedded non-modal Holmes is in Paris.
- 8.
The eavesdropper complication is introduced in (Egan et al. 2005).
- 9.
For all U knows, Holmes is in Paris or Berlin seems to have as its preferred reading that Holmes’ being in Paris is consistent with what U knows and his being in Berlin is consistent with what U knows. The mere consistency of the disjunction Holmes is in Paris or Holmes is in Berlin with what U knows only guarantees that at least one of the locations is consistent with what U knows. So if the goal is just to have some case of (+cf) accounted for by an argument like (a1)–(a9), this is it; the counterparts of (E) and (T) are very plausible for this operator.
- 10.
Of course, there are other objections to speaker-relative accounts of might. For example, there is the alleged phenomenon of ‘self-correction’: after Lestrade has spoken, Watson might concede with Then I was wrong (he clearly wouldn’t have been wrong at t, just before Lestrade spoke, if all he had said at t was For all I know, Holmes is in Paris). For scepticism about self-correction, see (Wright 2007). Other problems concern embedding epistemic modals in attitude ascriptions or conditionals; for discussion, see (Silk 2016, Chapter 3).
- 11.
Examples in which the domain of quantification is disputed play a central role in (Silk 2016).
- 12.
Wright (2005) notes that ‘there is a challenge involved in the question: if, as you say, [cheese grits are tasty], how come nobody here but you likes [them]? which goes missing if the proper construal of it mentions…standard-relativity in the antecedent’. Certainly, that no-one else likes them seems compatible with the mere fact that you find them tasty, but their unpopularity is a challenge to the idea that your taste-judgements are authoritative. In the same vein, one might ask If Rousteng polarises Paris, how come no-one in Clichy sous Bois has heard of him? If all parties were accepting the narrow use of Paris, the question would have no point. Its point is to challenge the narrow use.
- 13.
There is also a semantic version of consistency, satisfiability, which is an existential claim that a certain function exists. But in the mathematical realm, existence is grounded in consistency, so the existential claim rests on a consistency, i.e., negative existential, claim.
- 14.
Even those who have their doubts about the reading of ◇ U as epistemic possibility should agree to restricting (T) to detection of inconsistency, if they would like the argument to explain the (+cf) remarked upon in note 8.
- 15.
There are many kinds of non-monotonic entailment relations, and many relations of each kind. But we can illustrate in terms of ‘default assumption’ entailment (Makinson 2005:31). Define ‘cosat(\( \mathcal{P} \)(x),y)’ to be the set of all subsets of x that are cosatisfiable with y; i.e., z ∈ cosat(\( \mathcal{P} \)(x),y) iff z ⊆ x and ∃v: ∀σ ∈ z ⋃ y, v(σ) = ⊤. And say that z is maximal in a family of sets \( \mathcal{F} \) iff ∄z′ ∈ \( \mathcal{F} \): z ⊊ z′. Then, where K is a set of assumptions (e.g., {C, R, E, T}), we may define a simple non-monotonic semantic entailment relation Γ
p, read ‘Γ entails p relative to default assumptions K’ by:(
): Γ
p iff for each X maximal in cosat(\( \mathcal{P} \)(K), Γ), X ⋃ Γ ⊨ p.Here ⊨ is classical semantic consequence. In words, (
) says Γ
p iff p is a classical consequence of: Γ augmented by any subset of K maximal in cosat(\( \mathcal{P} \)(K), Γ); note how K has acquired a new role from (5). In terms of , the revised rule of ⋀I, from Σ 
p and Σ
q infer Σ
p ⋀ q, is clearly sound, since the augmentations of Σ allowed by () are the same for all three sequents. This justification cannot be given for the standard formulation, from Γ
p and Δ
q infer Γ ⋃ Δ
p ⋀ q: although the assumption Γ ⋃ Δ 
p ⋀ q gets us a counterexample with an X maximal in cosat(\( \mathcal{P} \)(K), Γ ⋃ Δ), such an X needn’t be maximal in cosat(\( \mathcal{P} \)(K), Γ) or cosat(\( \mathcal{P} \)(K), Δ). For example, let K = {A → B}, Γ = {A}, Δ = {¬B}. Then cosat(\( \mathcal{P} \)(K), Γ) = cosat(\( \mathcal{P} \)(K), Δ) = {∅, {A → B}}, whose sole maximal member is {A → B}. So Γ B since {A → B, A} ⊨ B, and Δ ¬A since {A → B, ¬B} ⊨ ¬A. But cosat(\( \mathcal{P} \)(K), Γ ⋃ Δ) = {∅}, whose sole maximal member is ∅. Hence Γ ⋃ Δ B ⋀ ¬A, since {A} ⋃ {¬B} ⋃ ∅ 
B ⋀ ¬A. Note that even if Γ ⊊ Δ, the X given by Γ ⋃ Δ
p ⋀ q needn’t be maximal in cosat(\( \mathcal{P} \)(K), Γ), which provides grounds for rejecting the deduction (a1)–(a9). - 16.
The conventional formulation of ¬I, from Γ
q ⋀ ¬q infer Γ\p
¬p, is sound for (see note 14 for definitions). For if Γ\p
¬p, then we have an X maximal in cosat(\( \mathcal{P} \)(K), Γ\p) for which there is a v satisfying Γ\p, X and falsifying ¬p. This v shows Γ
q ⋀ ¬q, so long as X is also maximal in cosat(\( \mathcal{P} \)(K), Γ), which it is: (i) X is in cosat(\( \mathcal{P} \)(K), Γ) since v satisfies Γ ⋃ X, and (ii) since X is maximal in cosat(\( \mathcal{P} \)(K), Γ\p), X is also maximal in cosat(\( \mathcal{P} \)(K), Γ) – clearly, if Y is in cosat(\( \mathcal{P} \)(K), Γ) then Y is in cosat(\( \mathcal{P} \)(K), Γ\p), so if X ⊊ Y, X is not maximal in cosat(\( \mathcal{P} \)(K), Γ\p). - 17.
In the late 70’s into 1980, Steve Ovett and Sebastian Coe were the world’s leading middle-distance runners, the two of them far ahead of the rest. In the year or so before the Moscow Olympics in 1980 they’d swapped the world 1500m and mile records back and forth, though they had deliberately avoided running in the same race. Ovett was coming off what is still one of the longest winning streaks in top-class 1500m races. But there had been a few he hadn’t been in, where Coe had run and won just as convincingly as Ovett did, or even more so (it was often hard to know how much Ovett could have won by, because of his habit of slowing down at the end of a race and waving to the crowd as he crossed the line). There was huge anticipation of their meeting in the 1500m final in Moscow, when both were in top form. As it happened, Ovett beat Coe to the gold earlier in the week in the 800m, and seemed to lose focus. Coe won the 1500; Ovett could only manage bronze.
- 18.
If Γ is empty, (6a) is false, since (6b) is.
- 19.
However, non-monotonic logic handles such cases well. Consider the example of the appointment committee again, and the consequence relation Γ
p defined in note 14. Here the premise-set Γ is expanded by new information about Professor X, to produce new premises Γ′ (Γ ⊊ Γ′). This prevents the inclusion of the Cooperativeness Principle (C) in any member, hence any maximal member, of cosat(\( \mathcal{P} \)(K), Γ′). So (C) is no longer available to play the crucial role it had in deriving (from Γ) the implicature that Dr. Y is a weak candidate. This is, unquestionably, a nice application. - 20.
For discussion of how a priori access squares with the necessary a posteriori, see (Forbes 1985: 230–1).
- 21.
Of course, one could take the cf contrast between (7a) and (7b) as evidence that will is not a simple existential over future times, but involves a universal modal: Socrates will become a lawyer means not that at some time in the future, Socrates becomes a lawyer, but rather that in each possible future, Socrates becomes a lawyer (see Klecha 2014 and references therein), and the necessity operator explains the lack of cf. Prior called these contrasting accounts of will ‘Ockhamist’ and ‘Peircian’ respectively (Prior 1967:128–36). A serious problem for the Peircian view, noted by Thomason (1970:267), is that it renders an example like either we’ll arrive on time or we’ll fail to arrive on time (\( \mathbb{F} \) p ∨ \( \mathbb{F} \)¬p) invalid, though it certainly sounds trivial; see (Forbes 1996) for further discussion.
- 22.
Richard’s point here threatens to show that the entire literature on free-choice disjunction with modals rests on failing to notice the typical compatibility of ◇p and ◇q. So intuitions of cf in cases with the form ◇(□p ∨ □¬p) will be important. Natural cases of this sort are hard to come by. I offer: “it’s consistent that Goldbach’s conjecture is provable or its negation is”, which sounds (+cf) to me even if we assume S5 modalities (so that it’s false).
- 23.
An alternative account of the scalar implicature some ↝ some but not all might say that the enrichment only arises occasionally, when U is taken by the audience to satisfy a knowledgeability condition, that if all were F, U would know this (cf. Professor X’s knowledgeability with respect to Dr. Y’s suitability for the job). The problem is then to explain how such an occasional conversational implicature turns into a standing one.
- 24.
If what’s reasonably suspected to be a biased coin is tossed, rationality requires suspension of judgement about this coin will always fall heads. But this coin will sometimes fall heads still conveys not always. And for a fair coin on a particular occasion, this coin may fall heads or tails is (+cf), though rationality requires suspension of judgement about the individual disjuncts.
- 25.
In writing and revising this paper, I have been helped by comments from Michael Glanzberg, Mike Huemer, David Makinson, Stephen Neale, Graham Oddie, Francois Recanati, Mark Richard, Yael Sharvit and Una Stojnic.
p, read ‘Γ entails p relative to default assumptions K’ by:
p and Σ 
p ⋀ q gets us a counterexample with an X maximal in cosat(
B ⋀ ¬A. Note that even if Γ ⊊ Δ, the X given by Γ ⋃ Δ References
Barker, C. (2010). Free choice permission as resource-sensitive reasoning. Semantics and Pragmatics, 3, 1–38.
Egan, A., Hawthorne, J., & Weatherson, B. (2005). Epistemic modals in context. In G. Preyer & G. Peter (Eds.), Contextualism in philosophy. Oxford: Oxford University Press.
Forbes, G. (1985). The metaphysics of modality. Oxford: Oxford University Press.
Forbes, G. (1996). Logic, logical form, and the open future. In J. Tomberlin (Ed.), Philosophical perspectives (Vol. 10, pp. 73–92). Oxford: Blackwell.
Forbes, G. (2006). Attitude problems. Oxford: Oxford University Press.
Forbes, G. (2014). A truth-conditional account of free-choice disjunction. In D. Gutzmann, J. Köpping, & C. Meier (Eds.), Approaches to meaning: Composition, values and interpretation (pp. 167–186). Leiden: Brill.
Fox, D. (2007). Free choice and the theory of scalar implicatures. In U. Sauerland & P. Stateva (Eds.), Presupposition and implicature in compositional semantics. New York: Palgrave Macmillan.
Franke, M. (2011). Quantity implicatures, exhaustive interpretation, and rational conversation. Semantics and Pragmatics, 4, 1–82.
Fusco, M. (2014). Free-choice permission and the counterfactuals of pragmatics. Linguistics and Philosophy, 37(4), 275–290.
Grice, P. (1975). Logic and conversation. In D. Davidson & G. Harman (Eds.), The logic of grammar. Encino: Dickenson.
Grice, P. (1989). Studies in the way of words. Cambridge: Harvard University Press.
Humberstone, L. (2011). The connectives. Cambridge: The MIT Press.
Klecha, P. (2014). Diagnosing modality in predictive expressions. Journal of Semantics, 31, 443–455.
Larson, R. (1988). Scope and comparatives. Linguistics and Philosophy, 11, 1–26.
Levinson, S. (2000). Presumptive meanings. Cambridge: The MIT Press.
Makinson, D. (1984). Stenius’ approach to disjunctive permission. Theoria, 50, 138–147.
Makinson, D. (2005). Bridges from classical to nonmonotonic logic. London: King’s College Publications.
Prior, A. (1967). Past, present and future. Oxford: Oxford University Press.
Silk, A. (2016). Discourse contextualism. Oxford: Oxford University Press.
Simons, M. (2005). Dividing things up: The semantics of ‘Or’ and the modal/‘Or’ interaction. Natural Language Semantics, 13, 271–316.
Spector, B. (2007). Scalar implicatures: Exhaustivity and gricean reasoning. In M. Aloni & P. Dekker (Eds.), Questions in dynamic semantics. Amsterdam: Elsevier.
Stenius, E. (1982). Ross’ paradox and well-formed codices. Theoria, 48, 49–77.
Thomason, R. (1970). Indeterminist time and truth-value gaps. Theoria, 36, 264–281.
van Rooij, R. (2010). Conjunctive interpretation of disjunction. Semantics and Pragmatics, 3, 1–28.
Wright, C. (2005). Realism, relativism and rhubarb. Unpublished MS.
Wright, C. (2007). New age relativism and epistemic possibility: The question of evidence. Philosophical Issues, 17, 262–283.
Zimmerman, T. E. (2000). Free choice disjunction and epistemic possibility. Natural Language Semantics, 8, 255–290.
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Forbes, G. (2018). An Investigation of a Gricean Account of Free-Choice or . In: Capone, A., Carapezza, M., Lo Piparo, F. (eds) Further Advances in Pragmatics and Philosophy. Perspectives in Pragmatics, Philosophy & Psychology, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-319-72173-6_4
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