1 Introduction

There has recently been a surge of arguments in the literature that put pressure on what is sometimes called intensional semantic theories such as Stalnaker (1968) and Lewis (1973).Footnote 1 For instance, Ciardelli et al. (2018b) have recently argued that intensional theories of counterfactuals are inadequate, because they cannot distinguish the meanings of antecedents that are De Morgan equivalents, e.g. \(\lnot (\varphi \wedge \psi )\) and \(\lnot \varphi \vee \lnot \psi \). It has also been argued by many that a seemingly-valid inference pattern known as Simplification of Disjunctive Antecedents (SDA) seems to support semantic theories that can distinguish the meanings of intensionally equivalent sentences.Footnote 2 Such theories are generally called hyperintensional. Yet not all hyperintensional theories are created equal. They can be distinguished among themselves according to which intensionally equivalent sentences they accept and reject to be equivalent in their theories. In this paper, instead of providing more cases that make a case in favor of hyperintensional theories over intensional ones as in Ciardelli et al. (2018b), I aim to provide a couple cases that speak in favor of some hyperintensional theories over others (Fig. 1).

I aim to do this by relying on two observations from two versions of a scenario discussed by Romoli et al. (2022). It is best to start with these observations.Footnote 3 The first scenario goes as follows [N.B. for black-and-white version: the slightly darker t-shirt is Blue and the lighter one is Red]:

Two children, Blue and Red according to their t-shirt colors, are playing on a seesaw. Their weights are exactly the same, so when they are sitting on the opposite sides of the seesaw, the seesaw is balanced and if they are sitting on the same side, the seesaw is unbalanced. The only places children can be are either the left or right of the seesaw. Right now both Blue and Red are on the right side and the seesaw is unbalanced as displayed in the figure below. But things could be otherwise...

Fig. 1
figure 1

Scenario 1 describing two children sitting on the right side of a seesaw

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Fig. 2
figure 2

Scenario 2 describing children sitting on opposite sides of a seesaw

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Given this scenario, consider whether (1) sounds true or not:

figure a

Now take a different iteration of this scenario where the initial setup describes Blue on the left and Red on the right (as displayed in the Fig. 2 above).

Consider whether (2) sounds true or not:

figure b

If (1) sounds false, but (2) sounds true to the reader, then there arises a puzzle of sentential meaning affecting a number of semantic theories.

The goal of this paper is to investigate this puzzle. I aim to do this by comparing two classes of semantic theories and their predictions for (1) and (2). In Sect. 2 I will repeat Scenario 1 and consider two more counterfactuals in addition to (1) so that we get a better feeling of how intensional equivalents behave in antecedents. In Sect. 3 I look at the predictions by various semantic theories for these counterfactuals. These theories fit into two distinct classes for our purposes: given three intensionally equivalent sentences, those that distinguish the meaning of each of them (Alonso-Ovalle, 2009; Fine, 2012, 2017), which I call more fine-grained theories, and those that distinguish the meaning of some, but not all of them (Ciardelli et al., 2018a; Santorio, 2018), which I call less fine-grained theories. It turns out that less fine-grained theories predict the wrong truth-value for (1) whereas more fine-grained theories predict the right one. In Sect. 4 I discuss a way out of this result for less fine-grained theories.Footnote 4 The proposal stresses that the counterfactuals under investigation involve Hurford disjunctions and the covert logical form (LF) of these disjunctions allow less fine-grained theories to make the right predictions. In Sect. 5 I repeat Scenario 2 and show that less fine-grained theories with the adjustments from Sect. 4 predict the wrong truth-value for (2). These two results pose a dilemma for less fine-grained theories: either (i) accept that they cannot accommodate (1) and (2) together or (ii) face arbitrariness in applying the solution from Sect. 4. In Sect. 6 I discuss a proposal that relies on exploiting questions under discussion (QUD’s) to avoid this dilemma.Footnote 5 I articulate this proposal and how a certain implementation of this proposal seems to accommodate both (1) and (2). In Sect. 7 I discuss two issues which together suggest that this solution is unstable and ad hoc. In Sect. 8 I address why (2) sounds odd despite being true and how this bears on the general conclusion of the paper. In Sect. 9 I conclude that the truth-value judgments for the cases are more easily accommodated by more fine-grained theories and less so by less fine-grained theories and this may suggest for a more fine-grained treatment of sentential meaning in general on account of unification.

2 Children on a seesaw

First, I repeat Scenario 1 from Romoli et al. (2022).

Two children, Blue and Red according to their t-shirt colors, are playing on a seesaw. Their weights are exactly the same, so when they are sitting on the opposite sides of the seesaw, the seesaw is balanced and when they sit on the same side, the seesaw is not balanced. Right now both Blue and Red are on the right side and the seesaw is unbalanced. But things could be otherwise...

Consider again (3-a) ((1) above) given Scenario 1:Footnote 6

figure c

Then consider (4-a) and (4-b):

figure d

Given Scenario 1, (4-a) sounds true, whereas (3-a) and (4-b) do not (I summarize these judgments below in a Table 1 for ease of access).Footnote 7

Table 1 Expected truth-values in Scenario 1
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3 Hyperintensionality

Note that antecedents of (3-a), (4-a) and (4-b) are all intensional equivalents of each other, that is, these antecedents are all true in the same possible worlds. So it seems unlikely for an intensional theory of counterfactuals such as Stalnaker (1968) or Lewis (1973) to account for diverging truth-values for these counterfactuals, since the closest possible worlds where these antecedents are true will be the same set of closest possible worlds.Footnote 8

We need hyperintensional theories—that is, theories that can distinguish the meanings of intensionally equivalent sentences—such as Alonso-Ovalle (2009), Fine (2012, 2017), Santorio (2018) and inquisitive semantics (Ciardelli et al., 2018a). However, these theories do not predict the same set of intensional equivalents to be equivalent in their theories. For our purposes, these theories fit into two families that distinguish the meaning of (3-a), (4-a) and (4-b)’s antecedents to different extents. I will call the family to which Alonso-Ovalle’s and Fine’s theories belong, more fine-grained theories, and the family to which Ciardelli et al. and Santorio’s theories belong less fine-grained theories. Our naming convention will make sense after we study these theories a bit more.

3.1 More fine-grained theories

Given Scenario 1, more fine-grained theories predict different semantic values for antecedents of (3-a), (4-a) and (4-b):Footnote 9

\([\![Blue_{left}]\!]_{MFG}\)

\(\not =\)

\([\![Blue_{left}\vee (Blue_{left}\wedge Red_{left})]\!]_{MFG}\)

\(\not =\)

\([\![(Blue_{left}\wedge Red_{right})\vee (Blue_{left}\wedge Red_{left})]\!]_{MFG}\)

We briefly explain how these predictions come about. For Fine, sentence meanings are sets of exact truthmakers and falsemakers. An exact truthmaker for a sentence is a state that not only makes the sentence true, but it is also wholly relevant to the sentence (Fine, 2017, p. 558). The semantics is given relative to a partially ordered set of states that play the role of truthmakers and falsemakers for sentences. The states in Scenario 1 can be represented as \(blue_{left}/blue_{right}\), \(red_{left}/red_{right}\) and \(seesaw_{balance}/seesaw_{unbalance}\) for the state of Blue/Red being on the left/right and the seesaw being balanced/unbalanced respectively. These states are the exact truthmakers for \(Blue_{left}/Blue_{right}\), \(Red_{left}/Red_{right}\) and Balance/Unbalance.

The truthmakers for negation, conjunction and disjunction are given recursively. Exact truthmakers for \(\lnot Blue_{left}\) are the exact falsemakers for \(Blue_{left}\). Given the possible sides the children can be on in Scenario 1, this is the state of Blue being on the right, i.e. \(blue_{right}\).Footnote 10 The exact truthmaker for the conjunction \(Blue_{left}\wedge Red_{left}\) is the mereological sum of the exact truthmakers for \(Blue_{left}\) and \(Red_{left}\), denoted \(blue_{left}\sqcup red_{left}\).Footnote 11 Exact truthmakers for the disjunction \(Blue_{left}\vee Red_{left}\) is the set of exact truthmakers for each disjunct, i.e. \(\{blue_{left},red_{left}\}\). Given these clauses, the semantic values of (3-a), (4-a) and (4-b)’s antecedents are as follows in Finean truthmaker semantics:

\([\![Blue_{left}]\!]_{F}=\{blue_{left}\}\)

\(\not =\)

\([\![Blue_{left}\vee (Blue_{left}\wedge Red_{left})]\!]_{F}=\{blue_{left},blue_{left}\sqcup red_{left}\}\)

\(\not =\)

\([\![(Blue_{left}\!\wedge \! Red_{right})\!\vee \!(Blue_{left}\!\wedge \! Red_{left})]\!]_{F}\!=\!\{blue_{left}\sqcup red_{right},blue_{left}\sqcup red_{left}\}\)

For Alonso-Ovalle (2009, §2.2.2), sentence meanings are sets of alternatives for a given sentence. Alternatives are interpreted to be intensional propositions, that is, sets of possible worlds. Meanings of non-disjunctive sentences are singleton sets of propositions, since non-disjunctive sentences have only themselves as alternatives, i.e. \([\![Blue_{left}]\!]_{AO}=\{|Blue_{left}|\}\).Footnote 12 Meanings of disjunctive sentences are sets of alternatives corresponding to each disjunct:

\([\![Blue_{left}\vee (Blue_{left}\wedge Red_{left})]\!]_{AO}=\{|Blue_{left}|,|Blue_{left}\wedge Red_{left}|\}\)

\([\![(Blue_{left}\wedge Red_{right})\vee (Blue_{left}\wedge Red_{left})]\!]_{AO}\!=\!\{|Blue_{left}\wedge Red_{right}|,|Blue_{left}\wedge Red_{left}|\}\)

We summarize the semantic values predicted by Alonso-Ovalle’s framework as follows:

\([\![Blue_{left}]\!]_{AO}=\{|Blue_{left}|\}\)

\(\not =\)

\([\![Blue_{left}\vee (Blue_{left}\wedge Red_{left})]\!]_{AO}=\{|Blue_{left}|,|Blue_{left}\wedge Red_{left}|\}\)

\(\not =\)

\([\![(Blue_{left}\wedge Red_{right})\vee (Blue_{left}\wedge Red_{left})]\!]_{AO}\!=\!\{|Blue_{left}\wedge Red_{right})|,|Blue_{left}\wedge Red_{left}|\}\)

Thus we see that more fine-grained theories predict different semantic values for each antecedent in (3-a), (4-a) and (4-b).

3.2 Less fine-grained theories

There are hyperintensional theories that distinguish fewer of these intensional equivalents due to further restrictions on the range of semantic values they allow (Santorio, 2018; Ciardelli et al., 2018a, b). In these theories, some of the intensional equivalents are still equivalent:

\([\![Blue_{left}]\!]_{LFG}=[\![Blue_{left}\vee (Blue_{left}\wedge Red_{left})]\!]_{LFG}\)

But some of them are not:

\([\![Blue_{left}]\!]_{LFG}\not =[\![(Blue_{left}\wedge Red_{right})\vee (Blue_{left}\wedge Red_{left})]\!]_{LFG}\)

\([\![Blue_{left}\vee (Blue_{left}\wedge Red_{left})]\!]_{LFG}\) \(\not =[\![(Blue_{left}\wedge Red_{right})\vee (Blue_{left}\wedge Red_{left})]\!]_{LFG}\)

For inquisitive semantics, the meaning of a sentence is the set of weakest information states (with respect to entailment) that support the proposition expressed by the sentence (Ciardelli et al., 2018a, §2.3).Footnote 13 Information states are sets of possible worlds. An information state supports a proposition expressed by a sentence if it contains enough information to entail the proposition. We compute sentential meanings in two steps. First, we find the set of information states that support a proposition and then find the set containing the weakest of these information states. For example, we compute the meaning of an atomic sentence \(Blue_{left}\) as follows. Writing s for information states, we designate \(\{s:s\subseteq |Blue_{left}|\}\). Since the weakest s is just \(|Blue_{left}|\), we end up with the singleton \(\{|Blue_{left}|\}\). The meaning of a disjunction \(Blue_{left}\vee Red_{left}\) is given by the union of propositions expressed by each disjunct, i.e. \(\{|Blue_{left}|,|Red_{left}|\}\). However, if one of the disjuncts entails the other as in \(Blue_{left}\vee (Blue_{left}\wedge Red_{left})\), then the proposition expressed is the set containing the weakest information state that supports the proposition expressed by the weaker disjunct, \(Blue_{left}\). We can show this by computing the meaning of (3-a)’s antecedent:

\([\![Blue_{left}\vee (Blue_{left}\wedge Red_{left})]\!]_{IS}\)

=

\(\{s:s\subseteq |Blue_{left}|\}\cup \{s:s\subseteq |Blue_{left}\wedge Red_{left}|\}\)

=

\(\{s:s\subseteq |Blue_{left}|\text { or } s\subseteq |Blue_{left}\wedge Red_{left}|\}\)

=

\(\{s:s\subseteq |Blue_{left}|\}\)

=

\(\{|Blue_{left}|\}\)

For (4-b)’s antecedent: since there neither \(Blue_{left}\wedge Red_{right}\) entails \(Blue_{left}\wedge Red_{left}\) nor vice versa, the inquisitive recipe yields the following:

\(\{|Blue_{left}\wedge Red_{right}|,|Blue_{left}\wedge Red_{left}|\}\)

We sum up the semantic values predicted by inquisitive semantics as follows:

$$\begin{aligned}&\displaystyle [\![Blue_{left}]\!]_{IS}=\{|Blue_{left}|\}=[\![Blue_{left}\vee (Blue_{left}\wedge Red_{left})]\!]_{IS}\\&\displaystyle \not = \\&\displaystyle [\![(Blue_{left}\!\wedge \! Red_{right})\!\vee \!(Blue_{left}\!\wedge \! Red_{left})]\!]_{IS}\!=\!\{|Blue_{left}\!\wedge \! Red_{right}|, |Blue_{left}\!\wedge \! Red_{left}|\} \end{aligned}$$

For Santorio, the meaning of sentences are sets of syntactic truthmakers, that is, sets of sentences. These syntactic truthmakers are computed from Katzir’s complexity-based theory of alternatives (Katzir, 2007). Santorio proposes a recipe that generates stable and minimal subsets of Katzir alternatives. Truthmakers are the conjunctions of sentences in each of these minimal stable subsets. For our purposes, all we need to know about Katzir’s theory of alternatives is that the alternatives for a disjunction is the set containing both disjuncts, the disjunction itself and the conjunction of these two disjuncts:

\(ALT_{Katzir}(P\vee Q)=\{P\vee Q,P,Q,P\wedge Q\}\)

A stable subset \(A\subseteq ALT_{Katzir}\) for a sentence means that the sentences in A are consistent with the negations of the rest of the alternatives in \(ALT_{Katzir}\). Computing the truthmakers for (3-a), (4-a) and (4-b)’s antecedents, we find that \(Blue_{left}\) is the only truthmaker for both \(Blue_{left}\) and \(Blue_{left}\vee (Blue_{left}\wedge Red_{left})\). The latter might not be obvious, so I give a brief derivation. Let us write the Katzir alternatives for \(Blue_{left}\vee (Blue_{left}\wedge Red_{left})\) as follows:

$$\begin{aligned} ALT_{Katzir}([Blue_{left}\!\vee \! (Blue_{left}\!\wedge \! Red_{left})]) \!=\!\left\{ \!\! \begin{aligned}&Blue_{left}\vee (Blue_{left}\wedge Red_{left}), \\&Blue_{left}, \\&Blue_{left}\wedge Red_{left} \\ \end{aligned} \!\right\} \end{aligned}$$

The subset \(\{[Blue_{left}\vee (Blue_{left}\wedge Red_{left})],Blue_{left}\}\) is a stable subset, because the conjunction of these sentences is consistent with the leftover alternative \(\lnot (Blue_{left}\wedge Red_{left})\). This implies \(Blue_{left}\) is a truthmaker. However, the subset \(\{[Blue_{left}\vee (Blue_{left}\wedge Red_{left})],Blue_{left}\wedge Red_{left}\}\) is not a stable subset, because the conjunction of \(Blue_{left}\wedge Red_{left}\) and \(\lnot Blue_{left}\) is not consistent. This implies that \(Blue_{left}\wedge Red_{left}\) is not a truthmaker for Santorio. Checking all other possible stable subsets, we find that \(Blue_{left}\) is the only truthmaker for \(Blue_{left}\vee (Blue_{left}\wedge Red_{left})\).

Going through the same procedure for (4-b), we find that \(Blue_{left}\wedge Red_{right}\) and \(Blue_{left}\wedge Red_{left}\) are the truthmakers for \((Blue_{left}\wedge Red_{right})\vee (Blue_{left}\wedge Red_{left})\). We sum up the semantic values for Santorio as follows:

\([\![Blue_{left}]\!]_{S}=\{Blue_{left}\}=[\![Blue_{left}\vee (Blue_{left}\wedge Red_{left})]\!]_{S}\)

\(\not =\)

\([\![(Blue_{left}\!\wedge \! Red_{right})\!\vee \!(Blue_{left}\!\wedge \! Red_{left})]\!]_S\!=\!\{Blue_{left}\!\wedge \! Red_{right},Blue_{left}\!\wedge \! Red_{left}\}\)

For an interim summary: what we have done so far is to observe that Fine’s and Alonso-Ovalle’s theories predict different semantic values for the antecedents of (3-a), (4-a) and (4-b), whereas inquisitive semantics and Santorio’s theory predict the same semantic value for the antecedents of (3-a) and (4-b), while they assign a distinct semantic value for (4-b). The reason why we called the former theories more fine-grained and the latter less fine-grained should be clear—the former make more distinctions among intensionally equivalent sentences, whereas the latter make fewer distinctions. Now we move on to analyze the verdicts by these theories for (3-a), (4-a) and (4-b).

3.3 Predictions

We do not yet have a semantic entry for the counterfactual connective > for these theories. Fortu nately, in various writings both more and less fine-grained theories subscribe to slightly different versions of the essentially same semantic clause for >:Footnote 14

figure e

This clause is general enough to apply to both more and less fine-grained theories. Intuitively, \((>)\) is asking us to consider all the closest worlds where each element in the semantic content of the antecedent holds. A counterfactual is not true if there exists a closest world for some \(P\in [\![\varphi ]\!]\) such that the consequent is not true there. Why are we saying not true instead of false? This is because such an assumption is controversial and unnecessarily strong for our purposes. Some might want to say that when only some of the closest worlds are where the consequent is true, the counterfactual is indeterminate rather than false.Footnote 15 The weaker result is sufficient for the conclusions of the paper to go through.

Given \((>)\), the truth-value of (3-a) is a problem for less fine-grained theories. This is because less fine-grained theories have a single alternative for (3-a)’s antecedent, i.e. \([\![Blue_{left}\vee (Blue_{left}\wedge Red_{left})]\!]_{LFG}=\{Blue_{left}\}\), and all the closest worlds where this alternative holds are worlds where the seesaw is balanced. This means that \((>)\) coupled to less fine-grained theories predicts (3-a) to be true contrary to expectations. As a result, less fine-grained theories cannot predict the truth-value divergence of (3-a) and (4-a). Still they predict (4-b) to be not true in line with the expectations. This is because one of the alternatives for (4-b)’s antecedent corresponds to both of the children being on the left and the closest worlds where this is the case are worlds where the seesaw is unbalanced. Since the consequent is not true in all the antecedent-worlds, (4-b) is not true (results are summed up in the Table 2 below).

Table 2 Truth-value predictions of less fine-grained theories for Scenario 1
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On the other hand, more fine-grained theories coupled with \((>)\) will predict (3-a) and (4-a) to have different truth-values. In particular, more fine-grained theories predict (4-a) to be true, while (3-a) and (4-b) to be not true as expected. Importantly, (3-a) is predicted not true, because more fine-grained theories predict the existence of an alternative corresponding to both children being on the left of the seesaw for (3-a)’s antecedent. The closest worlds where this alternative is true are worlds where the consequent of (3-a) is not true. So it seems that the extra grain that more fine-grained theories bring to the table is needed to predict the right result for (3-a) (results again summed up in the Table 3 below).

Table 3 Truth-value predictions of more fine-grained theories for Scenario 1
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4 Hurford disjunctions and exhaustification

As matters stand in Sect. 3, less fine-grained theories underpredict for (3-a). Is there a way to accommodate (3-a) in less fine-grained theories? In this section I will discuss one proposal to do so.Footnote 16 We have briefly mentioned that one of the disjuncts in the antecedent of (3-a) entails the other. This is essentially why less fine-grained theories made identical predictions for (3-a) and (4-a). Such disjunctions are called Hurford disjunctions. They received a lot of attention in the linguistics literature.Footnote 17

Hurford disjunctions are of the type \(P\vee Q\) where one of disjuncts entails the other. Hurford observed that such disjunctions are infelicitous:

figure f

However, as observed by Gazdar (1979), some Hurford disjunctions are perfectly fine:

figure g

Although their disjuncts stand in an entailment relation, there is an asymmetry between (5-a)–(5-b) and (6-a)–(6-b). Recent work on Hurford disjunctions explains the infelicity of (5-a) and (5-b) by appealing to redundancy.Footnote 18 Redundancy here means that the whole disjunction is equivalent to one of its disjuncts. Given the classical treatment of disjunction, (5-a) is equivalent to its weaker disjunct, i.e. Sonya is American. This renders the whole disjunction redundant, since the weaker disjunct would have conveyed the exact same meaning as the whole disjunction.

There are two prominent approaches to explaining the asymmetry between (5-a)–(5-b) and (6-a)–(6-b): global-pragmatic approach and local-grammatical approach. Here I assume the local-grammatical approach.Footnote 19 Local approach explains the felicity of (6-a)–(6-b) by postulating covert exhaustification operators at the grammatical level (denoted henceforth as exh). Exhaustification operators work essentially like sticking an only to weaker disjuncts in Hurford disjunctions. For instance, Blue or both of them are on the left is interpreted as Only Blue or both of them are on the left. Applying such an operator to the weaker disjunct breaks the entailment and in consequence the redundancy. Formally, exh is defined with respect to a set of alternatives ALT for a given sentence. The exhaustification operator exh acts on a sentence \(\alpha \) and yields a stronger sentence \(\alpha '\) by conjoining \(\alpha \) with the denial of \(\alpha \)’s alternatives other than itself.

Two questions need answering here: (i) what is the procedure for determining alternatives and (ii) which alternatives are denied? Answering (i): it is generally agreed that the set of alternatives are codetermined by the grammar and context (e.g. Fox and Spector, 2018). Both supply a set of alternatives and their intersection is the ultimate set of alternatives relative to which exhaustification operators are defined. However, grammatical alternatives are usually invoked only for scalar items such as numerals and quantifiers. For nonscalar items, the alternatives for exh are assumed to be provided by questions under discussion (QUD).Footnote 20 Answering (ii): we do not deny every alternative in ALT. There are two reasons for this. The first is that every sentence is an alternative to itself and strengthening any sentence with its own negation leads to a contradiction. The second reason is that sometimes the alternatives are given by a set of sentences each of which can individually be denied without a contradiction, but not together.Footnote 21 Therefore, only a special subset called innocently excludable alternatives are denied. An innocently excludable subset \(IALT_{P}\) of \(ALT_{P}\) is the largest set of alternative sentences for P such that conjoining P with the negation of any A in \(IALT_{P}\) does not lead to a contradiction. Given this definition, exh strengthens the entailed disjunct by denying the sentences in the innocently excludable subset of alternatives.

Now let us see what this means for (6-a) (and ultimately for (3-a)):

figure h

For (6-a), the set of alternatives for the entailed disjunct is

$$\begin{aligned} ALT_{Blue_{left}}=\{Blue_{left},Red_{left}, Blue_{left}\wedge Red_{left}\}. \end{aligned}$$
(1)

Here \(ALT_{Blue_{left}}\) is determined by the QUD Who is on the left side (of the seesaw)? We take the denotation of QUD’s to be Hamblin sets (1973) in line with Fox and Hackl (2006) and Singh (2008). This yields the following alternative set for (6-a):

\(Q_{Left}=\{Blue_{left},Red_{left},Blue_{left}\wedge Red_{left}\}\) Footnote 22

The only innocently excludable subset of \(Q_{Left}\) is \(\{Red_{left},Blue_{left}\wedge Red_{left}\}\), because \(Blue_{left}\wedge \lnot Blue_{left}\) is obviously a contradiction. This gives us the final result:

\(\textsf {exh}(Blue_{left})\vee (Blue_{left}\wedge Red_{left})\)

\(\equiv \)

\([Blue_{left}\wedge \lnot Red_{left}\wedge \lnot (Blue_{left}\wedge Red_{left})]\vee (Blue_{left}\wedge Red_{left})\)

\(\equiv \)

\((Blue_{left}\wedge \lnot Red_{left})\vee (Blue_{left}\wedge Red_{left})\)

The left disjunct is equivalent to saying that only Blue is on the left. Hence the whole disjunction (3-a) is equivalent to the following:

figure i

Exhaustifying (6-a) prevents the whole disjunction from being equivalent to one of its disjuncts and the entailment between the disjuncts is also blocked. According to the local approach, the existence of such covert exhaustification is the reason why (6-a) sounds fine.

Applying this to (3-a) given Scenario 1, we exhaustify the left disjunct of (3-a)’s antecedent, yielding:

figure j

Note that (8) is just equivalent to (4-b):

figure k

This way less fine-grained theories predict (4-b) to be not true by less fine-grained theories in line with the expectations. Appealing to the relevant exhaustification on the disjunction in (3-a), less fine-grained theories can predict the right results for (3-a), (4-a) and (4-b). This way less fine-grained theories make up for the underprediction for (3-a) by utilizing the tools afforded by the literature on Hurford disjunctions (summarizing these results in the Table 4 below).Footnote 23

Table 4 Truth-value predictions of less fine-grained theories for Scenario 1 with exhaustification
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5 Children on a Seesaw, v.2

Thus far more fine-grained theories predict the right results for (3-a), (4-a) and (4-b) due to their semantic entries for logical operators and less fine-grained ones predict the right results due to exhaustification on Hurford disjunctions. We may think at this point that predictions are extensionally equivalent and this is the end of the debate. Fortunately, that is not the case and we can tease these predictions apart. First, we change Scenario 1 to Scenario 2 (depicted in Fig. 2 above).

In Scenario 2 the initial setup describes Blue on the left, Red on the right and the seesaw as balanced. First, consider (9-a) ((2) in the introduction):

figure l

(9-a) sounds true given the setup. Also consider (10-a) and (10-b):

figure m

Here (10-a) sounds true, whereas (10-b) sounds not true. Expected truth-value judgments for (9-a), (10-a) and (10-b) are given in the Table 5 below.

Table 5 Expected truth-value judgments for Scenario 2
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Now we look at the predictions. First, more fine-grained theories coupled with \((>)\) predict (9-a) and (10-a) to be true and (10-b) to be not true in line with the expectations. This is because the closest worlds for each \(P\in [\![B_{right}\vee (B_{right}\wedge R_{right})]\!]_{MFG}\) are those where the seesaw is unbalanced. The closest worlds where Blue is on the right are also worlds where Red is on the right and the seesaw is accordingly unbalanced just as for the closest worlds where both children are on the right. Hence (9-a) and (10-a) are true. By similar reasoning, (10-b) is not true (Table 6).

Table 6 Truth-value predictions of more fine-grained theories for Scenario 2
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For less fine-grained theories, we note that the disjunction of (9-a) is a Hurford disjunction as in (3-a), so we exhaustify it before computing the truth-value:

figure n

However, note that (11) is equivalent to (10-b) and (10-b) is predicted to be not true by less fine-grained theories. This is because the closest worlds where \(Blue_{right}\wedge Red_{left}\) is true are worlds where the seesaw is balanced and this implies (10-b) is not true. Thus, it appears less fine-grained theories strengthened with exh operators seem to predict (9-a) to be not true and this is the wrong prediction (Table 7).

Table 7 Truth-value predictions of less fine-grained theories for Scenario 2 with exhaustification
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Here is an informal gloss on what has been happening so far. Less fine-grained theories initially make the wrong prediction for (3-a) due to not distinguishing \(\varphi \vee (\varphi \wedge \psi )\) from \(\varphi \) in general. So, these theories need to strengthen themselves to ensure that the weaker disjunct in \(\varphi \vee (\varphi \wedge \psi )\) says \(\textit{only }\varphi \), which helps them get (3-a) right. This treatment forces less fine-grained theories to apply the same recipe to (9-a), since the antecedent of (9-a) is also a Hurford disjunction. However, getting (9-a) right requires not distinguishing between \(\varphi \vee (\varphi \wedge \psi )\) and \(\varphi \) and consequently not exhaustifying (9-a)’s antecedent for less fine-grained theories. In sum, less fine-grained theories seem to face an arbitrary choice in terms of when to exhaustify at this stage.Footnote 24 It is important to note that this arbitrary choice is only facing less fine-grained theories, since more fine-grained theories semantically distinguish \(\varphi \vee (\varphi \wedge \psi )\) from \(\varphi \) and get the right results both for (3-a) and (9-a) as seen above. It is only when a theory does not semantically distinguish between \(\varphi \vee (\varphi \wedge \psi )\) and \(\varphi \), and explain (3-a) via exhaustification that it faces this problem of arbitrary choice.Footnote 25

6 Determining the set ALT

We have started with Scenario 1 and observed that less fine-grained theories predict the wrong results for (3-a) given Scenario 1, whereas more fine-grained theories predict the right results. Then we considered a way less fine-grained theories can accommodate (3-a). But this proposal turned out to make the wrong predictions for (9-a). Where do we go from here?

I would like to consider a further modification to the exhaustification story that may be able to enable less fine-grained theories to accommodate both (3-a) and (9-a).Footnote 26 We have seen that defining exhaustification relative to the same set of alternatives for (3-a) and (9-a) yields the incorrect predictions for (9-a), even if it does the right ones for (3-a). The relevant QUD for these predictions was who is on the left?, which yielded the following set of alternatives:

\(ALT_{Blue_{left}}=\{Blue_{left},Red_{left},Blue_{left}\wedge Red_{left}\}\)

In counterfactual contexts, the salient QUD might be the one representing the changes invoked by the antecedent such as Who switches sides in the counterfactual alternatives? rather than Who is on the left of the seesaw? This is a salient possibility, because sometimes QUD’s may not be explicit, but ‘inferred on the basis of other cues’ (Roberts, 2012, p. 68). Here the relevant cue might be the subjunctive marking of antecedents. So perhaps exhaustification is not applied relative to the QUD Who is on the left?, but to the QUD Who switches sides in the counterfactual alternatives?.

There is one wrinkle before us before we can evaluate the merits of this story. The surface form of (3-a) and (9-a)’s antecedents are disjunctions expressing which sides Blue and Red are sitting on, while not saying anything about children switching sides. The possibility of children switching sides is raised to salience by the contrary-to-fact situations expressed by the antecedents in question. In order to formulate an exhaustification operator that can exhaustify the antecedents of (3-a) and (9-a) in the intended way, we need the surface forms of (3-a) and (9-a)’s antecedents to match with the alternatives provided by the QUD Which children switch sides?.

First, the Hamblin set corresponding to the QUD Who switches sides in the counterfactual alternatives? is as follows:

$$\begin{aligned} Q_{Switch} = \left\{ \begin{aligned}&Blue_{switch}, \\&Red_{switch}, \\&Blue_{switch}\wedge Red_{switch} \end{aligned} \right\} \end{aligned}$$

Here \(Blue_{switch}/Red_{switch}\) stands for Blue/Red switches sides. Given \(Q_{Switch}\), we can translate (3-a) and (9-a)’s antecedents into forms that correspond to children switching sides as expressed by the subjunctive antecedents. This would provide matching surface forms between the alternatives and antecedents for exhaustification. For instance, we can translate (3-a)’s antecedent as (12):

figure o
figure p

(12) reflects the changes demanded by the antecedent given Scenario 1. In Scenario 1 Blue switching sides leads to Blue being on the left and both children switching sides end up with both of them on the left just as in (3-a). We can exhaustify (3-a)’s antecedent with respect to \(Q_{Switch}\). Since the only innocently excludable subset is \(\{Red_{switch},Blue_{switch}\wedge Red_{switch}\}\), we strengthen \(Blue_{switch}\) as follows:

\([Blue_{switch}\wedge \lnot Red_{switch}\wedge \lnot (Blue_{switch}\wedge Red_{switch})]\vee (Blue_{switch}\wedge Red_{switch})\)

\(\equiv \)

\((Blue_{switch}\wedge \lnot Red_{switch})\vee (Blue_{switch}\wedge Red_{switch})\)

This reproduces the right result for (3-a) in Scenario 1 (see Fig. 1 above). Since both children changing sides (hence being on the left) causes seesaw to unbalance, (3-a) is not true. Shifting to \(Q_{Switch}\) seems to reproduce the right results for Scenario 1.

What about (9-a)? Recall Scenario 2 (see Fig. 2 above). We translate (9-a)’s antecedent just as in the case of (3-a):

figure q
figure r

One important thing to note here is that the conjunction in (13) has Red staying the same rather than changing sides, since Red is already on the right. Now we exhaustify (9-a)’s antecedent. Alternatives given by \(Q_{Switch}\) are as follows:

$$\begin{aligned} ALT_{Blue_{switch}} = \left\{ \begin{aligned}&Blue_{switch}, \\&Red_{switch}, \\&Blue_{switch}\wedge Red_{switch} \end{aligned} \right\} \end{aligned}$$

The only innocently excludable subset of \(ALT_{Blue_{switch}}\) is \(\{Red_{switch},Blue_{switch}\wedge Red_{switch}\}\). Strengthening \(Red_{switch}\) with the negation of other alternatives yields the following:

\(\textsf {exh}(Blue_{switch})\vee (Blue_{switch}\wedge Red_{same})\)

\(\equiv \)

\((Blue_{switch}\wedge \lnot Red_{switch})\vee (Blue_{switch}\wedge Red_{same})\)

\(\equiv \)

\((Blue_{switch}\wedge Red_{same})\vee (Blue_{switch}\wedge Red_{same})\)

Note that the entailment between the disjuncts is not blocked. But given the set of alternatives \(ALT_{Blue_{switch}}\), there is really no way of exhaustifying \(Blue_{switch}\) such that the entailment is blocked. So, this LF is our only option. This exhaustification yields the following form for (9-a)’s antecedent:

figure s

When (9-a)’s antecedent is interpreted as (14), less fine-grained theories predict (9-a) to be true, because only Blue switching sides leads to Blue being on the right, which the seesaw to unbalance. In this way, less fine-grained theories predict (9-a) and (10-a) to be true, while predicting (10-b) to be not true in line with expectations (Table 8).

Table 8 Truth-value predictions of less fine-grained theories for Scenario 2 with exhaustification and QUD-adjusting
Full size table

It appears that changing the QUD to reflect the changes in the counterfactual possibilities invoked by (3-a) and (9-a)’s antecedents provides the right results for less fine-grained theories. By taking exhaustification along with some QUD-sensitivity on board less fine-grained theories seem to replicate the results provided by more fine-grained theories.Footnote 27

7 Problems with the counterfactual-sensitive QUD proposal

We have seen above that less fine-grained theories with the right type of exhaustification gets the right result. I will argue in this section that this maneuver is unsatisfactory because of two related reasons: (i) it fails to accommodate only implicature generalization (OIG) proposed by Singh (2008) and (ii) slightly different, but nearby QUD’s lead to extensionally inadequate predictions by less fine-grained theories. We will see that interpreted in the right way (i) may not be a problem, but a boon for less fine-grained theories, since the fact that (9-a) cannot be exhaustified in the way a Hurford disjunction would seems to be attested by the oddness of (9-a) even when true. I will still discuss this issue, because it provides a smooth transition to (ii), which is the real problem for less fine-grained theories. (ii) illustrates that there are similar QUD’s to the one picked to get the right results for (9-a) which generates readings of (9-a) that are not true and intuitively not attested. This suggests that less fine-grained theories get the right results for (9-a) only by way of an arbitrary selection from a class of available QUD’s for Scenario 2.

7.1 Only implicature generalization

First, there is a plausible principle for what a legitimate insertion of the exhaustification operator does for Hurford disjunctions. Such an exhaustification is supposed to generate an only implicature on the weaker disjunct so that the stronger disjunct does not entail the weaker one:Footnote 28

Only Implicature Generalization (OIG): The meaning of a sentence S strengthened by exh can always be paraphrased by asserting only \(S'\), where \(S'\) is like S but with focus on the relevant items.

What this principle achieves is to break the entailment among disjuncts in a Hurford disjunction thereby removing redundancy. If two disjuncts stand in an entailment relation, then a legitimate insertion of exh should be able to strengthen the weaker disjunct to generate an only implicature that can disrupt the entailment. For instance, let us take a felicitous unembedded Hurford disjunction:

figure t

Exhaustifying the former disjunct of (15) with the relevant alternatives generates the strengthened sentence Only Blue is on the left. Here only plays the crucial role in establishing that the latter disjunct does not entail the former. The insertion of exh in the weaker disjunct of (15) leads to an instance of exhaustification that satisfies OIG.Footnote 29

Does exhaustification relative to the QUD Who switches sides in the counterfactual alternatives? satisfy this principle in Scenario 1 and Scenario 2? For Scenario 1, it does, since (3-a) as exhaustified relative to the QUD Who switches sides in the counterfactual alternatives? is equivalent to saying that only Blue changes position:

figure u

And this breaks the entailment between the disjuncts. However, for Scenario 2, exhaustification relative to the QUD Who switches sides in the counterfactual alternatives? does not satisfy OIG when applied to the antecedent of (9-a). This is because the relevant exhaustification yields the following for the antecedent of (9-a):

figure v

Even though exhaustification generates the only implicature for the former disjunct of (17), this implicature does not break the entailment between the disjuncts, because the latter disjunct already says that only Blue switches sides. Such an application of exhaustification makes both disjuncts equivalent to each other rather than exhaustifying the weaker disjunct to ensure that it is not entailed by the stronger disjunct. If less fine-grained theories are to predict the right results both for (3-a) and for (9-a) through a general mechanism of exhaustification, this exhaustification should not break the entailment between the disjuncts of (9-a)’s antecedent. Only then can they predict the right result for (9-a). Conversely, if the role of exhaustification is to break the entailment between a conjunction and a conjunct in a Hurford disjunction, then less fine-grained theories cannot exhaustify (9-a) to get the right results.

This suggests that the antecedent of (9-a) cannot be exhaustified relative to the QUD Who switches sides in the counterfactual scenarios?, since such an exhaustification violates OIG.Footnote 30 Perhaps this is the right result after all, since (9-a) sounds odd, even if true, and perhaps this is due to the fact that we cannot exhaustify (9-a)’s antecedent. Given the story we have told so far, this is because we have assumed a particular QUD that yielded a set of alternatives relative to which we could exhaustify the antecedent of (3-a) in the right way. At the same time this set of alternatives also prevented us from exhaustifying the antecedent of (9-a) in a way that satisfies OIG.

Perhaps we should conclude from this result that Who switches sides in the counterfactual alternatives? is the QUD when the reader evaluates (3-a) and (9-a) in their respective scenarios and less fine-grained theories accommodate the right results for (3-a) and (9-a). However, this would be too hasty. In the next section I argue that holding onto a particular QUD for the puzzle we have raised above is an unstable solution for less fine-grained theories, since it relies on less fine-grained theories making an arbitrary choice among similar QUD’s.

7.2 Nearby QUD’s

The set of alternatives generated by the QUD Who switches sides in the counterfactual alternatives? is exactly the right set of alternatives to exhaustify (9-a)’s antecedent such that the exhaustified antecedent still receives a redundant interpretation and suffices to predict the right truth-value for (9-a). Is there anything special about this QUD given the scenarios and counterfactuals we are considering? For instance, is there anything about the scenarios and the fact that we are assessing counterfactuals relative to these scenarios which force this QUD to generate alternatives? I think not. For instance, there are other candidates for a QUD suitable for Scenario 2 such as What happens to the children in the relevant counterfactual alternatives?:

$$\begin{aligned} Q_{Happens} = \left\{ \begin{aligned}&Blue_{same}, \\&Red_{same}, \\&Blue_{same}\wedge Red_{same}, \\&Blue_{switch}, \\&Red_{switch}, \\&Blue_{switch}\wedge Red_{switch} \end{aligned} \right\} \end{aligned}$$

\(Q_{Happens}\) is fairly close to Who switches sides in the counterfactual alternatives? in that it merely adds the possibilities where children may retain their sides. One can even argue that such possibilities are especially salient for (9-a), because the stronger disjunct in (9-a)’s antecedent explicitly raises to salience the situation that Red stays the same, while Blue switches sides. When this QUD is salient, we can exhaustify (9-a)’s antecedent and break the entailment between disjuncts. When we exhaustify (9-a)’s antecedent relative to \(Q_{Happens}\), we end up with two candidates for the innocently excludable sets of alternatives. One of them generates the inexhaustified reading of (9-a) as we saw above. But now there is also the non-redundant interpretation (18) generated by the subset of alternatives that includes children remaining the same on the seesaw:

figure w

(18) is equivalent to (19):

figure x

This yields (20) as a reading for (9-a):

figure y

(20) is not true, since both children switching sides would cause the seesaw to be balanced after all. This reading should be available for (9-a)’s antecedent with \(Q_{Happens}\) if there is a preference for non-redundancy. But it is manifestly not available. The complaint here is that, if less fine-grained theories explain the infelicity of (9-a) by arguing that (9-a) is not exhaustifiable, then we have provided here a plausible route with a salient QUD through which we can exhaustify (9-a). Why is such a reading not available at all?Footnote 31 Compare this to more fine-grained theories. More fine-grained theories predict that (19) as an interpretation of (9-a) is not available, because it is semantically ruled out. The semantic explanation for the unavailability of (19) is more rigid than that of exhaustification provided by less fine-grained theories and such rigidity in (9-a) seems to be attested.

I take this argument to suggest that the solution less fine-grained theories bring to the table requires quite a bit of fine-tuning in picking QUD’s to get the right results for (3-a) and (9-a). Slight variation in QUD’s, e.g. switching from \(Q_{Switch}\) to \(Q_{Happens}\), makes some non-redundant readings available for (9-a) that cannot actually be attested. The predictions by more fine-grained theories, on the other hand, are semantically fixed and do not allow this variation. The rigidity in the interpretation of (9-a) is better explained by the semantic rigidity of more fine-grained theories.

7.3 General moral from the problems

In hindsight, we can see what the twists and turns with exhaustification and carefully picking QUD’s are supposed to do for less fine-grained theories. I believe that less fine-grained theories are trying to capture a phenomenon that does not really belong to the realm of exhaustification. They are trying to capture the similarity considerations that come with counterfactuals by adjusting the QUD. Let me illustrate this with (9-a):

figure z

A straightforward evaluation of (9-a) seems to be a two-step procedure. We take the former disjunct and look at the most similar worlds where it is true. These are all worlds where the seesaw is unbalanced, since we keep the rest of the facts fixed. Then we take the second disjunct and look at the most similar worlds where it is true. Again the seesaw is unbalanced in these worlds. Since both disjuncts affirm the consequent, (9-a) rings true. While evaluating (9-a), we keep certain background facts about the scenario fixed. This includes the position of Red while varying the location of Blue. This share of the burden about the evaluation of counterfactuals is contributed by the similarity-based nature of \((>)\). However, a theory can help itself to this explanation only if one admits multiple alternatives for the antecedent of (9-a). Because less fine-grained theories by their very formulation do not predict the existence of these alternatives, they are appealing to gerrymandering QUD’s for exhaustification.

In sum, I have provided two related considerations against employing exhaustification to explain why (3-a) does not sound true, whereas (9-a) does. Even though these considerations do not kill the prospect of explaining (3-a) and (9-a) under less fine-grained theories, they raise worries that these solutions are ad hoc. I believe that they at least provide enough evidence to shift the burden of explanation to less fine-grained theories.

8 Redundancy and pragmatics of counterfactuals

While concluding Sect. 7.1, we have mentioned that (9-a) is odd, even if true. This oddness is attested by many.Footnote 32 As it stands, more fine-grained theories seem to say nothing about this widely attested oddness, even if they get the right truth-value of (9-a) in a more uniform way. The situation might even be comparatively worse for more fine-grained theories, since we have observed that less fine-grained theories might have a way of explaining the oddness of (9-a), e.g. by simply pointing out that its antecedent cannot be exhaustified for a particular choice of QUD. This would put less fine-grained theories in a better position to explain the felt oddness of (9-a), notwithstanding the issues raised so far.Footnote 33 In this section I argue that there is a general pragmatic explanation of this oddness independently of Hurford disjunctions. After detailing this pragmatic explanation, I will also conjecture that such an explanation might even be related to explaining the infelicity of so-called true-antecedent counterfactuals.Footnote 34 If such a conjecture is true, then this will also make more fine-grained theories more parsimonious than less fine-grained ones, since less fine-grained theories should also appeal to this pragmatic explanation in cases of true-antecedent conditionals.

Pragmatic explanation I have in mind is roughly as follows. When we evaluate a counterfactual whose antecedent gives rise to multiple alternatives, we expect the antecedent to give rise to qualitatively different scenarios or closest possible worlds relative to which we assess the consequent. Otherwise, the counterfactual would have redundant components in its evaluation. After establishing whether the consequent holds in one of these qualitatively identical hypothetical scenarios, checking other scenarios makes no informative contribution to the overall evaluation of the counterfactual. Crucially, this is not merely a matter of an antecedent’s LF. Such informativeness is codetermined by the antecedent and the background conditions against which the counterfactual is evaluated. (9-a) illustrates this perfectly:

figure aa

The antecedent of (9-a) invokes multiple alternatives and gives rise to two scenarios which are qualitatively identical: one where Blue hops to the right and both children end up on the right and another where again only Blue hops to the right (since Red is already on the right) and both children again end up on the right. This is a roundabout way of ending up in the exact same situation, namely, one where the seesaw is not balanced with both children sitting on the right. (9-a) prompts us to consider identical hypothetical scenarios where we evaluate the consequent and such a counterfactual contains redundancy in the hypothetical scenarios it raises to salience. This is what explains the oddness of (9-a). It is important to note that explanation for this redundancy cannot be complete by appeal to the LF of the antecedent alone. What gives rise to this redundancy is the combination of the alternatives generated by (9-a)’s antecedent and background conditions for Scenario 2, e.g. the fact that Scenario 2 starts with Red being on the right. This is a pragmatic explanation in that it is constraining the range of informative counterfactuals in a given context. In short, each component of the counterfactual must make an informative contribution to the evaluation of its consequent.

I suspect this pragmatic explanation also has something to do with the infelicity of true-antecedent counterfactuals. Philosophers and linguists have discussed the oddness of counterfactuals with true antecedents. The consensus is that there is nothing semantically wrong with a true-antecedent counterfactual, but it is mistaken or misleading (Lewis, 1973, p. 27). What grounds this pragmatic response is not usually made explicit, but it is usually asserted without explanation that using a counterfactual has a pragmatic presupposition that its antecedent is false.Footnote 35 This may be a brute fact about the use of counterfactuals, but armed with the pragmatic explanation we have given above, perhaps we can explain the existence of such a pragmatic presupposition by appeal to the pragmatic explanation we have used to explain the oddness of (9-a). Here is an attempt.

We have said above that a counterfactual must not involve redundant scenarios it brings to salience for evaluation of its consequent. However, we can suppose in a context that one usually has the actual scenario available to them when they are evaluating a counterfactual. When one says If it had rained, the picnic would have been canceled, they compare the actual situation to the hypothetical one raised by the counterfactual. Because these scenarios qualitatively differ, there is nothing odd about the counterfactual. On the contrary, suppose that we both know that it did indeed rain and the picnic was canceled. Then the counterfactual does not generate a hypothetical scenario that differs from the actual scenario taken for granted and hence it is not informative. The relevance of the pragmatic explanation for (9-a) to true-antecedent counterfactuals is that (9-a) gives rise to two identical hypothetical scenarios, while true-antecedent counterfactuals involve the identity of a hypothetical and an actual scenario. However, in both cases there is arguably a case of redundancy in the use of a counterfactual, since neither makes a non-trivial contrast between the scenarios they invoke for the evaluation of their consequents.Footnote 36

Arguing for the thesis that this pragmatic rule is what explains the oddness of true-antecedent counterfactuals will take much more work than I can undertake here. But if such a pragmatic explanation turns out also to ground the oddness of true-antecedent counterfactuals, then this will be needed by more and less fine-grained theories alike. But then more fine-grained theories will be more parsimonious in general, because they will have to employ only this pragmatic principle about the use of counterfactuals to explain both the oddness of (9-a) and that of true-antecedent counterfactuals. By contrast, less fine-grained theories will have to appeal to both this pragmatic principle and facts about exhaustification to get all of the data right. No matter which way the story goes, it would be nice to confirm or refute whether pragmatic facts about true-antecedent counterfactuals rise and fall with the oddness of (9-a).

9 Conclusion

In this paper I have argued that we need the extra semantic fine-grain at least for antecedents of counterfactuals. I have done this by systematically investigating the predictions of various hyperintensional theories for two cases. In order to account for the intuitively correct results for these counterfactuals, we seem to need either the extra fine-grain for propositions that more fine-grained theories provide or we need some complicated mechanism for handling Hurford disjunctions in antecedent environments. The latter horn seems to face difficulties in telling a non-arbitrary story about Hurford disjunctions in embedded environments that can systematically explain the intuitive verdicts for our cases. By contrast, more fine-grained theories get the right results without getting entangled in issues faced by less fine-grained theories. This suggests that the extra propositional fineness-of-grain is desired for the right verdicts of the cases considered. The argument of this paper does not spell doom for less fine-grained theories, but it shifts the burden of explanation from more fine-grained theories to less fine-grained ones.

Shifting this burden does not mean that more fine-grained theories semantics does not have their own burden to bear. Embedded and unembedded Hurford disjunctions need to be handled in a principled way and nothing said in this paper can explain why the bad-sounding Hurford disjunctions are bad and the good-sounding ones are good, though footnote 24 might constitute the foundation of such an explanation for Finean truthmaker semantics. It seems to me that more fine-grained theories have a much easier time explaining the correct verdicts for (3-a) and (9-a). Even if this conclusion was not convincing to everyone, I hope to have at least provided interesting cases where the seemingly unrelated literatures on counterfactuals, hyperintensional semantics and Hurford disjunctions converge.