Yalcin 2012’s intensional implementation

In Gibbard’s approach, hyperplans are primitive. That serves his purpose of pushing an illustra-tive parallelism with intensional semantics, as we have seen: just as one uses possible worlds to model the logical relations between descriptive judgments, one can use hyperplans to similarly model logical relations between normative judgments. However, Yalcin2012argues that Gib-bard’s approach obscures two important points about hyperplans: (i) hyperplans can be defined in terms of possible worlds and (ii) hyperplans can be integrated in compositional semantics.

Importantly, those two observations are independent: one can give a compositional semantics for normative language taking hyperplans as primitives, and one can cast the previous Gibbar-dian story about normative judgment using a non-primitive notion of hyperplan. Nonetheless, by both defining hyperplans in terms of possible worlds and giving a compositional semantics, Yalcin aims to show that the Gibbardian view on content is compatible with standard inten-sional semantics (see also Charlow2015, 6 and ff).

Let us review how this works.⁹ Yalcin’s proposal is to define hyperplans as a functions from sets of worlds to sets of worlds—making good on point (i) above—and have declarative sentences denote sets of fact-prac worlds rather than sets of worlds—making good on (ii). A hyperplan, in this view, is no longer a primitive. Rather, it is a function from a set of possible worlds to a non-empty subset thereof where the impermissible options at the former set are false. For example, a hyperplan is a function that takes as argument the proposition that it is late, and returns the proposition that Camila starts packing.

9Another signpost: I will ultimately settle for a view in which hyperplans are not primitive, although they are not defined in the same way that Yalcin defines them—for reasons that will soon become clear. In particular, whereas Yalcin defines hyperplans as functions from sets of worlds to sets of worlds, I will define them as functions from sets ofsetsof worlds to sets ofsetsof worlds.

Implementing this in a standard intensional and compositional semantics is relatively straight-forward. All that one needs to do is assign as the semantic value of declarative sentences fact-prac worlds rather than worlds, and the semantics essentially falls out from the Gibbardian proposal about descriptive/normative judgment just reviewed.¹⁰

To see this, assume a simple propositional language containing a set of sentential constants p, q, r, ... representing a set of simple sentences of English (it’s raining, Paris is in France, Camila packs, ...). These are the descriptive sentences. Let us add to this language a unary sentential operator, ought. Where ϕis a descriptive sentence, sentences of the form oughtϕ are the normative sentences (there are Boolean connectives too, but we ignore them).

On the semantic side, we add to our intensional semantic structure a set of hyperplans and an information state. A semantic structureS consists, then, of the usual set of possible worldsW, a set of possible hyperplansHand a set of possible information statesE.

Definition 5 (Yalcinian semantic structure) S= ⟨W, H, E⟩

As we said, a hyperplan is a function h from subsets to subsets ofW such that, for any set X ⊆ W, h(X) is the subset of X where the impermissible outcomes at X are false.¹¹ An information state, on the other hand, is a sphere of epistemic accessibility, that is, a set of worlds that for all that is known could be the actual world:¹²

Definition 6 (Yalcinian Hyperplans) A “Yalcinian” hyperplan is a total functionhfrom non-empty sets of worlds to non-non-empty sets of worlds such that, for every set of worlds u, u^′ such thatu^′⊆u,h(u) =u^′just in case all the impermissible outcomes atuare false atu^′.

Definition 7 (Epistemic state) An epistemic state is a function efrom possible worlds to sets of possible worlds such that, for every worldwand set of worldsu, e(w) =ujust in caseuis the set of worlds that are epistemically accessible fromw.

A semantic model M is a tuple containing a structureS and a valuation function V mapping the descriptive sentences onto S, more specifically, onto sets of triplets ⟨w, h, e⟩ of world, hyperplan and information state.

Definition 8 (Model) M = ⟨S, V⟩

Subsequently, we define an index of evaluationias a triplet of elements from the structure S, that is, a world-hyperplan-information state triplet:

Definition 9 (Yalcinian Index) ⟨w_i, h_i, e_i⟩

Importantly,e_i should be some sete(∈ E)of epistemically accessible worlds, defined relative to the world of the index. That is,e_i=e(w_i).

10Making this fully explicit would require incorporating time-sensitivity into the picture as well, but we leave it aside to avoid clutter.

11Yalcin writes: ‘A hyperplan is a function that takes a set of possible worlds (a set which reflects a possible informational situationvis-à-viswhat the world is like; a set reflecting ‘an occasion of choice’) to some non-empty subset of that set (a set reflecting outcomes which it is permissible to realize according to the hyperplan, given the informational situation)’ (Yalcin2012, p. 147). The idea is that a hyperplan takes you from a set of options to a smaller set where only the permissible options remain, or alternatively, the impermissible options have been discarded. Yalcin’s definition is not reproducedverbatimso as to keep definitions as uniform as possible.

12It is standard to posit this type of parameter in the literature on epistemic and deontic modality. The moti-vation in the case of deontic modality comes from cases in which the body of information available to a subject can change the truth value of a deontic statement. A well-known example is the Miners’ puzzle (Kolodny and Macfarlane2010; see also Cariani2013; Kratzer2012; Yalcin2012,a. m. o.).

All sentences are assigned uniform semantic values—sets of ⟨w, h, e⟩triplets. But sentences can be descriptive or normative, and the difference consists in whether they impose a condition on the world or on the hyperplan and information parameters of the index: descriptive sentences are true at the world of the index but impose no condition on the hyperplan nor the information parameter; normative sentences do the opposite: they have to be true relative to the hyperplan of the index given a certain state of information, but leave the world-parameter untouched.

First, consider descriptive sentences such as (3.10).

(3.10) Camila packs.

The semantic value of a sentence like (3.10), assigned by V, is a set of world-hyperplan-information triplets. (3.10) is true at an index of evaluation⟨w_i, h_i, e_i⟩just in case⟨w_i, h_i, e_i⟩ belongs in its denotation (we omit reference to the modelM in what follows):

(3.11) [[Camila packs]]^M

⟨wi,hi,ei⟩=1iff⟨wi, hi, ei⟩ ∈V(Camila packs)

We said that descriptive sentences like (3.10) impose a condition on the world but not on the hyperplan nor on the information state parameter of the index. To capture that, all we need is for V to uniformly assign semantic values to atomic, descriptive sentences that result from pairwise combining each of a subset of worlds (those in which Camila packs) with every pos-sible hyperplan and every pospos-sible information state. In other words, (3.10) is world-sensitive, but it is hyperplan- and information state-insensitive. This is the right result, if we want to rep-resent the fact that sentences like (3.10) only offer factual information, but nothing normative nor epistemic.

Now let us turn to normative sentences. In this language, normative sentences are formed by applying the operatoroughtto descriptive sentences. Whereϕis a descriptive sentence,ought has the following meaning (Yalcin 2012, p. 148) (remember that Boolean connectives are set aside):

(3.12) [[oughtϕ]]_⟨w

i,hi,ei⟩=1iff∀w^′∈h_i(e_i)is such that[[ϕ]]_⟨w′,hi,ei⟩=1

Oughtϕis true, relative to a world-hyperplan-information state triplet, just in case every world in the set of worlds that results from applying the information state to the hyperplan of the index is a world that makesϕtrue.

When applied to (3.10), the result is Camila ought to pack, which has the following truth-conditions:

(3.13) [[Camila ought to pack]]_⟨w

i,hi,ei⟩=1iff∀w^′∈h_i(e_i)is such that [[Camila packs]]_⟨w′,hi,ei⟩=1

Just like descriptive sentences, normative sentences denote a set of world, hyperplan and information state triplets. But in contrast to descriptive sentences, normative sentences are hyperplan- and information-sensitive, although world-insensitive. Note that the sentence im-poses a condition both on the hyperplan and information state parameters of the index, but not on its world parameter. In order forCamila ought to packto be true at an indexi, the hyperplan ofihas to be such that, relative to the information state ati, it is required that Camila packs.¹³

13Note that, in this view, deontic force would be capturedviaquantification over the worlds in the domain of a

Two problems for Yalcin’s proposal

Could this proposal be applied to evaluative sentences (unembedded sentences containing eval-uative adjectives)? Since evaleval-uative language is a species of normative language, we could try to understand evaluatives as imposing certain conditions on the plans of interlocutors, relative to their epistemic state. In a slogan, the idea would be to cash out the linguistic expression of value in terms of plans (and model the content of plans using hyperplans).

As it stands however, Yalcin’s proposal cannot be straightforwardly applied to evaluatives.

First, because it predicts that everything that is taken to be true across an epistemic state is normatively required by any hyperplan given that epistemic state. And secondly, Yalcin’s se-mantics is not scalar, which means that it needs to be refined in order to represent the meaning of evaluative adjectives, which are gradable. Let us review these issues in turn.

The first problem is one version of a general problem for Kratzer semantics for modals, which Yalcin’s proposal inherits, and was raised by Frank (1997) and Zvolenszky (2002). Recall that a hyperplan is a function that, relative to an epistemic statee, will return a subset ofewhere all the permissible options ateare true. A propositionpought to be the case relative to a hyperplan h and epistemic state ejust in case h(e) entailsp; that is, just in case all worlds in h(e) are worlds wherepis true. Conversely, if a proposition is entailed by ah(e), then it ought to be the case. The problem is, then, that any proposition that is true acrossewill also be true at h(e). In other words, everything that is known iseo ipsonormatively required.

To see how this is a problem, consider the following situation: Camila needs to pack a bag and go catch her train. All her evidence suggests that it is late. This means that her epistemic state, call ite, is such that the proposition that it is late is true at every worldwine. But if the proposition that it is late is true at every world ine, then it is true at all the worlds in the set that results from applying any hyperplanhto her epistemic state. Therefore, it ought to be the case that it is late.

Importantly, this is not a fatal blow to this proposal. For example, one could say that the result of applying a hyperplan to a set of worlds relative to which a proposition p is true is not a subset of those worlds, but rather a different set of worlds altogether, maybe one where not-p is an open possibility (Frank1997). Or one could say that Yalcin’s truth conditions forought ϕactually state only a necessary condition for the truth ofoughtϕ. However, rather than look for ways of fixing Yalcin’s view, I think we had better replace certain key elements altogether.

We will see why in the following subsection.

The second issue with Yalcin’s (and Gibbard’s) view is that it is not scalar: propositions are either required or not required (they are or are not the thing to do, they do or do not make sense, etc.). In terms of the hyperplan semantics just given, this means that the speaker either plans or does not plan to make the proposition true (under certain circumstances). However, as we saw in Chapter2, in order to account for the scalar properties of evaluative adjectives, we need a more sophisticated story than a simple non-factualist story in which evaluative sentences express outright practical attitudes (in this case, an attitude of planning to make a proposition true). For an illustration, consider the following sentences:

(3.14) Volunteering is better than donating.

hyperplan, relative to an epistemic state. That is:pought to be the case relative to a hyperplanhand information stateejust in case every world inh(e)makesptrue;pmay be the case relative toh, ejust in case some world in h(e)makesptrue; etc. See Yalcin2012, p. 148.

(3.15) It is good that you sent that e-mail.

(3.16) It is extremely good that you sent that e-mail.

First, in order to account for (3.14) we need to be able to compare the value that a speaker assigns to eachrelata. In a Gibbard-Yalcin framework, we would need to say something about the plan that the speaker of (3.14) is advocating for. But the story given so far only lets us say something to the effect that the speaker plans to volunteer; or plans to donate; or plans to volunteer and donate, etc. None of these options apply to (3.14). Similarly, how could we account for the difference between (3.15) and (3.16)? Suppose that we assign to (3.15) a roughly equivalent meaning asoughtp. What meaning could we give (3.16) then? There is no straightforward way of strengtheningought pinto something that captures the addition of the modifier in (3.16).

Recall however, that Yalcin is taking resources from Kratzer semantics for modals. And even though Yalcin’s proposal is not scalar, Kratzer’s is. So one could think that, in order to make Yalcin’s proposal scalar, one simply needs to incorporate more Kratzerian (or Lewisian) el-ements (Kratzer 2012; D. Lewis 1973). An obvious strategy would be to bring ORDERING SOURCES into the picture. Here is how it might work: rather than have a hyperplan filter out the non-permissible worlds of an epistemic state, we could let an ordering source order—rather than rule out—those same worlds in terms of their closeness to an ideal. Then, we could cash out the contrast between (3.15) and (3.16) by saying that a proposition is good just in case it satisfies the relevant ideal to some contextually specified extent; and we could say that a proposition isextremely goodjust in case it satisfies the same ideal to some “extreme” extent.¹⁴ This is a possible strategy, but not the one that I will pursue, for two reasons. First, ordering sources do not immediately help with our first problem. And secondly, it is not easy to capture the scalar properties of relative-standard gradable adjectives in Kratzer’s semantics, a problem pressed by Lassiter (2017). Nonetheless, remember that Yalcin was only trying to show that Gibbard’s hyperplans were compatible with a standard story about deontics, and the standard story about deontics is basically Kratzer’s. Nothing commits us to the details of Kratzer se-mantics for deontic modals. So rather than explore further ways of building a scalar system for evaluatives based on Kratzer semantics, we will take a slightly different route.