Fine-grained Semantics for Attitude Reports

Harvey Lederman

Comments welcome, but please do not cite without permission!∗

December 1, 2019

Abstract

I observe that the “concept-generator” theory of Percus and Sauerland [2003], Anand[2006], Charlow and Sharvit [2014] cannot deliver an intuitive true interpretation of simplesentences like “Plato did not know that Hesperus was Phosphorus”. In response, I de-velop a new theory of attitude reports, which employs a fine-grained semantics for names,according to which the semantic value of a name is not the individual the name names. Ishow how to extend this theory to handle generalized quantifiers, and then present threeexamples showing that proponents of fine-grained theories, too, should adopt key aspectsof the concept-generator theory. These examples are of interest independently of my fine-grained semantics for names, since two of them constrain the concept-generator theoryitself more tightly than previously discussed examples had.

1 Introduction

In the wake of Gottlob Frege’s seminal 1892 paper “On sense and reference”, it has become

standard among philosophers to categorize semantic theories of attitude reports in terms of

their treatment of proper names. Millianism is the thesis that the meaning of a name is the

individual it names. So, for instance, the Greeks used the name “Hesperus” for the planet

Venus when they saw it in the evening sky, and “Phosphorus” for the same planet when

they saw it in the morning sky. According to adherents of Millianism, all occurrences of the

names “Hesperus” and “Phosphorus” have the same meaning, the planet Venus, and the two

sentences

1. Plato believed Hesperus was visible in the evening; and

∗Thanks to audiences at Philosophical Linguistics and Linguistical Philosophy (PhLiP) 5, and the PrincetonTalks in Epistemology and Metaphysics for their questions, to Chris Barker, Seth Cable, Sarah Moss and PaoloSantorio for conversations and correspondence, and to Kevin Dorst, Ben Holguın, Matt Mandelkern and DanielRothschild for comments on an earlier draft. I’m especially grateful to Cian Dorr and Kyle Blumberg, eachof whom read two lengthy drafts and gave insightful detailed comments on both of them. I’ve learned a hugeamount about these issues from my joint work with Jeremy Goodman, and the paper is heavily indebted tothe many many many conversations we have had about them.

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2. Plato believed Phosphorus was visible in the evening

are synonymous. This consequence of Millianism has been perhaps the main source of resis-

tance to the theory. Supposing that Plato nightly pointed to the planet and said “Hesperus

is visible now, but Phosphorus never is” many are inclined to judge that 1 is true, and 2 is

false.

Traditionally, Millianism has been opposed to Fregeanism. Fregeans distinguish two as-

pects of the meaning of occurrences of expressions, what they refer to, and what they express.

When names occur outside of the scope of any attitude verbs, Fregeans say that the occur-

rences refer to the name’s customary referent and they express the name’s customary sense.

For instance, in “Hesperus is bright” the name “Hesperus” refers to the planet Venus, and it

expresses its customary sense. But when expressions occur inside the scope of attitude verbs,

they change what they refer to (and possibly what they express, too); such occurrences do not

refer to the customary referent of the expression, but instead to the expression’s customary

sense. For instance, in 1 and 2 the occurrences of “Hesperus” and “Phosphorus” refer to the

customary senses of those names, not to the planet Venus. Fregeans typically hold that the

customary sense of a proper name is in some manner intimately associated with a definite de-

scription (or a collection of them), e.g. “the planet visible in the evening” for “Hesperus” and

“the planet visible in the morning” for “Phosphorus”. But all Fregeans, descriptivist or not,

hold that “Hesperus” and “Phosphorus” have different customary senses, so that in 1 and 2

the occurrences of “Hesperus” and “Phosphorus” have different referents, and hence different

meanings; Fregeans reject Millianism. Moreover, Fregeans hold that if two expressions have

different customary senses, any sentences which differ only by substituting an occurrence of

one for an occurrence of the other inside the scope of an attitude report will differ in meaning

(in a slogan: senses are structured). Thus Fregeans hold that 1 and 2 are not synonymous,

and in fact, they hold that in the scenario above the first would be true, and the second false.

As this rough description makes clear, Fregeanism involves a great deal of additional

apparatus beyond the denial of Millianism. And yet almost every non-Millian theory of

attitude reports makes significant further assumptions associated with Fregeanism. We do

not yet have a simple theory of attitude reports which deviates from Millianism only in ways

required to avoid Millianism’s questionable predictions. This paper aims to fill that gap. I

develop a simple, tractable non-Millian theory, which does not involve any of the usual further

Fregean commitments. In my semantics, expressions do not change what they refer to inside

the scope of attitude verbs, names are not assumed to be associated with definite descriptions,

and attitude verbs are not assumed to express relations to structured contents. The theory is

what I call a fine-grained theory of the semantics for proper names, i.e., it denies Millianism.

But I deliberately develop a bare-bones version of such a theory that is neutral on many

further substantive questions about the meaning of names; for example, the theory could

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be developed into a form of descriptivism, of predicativism, or of variabilism.1 By giving a

semantics for attitude reports while maintaining this studied neutrality about the meaning of

names, I have aimed to show that, aside from the motivations attitude reports may provide

for rejecting Millianism, the semantics of attitude reports imposes minimal constraints on the

semantics of proper names.

I start the paper by motivating a fine-grained theory. The orthodox theory of attitude

reports in semantics – first published by Percus and Sauerland [2003], and developed by

Charlow and Sharvit [2014] (cf. Anand [2006]) – is Millian.2 On this theory, attitude verbs like

“believe” are context-sensitive, and on different resolutions of this context-sensitivity, 1 may be

true, while on others it may be false. The theory provides a natural response to the traditional

challenge for Millians from 1 and 2. By claiming that the difference in wording (“Hesperus”

vs. “Phosphorus”) naturally suggests different resolutions of the context-sensitivity of the

verb “believe”, the orthodox theory can explain why 1 might strike us as true (since it is

naturally interpreted in one context, in which 2 is also true), while 2 strikes us as false (since

it is naturally interpreted in another, in which 1 is also false).

Section 2 argues against this orthodox “concept-generator” theory. The basic case is as

follows:

Context In Plato’s late dialogue the Laws, apparently unfinished at his death, the characters

discuss the question of whether the planets keep straight paths in the heavens (the Greek

cognate of “planet” means “wanderer”). The character Kleinias says that he has “often

noticed how Phosphorus and Hesperus and other stars never travel on the same course,

but ‘wander’ all ways” (821c). Some commentators have read the “and” as indicating

that Plato thought that the planet he saw in the evening and called “Hesperus” was

distinct from the planet he saw in the morning and called “Phosphorus”. If these

commentators are right, then:

3. Plato did not know that Hesperus is Phosphorus.

4. Plato was not sure that Hesperus is Phosphorus.

5. Plato did not believe that Hesperus is Phosporus.

These sentences, as Frege observed, are naturally interpreted as true in this scenario. But,

as I show, in section 2 the concept-generator theory predicts that there are no natural true

interpretations of them.

1For recent discussion of predicativism see Fara [2015]; for variabilism, see Cumming [2008], Schoubye[forthcoming]

2On some implementations of the theory, the meaning of every names is taken to be a constant functionfrom worlds to the individual the name names. This is strictly not Millianism on the definition above, but itcomes to much the same thing for my purposes, and I’ll typically ignore the difference between such theories.

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In response to this problem, I develop my fine-grained theory. I introduce the basics of

this theory in section 3 and show how it delivers a true reading of the sentences 3-5. On the

semantics I present, names which name the same thing may have distinct semantic values, and

the semantic values of predicates like “is visible in the evening” compose straightforwardly,

by function application, with the semantic values of names. This simple fine-grained theory

creates an initial difficulty with the treatment of generalized quantifiers. To see the problem,

note that Mercury and Venus are the only interior planets (i.e. planets closer to the sun than

earth). Suppose that Venus is visible in the evening, but that Mercury is not, and consider:

6. At least two interior planets are visible in the evening.

This sentence should be false: there is only one interior planet, Venus, which is visible in the

evening. But if the quantifier “at least two” ranges over the domain of semantic values of

names, the sentence would be predicted to be true: the semantic values of “Hesperus” and

“Phosphorus” are distinct and both “Hesperus is an interior planet which is visible in the

evening” and “Phosphorus is an interior planet which is visible in the evening” are true.3

Section 4 shows how this problem can be solved. Subsequent sections deal with further

subtleties in the development of the theory. Section 5 introduces three data which my basic

theory does not account for (but which the orthodox theory does). These examples are of

interest in their own right: they improve on arguments in the literature (e.g. Anand [2006],

Charlow and Sharvit [2014]) for the shape of the orthodox theory. But they also show that

the simple fine-grained theory needs to be supplemented. I introduce my final account, which

adapts key elements of the concept-generator theory to my fine-grained setting, in section 6.

Section 7 shows how the theory accounts for the new data, and discusses how the examples

in section 5 constrain this theory (and in fact even the concept-generator theory itself) more

tightly than existing arguments. Section 8 addresses data that suggest names should be taken

to be context-sensitive in my theory. Section 9 concludes, discussing two problems with my

own theory, and two alternative implementations which may help to solve them.

Appendix A addresses a question about the interpretation of my models, in particular

their use of a limited form of impossible worlds. Appendix B compares the initial theory

presented in sections 3-4 to the descriptivist theory of Aloni [2005]. Appendix C examines

some examples, due to Charlow and Sharvit [2014], which cannot be accommodated by the

3I introduced my fine-grained semantics as standing in opposition to both Fregeanism and Millianism.But some may prefer a different labeling; they might prefer to think of my theory as “Fregeanism light”, or“Fregeanism without reference shift”. Someone who wished to develop my theory in this direction might thinkof it as one in which the compositional semantic value of an expression is identified with its customary sense,even when the expression is not embedded in an attitude report. The problem with 6 above can be restatedin a Fregean idiom as arising because the quantifier “at least two” should not range over senses, but shouldinstead range over the referents they determine. I do not wish to debate the appropriate extension of “Fregean”here; my aim is simply to provide a simple theory which does not involve the assumptions described in thesecond paragraph of the paper.

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official theory of the paper, and shows how the theory could be extended to handle these

examples, if they are accepted.

2 A problem for the concept-generator theory

In this section I present the concept-generator theory (which I will refer to as CG-theory)

first published in Percus and Sauerland [2003] (building on notes of Irene Heim), and further

developed by Charlow and Sharvit [2014]. Since the theory I will develop later on will take

important ingredients from this theory, I will spend some time presenting it. But I will argue

that the theory cannot account for relevant true readings of 3-5. This problem with the

orthodox theory motivates my non-Millian alternative.4

The CG-theory is stated in a standard possible-worlds semantics for attitude verbs in the

tradition of Hintikka [1962]. We assume in the background a set of worlds W and a set of

individuals X, along with a function DOX : X → (W 9 P(W )) which delivers for each

individual x and every world w where x has beliefs, the set of worlds that are consistent

with x’s beliefs at w. The theory is distinctive in its use of “concept-generators”. A concept-

generator is a function from individuals to individual concepts, where an individual concept

is in turn a function from worlds to individuals. I will use @ throughout for the actual world,

and I will require in my discussion (though nothing essential will turn on it) that for any

individual x and concept-generator G, G(x)(@) = x.5 The basic idea of the CG-theory is

that when names occur within the scope of attitude verbs, they are the arguments of covert

pronouns whose denotations are concept generators. These concept generators operate on

individuals (the type of denotations of names) to produce individual concepts (the type of

denotations of definite descriptions).

Let’s first see how this theory works for 1. A simplified syntax of this sentence, at an

appropriate level of abstraction, would be:

4While writing Goodman and Lederman [2018, §9], Jeremy Goodman and I recognized a version of thisproblem for versions of our own theory. At the time I did not appreciate that the problem arose also for Percusand Sauerland [2003] and Charlow and Sharvit [2014].

5In practice, further conditions are imposed on concept-generators. In Percus and Sauerland’s statement(adopted by Charlow and Sharvit), these concept generators must be “acquaintance-based”, for example. Thesedetails won’t matter for our purposes.

5

Plato

believes

λG5

λs1

tG5 Hesperusts1 is visible in the evening ts1

First, I will show how (relative to an assignment function) the whole phrase below λs1

computes to a function from worlds to truth-values. Then I’ll turn to the whole sentence.

We assume that the usual assignment function is extended to the class of indices Gi and

the class of indices si, where i is a natural number, and that on the former class of indices it

takes concept generators as values, while on the latter it takes worlds as values. In the syntax

above, a bound pronoun which (relative to an assignment) denotes a concept generator occurs

as sister to the name “Hesperus”. These two elements compose by function application to

produce an individual concept; so for instance if the denotation of tG5 is a concept generator

G on an assignment g then the value JtG5 HesperusKg would be G(Hesperus), a function

from worlds to individuals. This value composes in turn with the (bound) world-pronoun

ts1 to produce an individual; if the value of g(s1) is a world w, then JtG5 Hesperus-ts1Kg is

G(Hesperus)(w). Next consider the predicate “is visible in the evening”. The semantic value

of this predicate is assumed to be a function from worlds to extensions (i.e. functions from

individuals to truth-values). This predicate combines with the semantic value of the (bound)

world-pronoun ts1 on an assignment to produce an extension. This extension in turn combines

with the individual G(Hesperus)(w) to produce a truth-value. So, JtG5 Hesperus ts1 is visible

in the evening ts1Kg evaluates to a truth-value: 1 if G5(Hesperus)(w) is in fact visible in the

evening at w, and 0 otherwise. And given this, the whole clause beneath λs1 evaluates to

λw.JtG5 Hesperus-ts1 is bright-s1Kg[w/s1], a function from worlds to truth-values. (In general

I use g[x/α] for the assignment function such that for every index β 6= α g[x/α](β) = g(β),

and g[x/α] = x.)

In the simplest, standard setting, we would be done at this point: the argument of “believe”

would just be a function from worlds to truth-values. But in the syntax above, there is an

additional abstraction over concept-generators below “believe”. So the argument of “believe”

will not simply denote a function from worlds to truth-values. Instead, it will denote a

function from concept-generators to functions from worlds to truth-values. To accommodate

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this difference, we use the following lexical entry for “believe”:

CG-Believes (preliminary) JbelievesK = λp.λx.λw. there is a G which is salient relative

to x and such that for all w′ ∈ DOX(x)(w), p(G)(w′) = 1.6

We assume informally that for each individual x, each context supplies a set of concept-

generators which are salient relative to x.

To see how this entry works we will suppose that Plato believes that the planet which

he calls “Hesperus” is visible in the evening and that Plato believes that the planet which

he calls “Phosphorus” is not visible in the evening, and we will consider two different kinds

of contexts. First, consider contexts where a concept-generator G which is salient relative to

Plato and which when applied to the planet Venus supplies the individual concept expressed

by the definite description “the planet which Plato calls ‘Hesperus”’. In such contexts, 1 will

be true: there is a concept generator such that at all of Plato’s belief-worlds w′, the result of

applying this concept-generator to the planet “Venus” is visible in the evening at w′. Second,

consider contexts where the only concept-generators which are salient relative to Plato are

such that when applied to the planet Venus they supply the individual concept expressed

by the definite description “the planet which Plato calls ‘Phosphorus”’. In such contexts, 1

will be false. Notice that the same points about contexts in which 1 will be true and false

also apply to 2: the names “Hesperus” and “Phosphorus” have the same individual as their

semantic value, so in a given context substituting one name for the other makes no difference

to the final computation. What makes a difference is not which name is used, but which

concept-generators are salient relative to Plato. In the present case, this is acceptable: we

may assume that the context made salient by an utterance of 1 is different from the context

made salient by an utterance of 2, and that 1 is true in the context it makes salient (and 2

would be true if it were interpreted in that context), while 2 is false in the context it makes

salient (and 1 would be false if it were interpreted in that context).

As we will see in a moment, this trick does not always work; sometimes there is no context

in which the appropriate interpretation of the sentence is available. But before I illustrate this

point, note that the entry I have given for the verb “believe” is only preliminary. The reason

is that there can be variation in how many concept-generators there is abstraction over in

the clause below “believe”. If no proper names or e-type pronouns occur in the complement

clause of “believe”, there might be no abstraction over concept-generators; if more than one

proper name or e-type variable occurs in the complement clause, then there will be more

than one abstraction over concept-generators. There are different ways of accommodating

6Strictly speaking, this clause only governs the case where DOX(x)(w) is defined; for the case where it isundefined, we assume that the entry returns 0 regardless of the complement. This issue won’t be importantfor the remainder of the section, so I won’t mention it again, but subsequent lexical entries for attitude verbsshould be understood to be restricted to the case where DOX(x)(w) is defined.

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this type-variability in the argument of “believes” formally. I will work with one on which

the verb “believes” is not itself ambiguous, but it can take arguments of different types:

CG-Believes JbelievesK = λp.λx.λw. for some n > 0, there are G1, ..., Gn which are salient

for x and such that for all w′ ∈ DOX(x)(w), p(G1)...(Gn)(w′) = 1.

Here and throughout, I associate function application to the left, so p(G1)(G2)(w) is properly

((p(G1))(G2))(w). If n = 0 then “p(G1)...(Gn)” is to be understood as simply p; in this case,

there are no concept-generators abstracted over, and the argument of “believe” is a function

from worlds to truth-values. In the more interesting cases, where n > 1, p will be a function

from concept-generators to functions from concept-generators...to functions from worlds to

truth-values. To accommodate these different types of arguments, the entry quantifies over

n, the number of concept-generators needed to saturate the argument to produce a function

from worlds to truth-values. In effect, the lexical entry introduces a sequence of existential

quantifiers over concept-generators, however many concept-generators are needed to saturate

the argument of “believes”.

We now turn to 5. According to the CG-theory, the following is the natural syntax for

the VP of 5, at an appropriate level of abstraction:

believe

λG5

λG7

λs1

tG5 Hesperusts1 is

tG7 Phosphorusts1

Given the lexical entry for “believe” we compute the following property as the denotation

of the VP of 5 with the above syntax:

7. λx.λw. there are concept generators G1 and G2 which are salient relative to x such that

for all w′ ∈ DOX(x)(w), G1(Hesperus)(w′) = G2(Phosphorus)(w′).

This property will be satisfied by any x and w whatsoever, provided there is a single concept-

generator G∗ that is salient for x. To see this, note that by instantiating the existential

quantifiers over concept-generators G1 and G2 in 7 with G∗ we obtain:

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8. λx.λw for all w′ ∈ DOX(x)(w), G∗(Hesperus)(w′) = G∗(Phosphorus)(w′).

Since Hesperus=Phosphorus, for any world w′, G∗(Hesperus)(w′) = G∗(Phosphorus)(w′).

And since this holds for all worlds w′, it follows that for any x and any w, it will hold for all

w′ ∈ DOX(x)(w). So the VP will be satisfied by any individual and any world in any context

where some concept-generators are salient relative to that that individual.

These very weak satisfaction conditions for the VP give very demanding satisfaction con-

ditions for the negated VP. In fact, they show that 5 can be true only in contexts in which

no concept-generators whatsoever are salient relative to Plato (and similar points apply to 3

and 4). If there are no such contexts, then the CG-theory cannot predict that these sentences

are true in any context. But even if there are some contexts in which no concept-generators

are salient relative to some individuals, the predicted truth-conditions of this sentence are

bizarre. To illustrate this point, note that in any context in which no concept-generators are

salient relative to Plato, pPlato did not believe a is Fq will be true for every name a and every

predicate F . If no concept generators are salient relative to Plato, then for any p, a fortiori

there is no sequence of salient concept-generators G1, G2, . . . Gn such that each of them is

salient for Plato and such that p(G1)(G2)...(Gn)(w) = 1 for all of Plato’s belief-worlds. So in

such contexts, “Plato did not believe Athens was a city”, “Plato wasn’t sure Athens was a

city”, “Plato didn’t know that Athens was a city” will be true, as will “Plato did not believe

Socrates was a philosopher”, “Plato was not sure Socrates was a philosopher” and “Plato did

not know Socrates was a philosopher”. Even if the proponent of the CG-theory claims that

there are contexts in which no concept-generators are salient relative to Plato, the theory will

thus fail to do justice to the claim that 3-5 have the intuitively true readings that they seem

to have, namely, ones on which they indicate that Plato was specifically ignorant of or did not

have an opinion concerning a particular fact about astronomy. Instead, the only true readings

of the sentence will be ones on which the sentence expresses a trivial fact about Plato, since

on the relevant interpretation of the verb “believe”, it is also true to say that Plato did not

believe that Athens was a city.7

The argument does not show conclusively that there is no way of producing a true reading

of the sentence within the CG-theory (for instance by adopting a different syntax for the

7Essentially the same points applies to different implementations of related ideas, like Ninan [2012] andRieppel [2017]. (For the kind of sentences we’ve considered in this section, Santorio [2014] is just a differentimplementation of the same truth-conditions as the CG-theory, and is subject to exactly the problems here.)Ninan only considers de re interpretations, and on these he will predict the truth of 5 only if there are nosalient acquaintance relations for Plato.

Rieppel [2017] proposes that verbs shift the assignment function, quantifying over variants of the assignmentfunction which assign to each index an individual concept, rather than an individual. He then suggests thatnames can move, leaving traces behind them, which can be bound by the quantification over the assignmentfunction he postulates. On the de dicto interpretation Rieppel predicts only a false reading of 5. On the doublyde re interpretation, Rieppel predicts a true reading only if no transformations of the assignment function areavailable for Plato. On a singly de re reading, Rieppel faces the problem just described; it is unclear whatproposal there could be as to when a subject’s belief-worlds would satisfy the relevant condition.

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sentence). But the obvious ways of reinterpreting the sentence either give up the spirit of

the CG-theory (for instance by claiming that sometimes names occurring in the scope of

attitude verbs are not always “wrapped” by concept-generators), or essentially replicate a

fine-grained semantics for names (for instance, by claiming that different domains of concept-

generators may be supplied for differently-indexed concept-generator pronouns).8 In section

9 I’ll discuss the virtues and vices of this second style of modification of the CG-theory in a

little more detail, but for now I will take the argument of this section to motivate rejecting

these modifications of this theory altogether.

The argument of this section is an argument against the CG-theory, but not against every

Millian theory; there are Millian theories which can give a better account of the data I’ve

discussed in this section than the CG-theory does.9 But for reasons I can’t go into here (see

8Perhaps the most obvious reply is as follows. We suppose that the world-pronouns occurring as argumentsof G1(Hesperus) and G2(Phosphorus) are not coindexed, and that one of them (for concreteness, let’s say theone for “Hesperus”) is bound by an abstractor over worlds taking highest scope in the sentence. To be true,the proposition expressed by the whole sentence would have to have the value true when applied to the actualworld, so we can further simplify by considering the result of applying the proposition to the actual world, @,so that this bound world-pronoun would denote @. In that case, the property that would need to be satisfiedwould be:

• λx. there are concept generators G1 and G2 which are salient relative x such that for all of x’s belief-worlds w, G1(Hesperus)(@) = G2(Phosphorus)(w).

Since G1(Hesperus)(@) =Hesperus, this simplifies to:

• λx. there is a concept generator G2 which is salient relative to x such that for all of x’s belief-worlds w,Hesperus= G2(Phosphorus)(w).

Suppose now that the sole concept generator salient relative to Plato has the individual concept denoted by“the planet which rises in the morning” as its value when Venus is its argument. The proponent of this responsemight then claim that it is not true that at all of Plato’s belief-worlds the individual Hesperus is the planetwhich rises in the evening.

This reply can deliver a true reading of 5. But there is a problem with it. If this response is to hold that 8 isa property it is interesting to deny that Plato has, it must explain the conditions under which a person wouldsatisfy this property. What more would Plato have had to do in order for the individual Hesperus to be theplanet visible in the morning at all of his belief-worlds? No appealing answer seems forthcoming. The answercannot be “He would have had to point to Hesperus and say ‘That planet is the planet visible in the morning’”, for we may suppose that he did do this, when he woke up in the morning and studied the planet he called“Phosphorus”. And similarly, for many variant replies to the question, the same point could be made. Indeed,for any purely physically specifiable way of being associated with the planet we can assume that Plato wasassociated with the planet in that way, without eliminating our sense that 5 is true. More abstractly, the pointis that the response is in tension with the conceptual underpinnings of the CG-theory. The motivating idea ofthe CG-theory is that for “Plato believes Hesperus is bright” to be true, it does not have to be the case thatat every belief-world of Plato, the planet Hesperus itself is bright. Instead, it may only be that there is anindividual concept which takes the value Hesperus in the actual world, and which is such that it returns, foreach of Plato’s belief-worlds, an entity which is bright at that world. Somewhat picturesquely, the idea is thatpeople’s belief-worlds do not “glom on” to individuals in such a way that the same individual has the relevantproperty at all of their belief-worlds. The present response abandons this motivating idea of the CG-theory,since it claims that for the relevant reading of 5 to be false about a person, that person would have to be suchthat the planet Venus itself rose in the morning at every one of their belief-worlds.

9There are Millian theories which predict a true reading of “Plato did not know that Hesperus is Hesperus”(and hence of 3). Cable [2018] is one such approach; I discuss it in fn. 49. Another is that of Crimmins andPerry [1989] and Crimmins [1992], as well as one of the theories discussed in Goodman and Lederman [2018,§9].

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Goodman and Lederman [2018, §9]), I’m skeptical that there are attractive Millian theories

which deliver an intuitive true reading of 5. So in response to the problem I will adopt a more

radical approach, rejecting not just the CG-theory, but Millianism as well.

3 A basic fine-grained semantics

Our first task is to provide a simple model which gives non-trivial truth-conditions for 5. In

this section I present the basic model, and discuss its conceptual foundations. Subsequent

sections then extend the fragment covered to include determiners, and motivate an altered

semantics for attitude verbs themselves.

In presenting the model-theory I’ll re-use some notation from my less formal presentation

of the CG-theory; from now on the notation should be taken to have the meanings I give it

here. Our basic class of models has the following ingredients:

• W , a non-empty set, thought of as the set of worlds;

• De, a set;

• DOX : De → (W 9 P(W )), a function which, for each element of De, returns a partial

function which maps each world where the individual corresponding to that element of

De has beliefs to a nonempty set of “doxastically possible” worlds for that individual at

that world;

• R ⊆W×W , an equivalence relation on W , thought of as representing relative possibility,

as used in the semantics for the modal “it’s necessary that”;

• E : W → P(De × De) a function from worlds to equivalence relations on De, used to

give the semantics for the “is” of identity, and such that if wRw′, then E(w) = E(w′).

For readability in what follows, I will often subscript world-arguments, so for example, I will

write Ew for E(w). I will use 2 for the set of truth values {0, 1} and Dt for the set of functions

from worlds to truth values, i.e. 2W (note that Dt will not be the set of truth-values itself).

I often call these “propositions”.10

Two aspects of this model will be unfamiliar. First, in not requiring R to be the universal

relation on W , we allow W to contain some worlds which are intuitively “impossible” relative

to others. Second, the “is” of identity is interpreted not by model-theoretic identity, but

by possibly non-trivial equivalence relations Ew on De, and these relations can vary across

impossible worlds. The elements of De are thus not to be thought of as individuals; individuals

are represented instead by equivalence classes under E@.

10For simplicity in the formal treatments in the paper I won’t consider variability across times; I will pretendthat the only dimension of variability for these relations is world-variability.

11

I’ll return to these aspects of the model theory in a moment, but first, let us see how the

semantics allows us to deliver a true non-trivial true reading of 5. Consider a toy model from

our class of models, in which De = {h, p, pl}, W = {@, i}, R is the identity relation on W ,

E@ is the smallest equivalence relation which relates h and p, Ei is model-theoretic identity

on De, and finally for all w ∈ W , DOX(pl)(w) = {i}. Here and throughout, I will use @ to

denote the actual world. Here then is a simple fragment interpreted on this model, with a

flatfooted entry for “believe” that I will revise later on (the entries here are all insensitive to

the assignment function g):

• JHesperusKg = λw.h, h ∈ De

• JPhosphorusKg = λw.p, p ∈ De

• JPlatoKg = λw.pl ∈ De

• JisKg = λw.λx.λy.xEwy;

• Jit’s not the case thatKg = λw.λx ∈ 2.1− x..

Note that I will assume that not just negation, but also conjunction and disjunction behave

classically at all worlds, both possible and impossible. The impossible worlds I employ will

thus differ very little from standard possible worlds.

Believe (Preliminary) JbelieveKg = λw.λp.λx.∀w′ ∈ DOX(x)(w) p(w′) = 111

The semantic value of each expression is a function defined on worlds. Thus, for instance,

even the name “Hesperus” must be saturated with a world to produce an individual. Through-

out the remainder of the paper I will be assuming an “extensional” treatment of modality,

in which covert world-pronouns occur in the syntax of sentences, and where abstraction over

world-pronouns is used to produce a proposition (a function from worlds to truth-values) when

one is required. For instance, “Hesperus is bright” would be given (at an appropriate level of

abstraction) the following syntax:“λw. Hesperus-w is bright-w”. A sentence which features

an intensional operator like “necessarily” or “believe”, which takes a proposition (and not a

truth-value) as its argument, will be uninterpretable unless an abstractor over worlds occurs

below the intensional operator. For instance, “ Necessarilyy, Hesperus is bright” could be

given (at an appropriate level of abstraction) the following syntax:“λw. Necessarily-w λw′.

Hesperus-w′ is bright-w′”. This kind of syntax was assumed in my treatment of the examples

in the previous section, though I didn’t write out all the world-pronouns; “Plato believed Hes-

perus was visible in evening” might be regimented (at an appropriate level of abstraction) as

11Again, technically, this only governs the case where DOX(x)(w) is defined; the sentence should be takento be false regardless of its complement if DOX(x)(w) is undefined. But this definedness issue won’t matterat all below, so I won’t mention it again.

12

“λw. Plato-w believed-w λw′. Hesperus-w′ was visible in the evening-w′”. There are powerful

arguments, which I won’t rehearse here, that this kind of syntax should be preferred over one

in which there are no explicit world-pronouns. 12 It will be a significant advantage of my

theory that it allows us to adopt this now-standard treatment; Fregean theories, which do

not not have a notion of “belief-world”, cannot adopt this standard treatment (though see

my “Fregeanism and the Problem of Scope” for attempts to overcome the problem).13

We can now give a straightforward treatment of 5. The set DOX(pl)(@) = {i}, and it

is not the case that hEip. So “Plato does not believe Hesperus is Phosphorus” is true at

all worlds in our model (as is “Plato believes Hesperus is not Phosphorus”). More generally,

in any model in which the set DOX(pl)(@) contains any (impossible) worlds w such that

¬hEwp then“Plato does not believe Hesperus is Phosphorus” will be true. In our model, the

sentence is true, even though Plato does believe certain other claims. For instance, “Plato

believes that Hesperus was Hesperus” will also be true on the same interpretation, as will

“Plato believes Hesperus is not Phosphorus”. Unlike the CG-theory, the present theory can

provide a true reading of 5 without appealing to a reading of “believe” on which Plato does

not believe (basically) anything at all.

In closing this section, I want to make some conceptual remarks about the model theory.

Philosophers often see semantic theories as (reasonably) giving a semantics, i.e. as a theory

of meaning for the language. Since giving a semantics in this weighty sense requires mapping

the expressions of the language onto their meanings, which might include (though they also

might not include) particular dogs, people, properties and so on, giving a semantic theory of

this kind requires claims about what entities there are. If the meaning of an expression is a

function which takes worlds as arguments, for example, then there must be such functions.

The semantic theory in this paper should not be thought of in this way: in using the model

theory described above I do not intend to make claims about what entities there are. The

model theory should be understood abstractly, as a formal tool for making predictions both

about the truth of sentences in context and about the entailment patterns among sentences;

12Arguments that such a theory is needed can be found in Fodor [1970], Bauerle [1983], Percus [2000],Keshet [2008], and Charlow and Sharvit [2014]. For the sake of familiarity, I’ll be using the simplest versionof this theory where every expression is assumed to have a world-pronoun as its sister. As is well known, thisstyle of theory overgenerates; further assumptions about the distribution of world-pronouns are needed. Forthe purposes of this paper, I won’t discuss this issue further, and in working examples, I’ll cherry-pick mypreferred syntax, assuming that this can be derived. My own preferred theory which uses world-pronouns isthat of Schwarz [2012]. Everything I do below could be done in that more restrictive setting, and since it ismore predictive, I’d ask the reader familiar with Schwarz’s paper theory to consider that the “official” theory.But since it is less familiar in general and a bit more complicated, and since nothing essential turns on it, I’veopted to present the simpler theory in the main text.

Everything I do later could also be done using alternative approaches to the “de re”/“de dicto” or “transpar-ent”/“opaque” ambiguity, for instance, a “split intensionality” theory ([Keshet, 2008, 2010, 2011]). (I myselfhave reservations about this treatment, but they are independent of the main data of this paper.)

13I won’t however be assuming that the only way of producing such de re readings is via the world-pronouns;it may be that movement sometimes occurs, too.

13

it should be judged on the basis of its simplicity, tractability and predictive strength.14 Along

these dimensions my model theory is comparable to standard possible-worlds models. As

noted above, I will assume that every world in every model I consider, Boolean connectives

such as “it’s not the case that” behave completely standardly. As a result the propositions

I will consider themselves form a Boolean algebra under the usual set-theoretic operations.15

The only non-standard feature of these worlds will be that the identity relation can vary from

world to world. And this small deviation from assumptions in possible worlds semantics is

precisely what allows us to deliver an intuitive, true reading of 5.

For most of the paper I’m not going to take a stand on what kind of metaphysical theory

is suggested by the models I’ll be using. But I’ve often encountered resistance to the use of

impossible worlds and distinct elements of De corresponding to a single individual in my

theory. In Appendix A I describe two ways in which one can view the elements of my

model theory as constructed out of ingredients available in more familiar model theories.

The second of these, in section A.2, shows that my class of models is isomorphic to one that

can be constructed only from resources available within the CG-theory (or the theory of Aloni

[2005]). Even someone who ‘takes the model theory seriously’, and commits themselves to the

existence of entities corresponding to those in the model theory should not see an important

contrast in the metaphysics they would be endorsing by endorsing the two theories.

4 Basic Surrogatism

The remainder of the paper presents some problems for this basic theory, and uses them to

argue for refinements of it. In this section, I deal with some basic issues about quantification.

In the following three, I present new examples which constrain the theory and present a

proposal which – within the fine-grained semantics – imitates key aspects of the CG-theory.

Recall the problem from the introduction (repeated here for ease of reference):

Context Mercury and Venus are the only interior planets (i.e. planets closer to the sun than

earth). Suppose that Venus is visible in the evening, but that Mercury is not.

6. At least two interior planets are visible in the evening.

This sentence should be false: there is only one interior planet, Venus, which is visible in the

evening. But our semantics will not obviously deliver this result, since there are two elements

14Yalcin [2018] describes a view of the role of models in semantics to which I’m very sympathetic.15I will also require that at all worlds, possible or impossible, identity is a congruence with respect to the

denotation of intuitively extensional predicates. For example, I will assume that at every world w, the semanticvalue of “is bright” applied to w and x ∈ De is 1 if and only if for every y such that xEwy, the denotationof “is bright” applied to w and y is 1. This constraint means that for intuitively extensional predicates F , wewill also have the law: if anyone believes that x is y then they believe that x is F if and only if they believethat y is F .

14

of De, the semantic value of “Hesperus”, and the semantic value of “Phosphorus”, which both

satisfy the predicate “is visible in the evening”.

This problem with 6 arises for fine-grained theories like mine on which the semantic values

of intuitively extensional predicates like “is an interior planet” are functions from worlds to

functions from the domain of the semantic values of names to truth-values. (It would also arise

for theories on which such predicates denoted functions from the semantic values of names to

propositions.) An alternative style of fine-grained theory (which is more properly Fregean)

takes intuitively extensional predicates to denote functions instead on equivalence-classes of

the domain of semantic values of names. The most natural theories of this alternative kind

require a nonstandard treatment of predicate abstraction, which seems to me more disruptive

than the need in the present theory to alter the semantics of quantifiers.16 But the goal of this

paper is not to argue against these alternative implementations; it is rather to show that one

can develop a theory like mine coherently. And the point here is just that the problem with

6 I have presented is not a problem in general for any style of fine-grained semantic theory,

but only for the style of theory I am developing.

The basic problem is clear: in giving a semantics for generalized quantifiers we should not

count every element of De, but somehow count individuals, i.e. equivalence classes of elements

of De, elements of Iw for some appropriate w. (Recall that Iw is the set of equivalence classes

of De under Ew.) The simplest way of fixing the problem – and the one I will adopt here – is

to assume a mandatory and stringent form of domain restriction, on which the only admissible

domains for the quantifier at a world draw exactly one element from each equivalence class at

that world. This element of De then acts as a “surrogate” or “proxy” for the equivalence class

to which it belongs; by counting such surrogates, we will in fact count equivalence classes.17

Formally, a function S : W → P(De) is a surrogate domain restriction if and only if for

every w ∈W and every X ∈ Iw there is exactly one x ∈ X in S(w). We assume that context

supplies a surrogate domain restriction S, and then use the following lexical entry for the

quantifier “at least two”:

Two

Jat least twoKg,S = λw.λF.λG. at least two x ∈ Sw are such that F (x) = 1 and G(x) = 1.

The imposition of these domain restrictions eliminates the problem with 6. For any S, the

proposition expressed by an utterance of that sentence (assuming the most natural syntax)

would be:

16Ordinary predicate abstraction would produce a function on the domain of semantic values of names, butsince the composition rules do not allow predicates with semantic values of this type, something must be doneto correct the mismatch. Yalcin [2015] and Richard [1990] with my “Fregeanism and the Problem of Scope”.

17To my knowledge, Kaplan [1986, p. 258-9] first gave the name “surrogatism” to a proposal along theselines (see Section XVI for development of the view). Aloni [2005] ()cf. Ninan [2018]) Dorr [2014] and Baconand Russell [2017] can also be thought of as “surrogatists” in Kaplan’s sense, though the parallel is not exact.On Aloni, see the next paragraph but two in the main text, with appendix B.

15

• λw. for at least two x ∈ S(w) x is an interior planet at w and visible in the evening at

w.

Regardless of the surrogate restriction this proposition will be false. For the equivalence class

corresponding to Mercury does not have an element which is visible in the evening, and no

equivalence class other than the ones corresponding to Mercury and Venus have elements

which are interior planets. Any element of the equivalence class corresponding to Venus will

be an interior planet at @ and also be visible in the evening at @, but that is only one such

entity; to be true, the proposition would require that there be two.

My use of surrogatist domain restrictions has some important similarities to Maria Aloni’s

use of conceptual covers (Aloni [2005], cf. Ninan [2018]). There also important differences

between the proposals, which are discussed in detail in appendix B. But someone who is

attracted to Aloni’s treatment as opposed to mine could see the remainder of the paper as

arguing that Aloni’s theory as it stands is incomplete: the best version of that theory would

be supplemented with key elements of the CG-theory. Indeed, for some readers, this may be a

helpful way of thinking of the project of the paper in general: as arguing that the best overall

theory of attitude reports combines key elements of Aloni’s proposal with key elements of the

CG-theory.

Here I’ve used locutions like “x is an interior planet at w” as a shorthand for “the de-

notation of ‘is an interior planet’ applied to w and then x is 1”, and I’ll continue to do this

throughout. These locutions may deserve special mention in the present setting since, as I

remarked earlier, the denotations of predicates operate on elements of De, not on individuals

(which correspond to equivalence classes of elements of De). So while I will say that such

elements “are interior planets at w”, we should remember that they are not individuals but

rather entities which stand for the semantic values of names.

I’ll call the proposal that all determiners are mandatorily restricted by surrogate domain

restrictions, while attitude verbs are given the simple semantics from section 3 Basic Surro-

gatism.18

18There might seem to be a range of alternatives to Surrogatism; in this note I’ll say briefly why I dispreferthem. Alternative “Existentialist” and “Universalist” proposals are as follow:

Existentialist TwoJat least twoKg = λw.λF.λG.λw′ for at least two Z ∈ Iw, ∃x ∈ Z such that F (x)(w) = 1, and ∃y ∈ Z,such that G(y)(w′) = 1.

Universalist Two Jat least twoKg = λw.λF.λG.λw′ at least two Z ∈ Iw are such that ∀x ∈ Z F (w)(x) = 1and ∀x ∈ Z G(w′)(x) = 1.

The generalizations of these proposals to all determiners are unattractive because they allow that in a singlecontext, there could be false instances of “not every F is G if and only if some F is not G” (where theconditional is interpreted as material ); i.e. that the universal and existential quantifiers would not be duals.For instance, the Existential proposal allows that an instance of “Every x is F” could be true in a context whilethe corresponding instance of “Some x is not F is also true in the same context. They also lead to problematicresults with determiners which involve counting e.g. an instance of “exactly half of the F s are G” could betrue in a context where the corresponding instance of “it’s not true that exactly half of the F s are not G” is

16

The way in which surrogate domain restrictions are defined gives the world-argument of

the determiner “at least two” (and other determiners) a distinctive role in our treatment. The

world at which we assess the determiner now controls which equivalence-classes are used as the

domain of individuals for the quantifier (reflected in the fact that Sw is defined with respect to

Iw, i.e. equivalence classes with respect to the identity relation as interpreted at that world).

We can motivate this feature of the proposals by considering two further examples:

Context Suppose Plato believed that earth was the planet closest to the sun so that there

were no interior planets. Suppose furthermore that he believed that Hesperus and

Phosphorus are two distinct exterior planets, and that they are bright, but he believed

that Mercury was not bright.

9. Plato believed at least two exterior planets were bright.

10. Plato believed exactly one interior planet was bright.

Each of these sentences has a true reading in this context. The second may be easier to access

by considering the dialogue “Venus and Mercury are the interior planets, Plato believed that

Venus was bright and Plato did not believe that Mercury was bright. So Plato believed at

least one interior planet was bright.”

The salient true reading of 9 results from an “opaque” or de dicto interpretation of “at least

two”, where its world argument is bound below the attitude verb “believed”. For instance, the

relevant syntax might be represented as “λw. Plato-w believed-w λw′. at least two-w′ exterior

planets-w′ were bright w′.” Using Surrogatist Two, the sentence on this regimentation would

express the following proposition:

• λw. for all w′ ∈ DOX(Plato)(w) for at least two x ∈ S(w′) x is an exterior planet at w′

and x is bright at w′.

Since exactly one x is chosen from each equivalence class in Iw′ , i.e. the individuals as they

are represented at Plato’s belief-worlds, this proposition requires us to count individuals as

they are represented at Plato’s belief-worlds. And the proposition will be true. For in this

scenario, it is clear that the denotations of “Phosphorus” and “Hesperus” occupy different

also true.The universalist proposal leads to odd results in other cases as well. Suppose that Plato thought that

Mercury rises in the evening, although it never does, and suppose he thought no planets other than Mercuryand Hesperus rose in the evening (in particular he did not think that Phosphorus rose in the evening). Evenso it seems true to say:

• At least one planet Plato thought rose in the evening, does rise in the evening.

The Universalist proposal predicts that the sentence would be false.Essentially any hybrid proposal (adopting mandatory surrogatist domain restrictions for some quantifiers,

and the version of Existentialism for others – and perhaps even the version of Universalism for yet others) willlead to similarly undesirable results about the entailment patterns between quantifiers.

17

equivalence classes at Plato’s belief-worlds (Plato thinks they are distinct planets). Since the

denotations of “Hesperus” and “Phosphorus” satisfy the restrictor (they are exterior planets)

and the nuclear scope property (they are bright) at Plato’s belief-worlds, every element of

their equivalence classes at those worlds must also satisfy both the restrictor and the nuclear

scope property at those worlds. (Recall that we are assuming that intuitively extensional

predicates are congruences with respect to Ew at every world w.) So, regardless of the choice

of surrogate from these equivalence classes, there will indeed be two distinct equivalence classes

with elements which satisfy these properties.19

The salient true reading of 10, by contrast, results from a “transparent” or de re inter-

pretation of “exactly one”, where its world argument (and the world argument of “exterior

planets) is bound outside the scope of the attitude verb “believed”. For instance, the relevant

syntax might be represented as “λw. Plato-w believed-w λw′. exactly one-w interior planet-w

were bright w′.” Using the obvious Surrogatist entry for “exactly one”, the sentence would

express the following proposition

• λw. for all w′ ∈ DOX(Plato)(w) exactly one x ∈ S(w) is an interior planet at w and is

bright at w′.

Note here that both the w in S(w) and in the assessment of the restrictor (“interior planet”)

are bound by the highest-scope binder over worlds; they are not assessed at Plato’s belief-

worlds. As a result this proposition will also be true. There are two Z ∈ I@ such that all of

their elements are interior planets at @: the classes corresponding to Venus on the one hand,

and Mercury on the other. By assumption one and only one of these classes has elements which

are bright at w′ for all w′ ∈ DOX(Plato)(@) (and we may assume that all of the elements of

this equivalence class, including the denotations of “Hesperus” and of “Phosphorus” satisfy

this condition). So, regardless of our choice of surrogate for these classes, the proposition

expressed will be true.20

The use of surrogate domain restrictions solves the problem with 6 and also gives us a

flexible way of altering how the individuals are understood – whether at a person’s belief-

worlds or at the worlds at which the whole sentence is assessed. It also allows us smoothly to

account for changing domains in iterated reports such as “John hopes Mary thinks two people

are coming for dinner”. Since the details of the treatment of such reports are straightforward

19Barker [2016] develops a rich and interesting theory which is in some important ways related to mine.But Barker’s theory cannot produce opaque (i.e. de dicto) readings of quantifiers inside attitude reports (heacknowledges this near the end of his paper). So, for example, he cannot produce the true reading of 9.

20My own view is that either the world-argument of a determiner and its restrictor should be jointly coin-dexed: it does not seem possible to separate the transparent/opaque interpretation of the restrictor from thechoice of which domain is used in counting by a determiner. In my preferred setting, that of Schwarz [2012],the only constituents which can take explicit world-arguments are determiners, so it is basically forced on onethat the restrictor and the determiner are assessed at the same world, automatically imposing this desirablefurther constraint.

18

I won’t dwell on them here. But I will say that Fregean, structured, treatments are often

extremely difficult to generalize to iterated reports. It is yet another advantage of the present

account that we face no difficulties in providing that generalization.

The central reason I offered for moving to a fine-grained theory was the importance of

allowing for true readings of 3-5.21 But given my use of surrogate domain restrictions, the

following, which might seem to be closely related to 3-5, are predicted not to have true

interpretations:

11. There’s an x and y such that x = y and Plato did not know that x = y;

12. There’s something such that Plato did not know that it was it.

This result will also be preserved in the final theory of the paper. This contrast between

11-12 and 3-5 might seem surprising: after all, 11 results from 3 by existential generalization.

Of course, neither 11 nor even 12 is as clear an English example as 3. But still ex ante one

might have preferred a theory which treated them in parallel. The problem is that it is hard

to see how to develop a fine-grained theory which on the one hand delivers intuitive results

about sentences that involve counting (like 6) and on the other also allows true readings of

sentences like 11. There are theories which avoid this choice-point altogether (for instance,

Millian theories which allow true readings of 3), but these theories tend to be unnatural in

other ways. The natural fine-grained theories I know of all present us with a choice between

allowing that 3 is true (and delivering the asymmetry I’ve just described) or rendering both 3

and 11 false. Given this choice, it seems to me that the asymmetry is clearly to be preferred.22

5 Three Problems for Basic Surrogatism

In this section I present three problems for Basic Surrogatism. The CG-theory has the re-

sources to solve these problems, and my response to the problems will be to present a theory

which combines the insights of the CG-theory with the fine-grained semantics I’ve developed

to this point.

The examples I will present go beyond and sharpen examples which have previously been

used to argue for various aspects of the CG-theory. Most notably, in the first subsection

I present a new style of example to motivate the use of existential quantifiers over concept

generators. Thus, the discussion in what follows can be applied more generally than the

21Related examples can be given with demonstratives, e.g. “John doesn’t know that is that” (when the twodemonstrations in fact pick out the same object); see Perry [1977, p. 12-13].

22Note that the theory to this point also predicts that

13. There’s something such that Plato believed it wasn’t it.

will be false. But as discussed below in section 7.3, my final theory will avoid this result, allowing this sentenceto be true.

19

present fine-grained setting; even those who are not moved by my earlier arguments to reject

Millianism should see the examples to come as strengthening the case that the CG-theory

should have the shape it does (and I will make the ways in which they do so explicit in section

7.4).

5.1 Beyond double vision

A traditional argument against theories like Basic Surrogatism, which hold that names and

variables are associated with (only) a single precise way of thinking about an individual, is

based on what is often called “double vision”. This argument, usually attributed to Quine

[1956], starts from the following example:

Context Ralph sees Ortcutt by the docks. Ralph concludes on the basis of what he sees that

Ortcutt is a spy, Later, Ralph watches Ortcutt’s mayoral inauguration address on TV.

Ralph thinks that no mayor could possibly be a spy; the background checks are simply

too careful. So he concludes that Ortcutt the mayor is not a spy.

13. Ralph believes that Ortcutt is a spy.

14. Ralph believes that Ortcutt is not a spy.

Since there is no precise way of thinking about Ortcutt relative to which Ralph both thinks

that Ortcutt is a spy and thinks that Ortcutt is not a spy, if 13 and 14 are true in the same

context, then “Ortcutt” cannot be associated with a single precise way of thinking about that

individual.23

This argument has played a central role in the development of semantic theories of attitude

reports. But it is not particularly powerful. One can readily deny that 13 and 14 are true in

the same context, while nevertheless maintaining that both sentences are typically true when

uttered. As I will discuss in more detail in section 8, in the fine-grained setting there is inde-

pendent reason to believe that names are context-sensitive, and can denote different elements

of De in different contexts. Someone who endorses this form of “nominal contextualism” could

allow for the truth of 13 and 14 by claiming that typical utterances of these sentences occur

23It might seem that for all I have said De could contain “relaxed” or “disjunctive” ways of thinking aboutindividuals as well as precise ones, so that “Ortcutt” could be associated with a single element of De even if itis not associated with a precise way of thinking about this individual. For instance, perhaps there could be asingle element o ∈ De, such that if one comes to believe that Ortcutt is a spy by seeing him at the docks, onebelieves the proposition λw. o is-a-spy-at-w, and if one comes to believe that Ortcutt is not a spy by seeinghim on TV, one believes the proposition λw. o is-not-a-spy-at-w. But the existence of such an o is ruled outby the fact that negation is interpreted classically at all worlds in the model theory. Provided a person has anybelief-worlds (and we may assume that Ortcutt does) they will not believe the proposition λw. x is-a-spy-at-wwhile also believing the proposition λw. x is-not-a-spy-at-w for any x in De. Of course we could relax thisassumption about negation in the model theory, but doing so would come at the cost of a significant loss inpredictive power.

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in different contexts. Although there are no overt linguistic cues in the sentences that might

tip a hearer off that they are to be assessed in different contexts, the mere fact that they are

uttered, along with hearers’ tendencies to charitably interpret utterances as true, might be

thought to suffice for them to be interpreted in different contexts. So the traditional argument

based on “double vision” on its own does not tell particularly strongly against against Basic

Surrogatism.24

I have presented this contextualist response not to endorse it, but to illustrate the weakness

of the traditional argument based on double-vision. In fact, the next example undermines the

contextualist approach. It provides strong evidence that, while the traditional argument

based on double vision was too quick, the conclusion that was drawn from it was nevertheless

correct.

Context Suppose John has four pictures in front of him, two pictures each of two teachers.

The teachers are A and B, and we may think of the photos of A as A1 and A2, and the

photos of B as B1 and B2. John thinks that the photos are of four distinct people. He

points at A1, A2 and B1 and says as he points to each of them “this person is Italian”.

He then points at the last picture, B2, and says “this person is French”. As a matter

of fact teacher A is Italian and B is French.25

15. Someone John thinks is French is French.

16. ?Everyone John thinks is Italian is Italian.

17. Someone John thinks is Italian is French.

18. ?No one John thinks is French is French.

The sentences 15 and 17 are naturally heard as true, whereas the sentences 16 and 18 are

naturally heard as false. (They all have true, and false, readings in this scenario; I am only

claiming that there is a contrast in immediate acceptability between these pairs.) Given very

natural assumptions our basic surrogatist theory – which in effect assigns traces, like names,

single elements of De – predicts that 15 is true in a context if and only if 16 is true in that

context, and that 17 is true in a context if and only if 18 is true in that context. Moreover,

15 is true in a context if and only if 18 is false in that context.

This situation is a mystery on the contextualist proposal. According to the contextualist,

13 and 14 are interpreted as true because hearers are charitably inclined to interpret them

in contexts where they would be true. This story works well to explain how both 15 and

24A similar point applies to the use of double-vision to motivate the use of existential quantification overconcept-generators within the CG-theory; see below n. 39.

25This style of “pictures” case was introduced by Charlow and Sharvit [2014]. The example sentences usedhere are new.

21

17 are interpreted as true, in spite of the fact that Basic Surrogatism predicts that there

are no (natural) contexts in which both are true. But why would 16 be heard as false? If

the contextualist is right, we would expect that here, too, hearers would work to interpret

this sentence in a context in which it is true (e.g. by holding fixed their interpretation, and

interpreting it in natural contexts in which 15 is true). But this does not seem to be what

we observe.26 The appeal to hearers’ charity wrongly predicts that all four of the sentences

would be equally acceptable.27

Basic Surrogatism cannot accommodate the data here. But the CG-theory can. As I will

show below, a theory which adapts the key insights of the CG-theory to a fine-grained setting

can accommodate these data, while also allowing a true reading of 3-5.

5.2 Problems with plural subjects

The following example, due to Cian Dorr, presents a different kind of problem for Basic

Surrogatism:28

Context (Based on Dorr, p.c.) Luthor knows that Superman has a secret identity as a

reporter, but he thinks that Clark Kent is a telephone-booth repairman; he doesn’t

realize Superman is Clark. Lois knows that Clark Kent is a reporter, but she doesn’t

26One might think that the different words “French” and “Italian” in the complement clauses of the reportsabove suggest different contexts for the relevant reports. But this feature of the examples is inessential. Wecould replace 16 with “Everyone John thinks is not French is Italian”, and so on for the other examples. Italso can’t just be the use of the universal quantifier and negative universal rather than the existential, since“Every teacher John thinks is French is French” is acceptable, while “Some teacher John thinks is French isItalian” is not.

27One might wonder why I have given this argument using the quantified sentences 15-18 rather than pre-senting a more direct argument based on 13-14. Given Basic Surrogatism, any context in which 14 is true,

19. Ralph does not think that Ortcutt is a spy

would also be true. If hearers really are charitable, they should then hear 19 as true, so if the sentencewere heard as false, that would be a problem for the contextualist proposal. In this case, however, I and myinformants do naturally access a true reading of the sentence. The true reading of this sentence may of coursehave to do with the tendency of “think” to exhibit “neg-raising”, i.e. for wide-scope negations (“does notthink”) to be interpreted as narrow-scope (“thinks it is not the case that”). To avoid this issue and find datawhich tell more clearly against the contextualist, one might instead consider:

20. Ralph is sure that Ortcutt is a spy

21. Ralph is sure that Ortcutt is not a spy

22. ? Ralph is not sure that Ortcutt is a spy

To me, the third of these sentences is less acceptable than the first two, and this is a mark against thecontextualist response to the data. But in this case, unlike the one in the main text, the contextualist mightclaim that 22 is less acceptable because it is interpreted in this scenario as if it were “Ralph is unsure whetherOrtcutt is a spy”, and that this latter sentence does not have a salient true interpretation. Alternatively theymight appeal to an independent pragmatic pressure, which trumps the usual charitability of hearers, againstaccepting the assertion of a sentence and its negation in quick succession. The examples I’ve relied on havenone of these problems: they don’t require assessing a wide-scope negation over an attitude verb, and don’trequire assessing a sentence and its negation in quick succession.

28Jeremy Goodman and I discussed versions of this example in earlier versions of our paper “Perspectivism”.

22

know that Superman has a secret identity, never mind a secret identity as a reporter.

Neither has encountered this person in any other way. On Monday at noon, Luthor

finds out that Clark is a reporter, and Lois finds out that Superman is a reporter.

19. On Monday at noon, Luthor and Lois learned that Kal-El is a reporter.

20. There’s someone Luthor and Lois learned is a reporter on Monday at noon.

These sentences are intuitively true in this scenario. But again this poses a problem for Basic

Surrogatism. It is natural to assume that if a person stands in the relation expressed by

“learns” in a context at a time t to a proposition p, then (i) the person did not stand in the

relation expressed by “knows” in that context to p in some interval of time starting earlier

than t and open at t, and (ii) the person does stand in the relation expressed by “knows”

in that context to p at t itself. The problem is that, to the extent that we have a grip on

when different names are assigned different element of De and how those elements compose

with the denotations of predicates, it is hard to see how there could be an element x of De

that composes with the denotation of “is a reporter” (given the appropriate abstraction over

world-pronouns) to produce a proposition p such that (i) neither Lois nor Luthor stood in the

relation expressed by “knows” to p before Monday at noon, and (ii) both Lois and Luthor

stood in the relation expressed by “knows” to p on Monday at noon. For example, if every

occurrence of “Clark Kent” in the vignette above expresses λw.x for the same x ∈ De as every

other occurrence, and similarly for “Superman”, then the (distinct) elements of De that are

the semantic values of those uses of “Clark Kent” and “Superman” will both fail (i): Lois

knew that Clark Kent was a reporter at all times on Monday morning, while Luthor knew

that Superman was a reporter at all times on Monday morning.

Once again, although Basic Surrogatism cannot handle this example, I will show that

a theory which adapts elements of the CG-theory to our fine-grained setting can handle it.

Moreover, in section 7.4 I’ll discuss how the constraints imposed on the CG-theory by this

example are independent of those required to handle the one in the previous section: the

aspect of theory which is used to handle this example does not on its own suffice to produce

the contrast between 15 and 16, while the aspect of the theory which delivers this contrast

does not on its own suffice to handle this example.29

29A different solution than the one I will adopt would be to allow type-raising of the semantic value of “Kal-El”, so that instead of denoting a constant function from worlds to an element of De, it denotes a functionfrom worlds to a function f : De → De. This function could be interpreted as “x’s Kal-El”; it would mapattitude holders to ways of thinking about Kal-El, allowing variability from attitude-holder to attitude-holder.

As far as I can see this proposal would handle the present example, but it does not give us a way ofhandling examples like 15-18. Those examples seem to require some kind of existential quantification overways of thinking about Kal-El. My implementation of this basic idea makes it natural to handle Dorr’s databy allowing the domain of permutations to vary from attitude-holder to attitude-holder. By comparison theapproach based on type-shifting is unattractive.

23

5.3 The bound de re

A final sort of problem for Basic Surrogatism was discussed in detail in philosophy in the

1980s (e.g. Soames [1989-90, p. 198f.]), and has recently been brought to the attention of

linguists by Sharvit [2010], Charlow and Sharvit [2014]:

Context John knows that Jupiter is distinct from Mars. But he thinks Hesperus is Jupiter

and thinks Phosphorus is Mars.

21. There’s something John thinks is Jupiter and is Mars.

Intuitively this sentence is true. But Basic Surrogatism cannot predict predict this result,

because there isn’t any particular way of thinking about Venus such that, relative to that way

of thinking about it, John thinks Venus is Jupiter and is Mars. After all, John knows that

Mars and Jupiter are distinct.

Charlow and Sharvit [2014] show how the CG-theory can accommodate examples like

these. I’ll show below that the same result holds for a fine-grained theory which incorporates

the insights of the CG-theory. Moreover, in section 7.4 I’ll discuss how the constraints imposed

on the CG-theory by this example are independent of those required to handle the ones in

the previous sections: the aspect of theory which is used to handle this example does not on

its own suffice to produce the contrast between 15 and 16 or to handle 19, while the aspects

of the theory introduced to handle those other examples do not on their own suffice to handle

this one.

6 Fine-grained Semantics

In section 2 I argued that the CG-theory is inadequate because it fails to make the correct

predictions about 3-5. But as I have noted, the CG-theory can handle all of the data presented

in the previous section. My strategy in what follows will therefore be to adapt the CG-theory

to my present fine-grained setting.

A bijection π : De → De is a permutation. A permutation π is w-admissible if and

only if for all x π(x)Ewx; for short I’ll call w-admissible permutations w-permutations. A

w-permutations can map different values within the same Ew equivalence class to different

values, but they can only map elements of an equivalence class to other elements of the same

equivalence class. For example, there is an @-permutation which maps the semantic value

of “Superman” in ordinary utterances of “Lois doesn’t know that Superman is a reporter”

(provided there is a unique one) to the semantic value of “Clark Kent” in ordinary utterances

of “Lois knows Clark Kent is a reporter” (provided there is a unique one), while also mapping

semantic value of “Clark Kent” in such utterances to the semantic value of “Superman” in

24

them. But there are no @-permutations that map the semantic value of “Superman” to the

semantic value of “Lois”.30

By analogy to the CG-theory, I will assume that any names or variables occurring in the

scope of attitude verbs have variables denoting permutations which “wrap” them. I assume

that the assignment function g is extended to be defined on new indices pi for all i > 0 and

that these indices are assigned permutations. I will also assume that whenever a name or a

variable occurs inside the scope of an attitude verb, it has some trace tpi as its sister, and

that such variables are obligatorily bound by an abstractor. Thus for instance, imitating the

syntax of the CG-theory, our syntax for the VP of 5 will be:

believe s2λp5

λp7

λs1

tp5Hesperus s1

is

tp7Phosphorus s1

We assume that context supplies a function f which, for each person and world, returns a

set of permutations which are salient relative to that person and admissible at that world. The

permutations salient relative to a person and world can be thought of as inducing, for each

way of thinking about a thing, a set of ways of thinking about that thing, which are treated

as contextually equivalent relative to that person and world. For instance, in some contexts

the way of thinking about the planet Venus associated with uses of the expression “Hesperus”

in the background story for 5 is contextually equivalent with relevant uses of “Phosphorus”

relative to Plato and the actual world, i.e. f supplies, relative to Plato and the actual world, a

permutation which maps one to the other. But in other contexts, these ways of thinking about

Venus are crucially not contextually equivalent: there will be no permutations belonging to

the value of f relative to Plato and the actual world, which map one to the other.31 In the

30There are no data I’m aware of that motivate using permutations rather than arbitrary functions from Deto De (including those which are not bijections). But since there are also no data I’m aware of that requireusing such functions that are not permutations, it seems preferable to use the more restrictive notion (andreaders have found it easier to work with, as well).

31This notion of “contextual equivalence” is not in good standing without further constraints on f . For itto induce an equivalence relation on De, the set of permutations supplied for any world and individual by fshould form a group: they should be closed under composition and inverses. For ease of exposition I won’tdiscuss this constraint further in what follows, but I think it is natural to impose it, since it is natural tothink that which permutations are salient relative to which individuals and worlds is back-formed from which

25

case of “believe” our proposal will be:

Believe JbelieveKg,S,f = λw.λp.λx. for some n > 0, and some π1 . . . πn ∈ f(x,w), ∀w′ ∈DOX(x)(w), p(π1) . . . (πn)(w′) = 1.

Here we take “p(π1) . . . (π0)” to abbreviate “p”. As in the case of the CG-theory, the quantifi-

cation over n is to cover in a single clause the possibility of arguments with different types.32

To see how the clause interprets the displayed syntax for 5, assume that JHesperusKg,S,f =

h ∈ De and that JPhosphorusKg,S,f = p ∈ De. The material below λp7 then computes (after

simplifying (λw.h)w to h and (λw.p)w to p) to:

• λw.(Jtp5Kg,S,fh)Ew(Jtp7Kg,S,fp)

The material below “believe” then computes to:

• λπ1.λπ2.λw.(π1h)Ew(π2p)

So that, after simplifying away the quantification over n, the whole displayed clause comes

to:

• λx. there are π1, π2 ∈ f(x, Js2Kg,S,f ) such that for all w ∈ DOX(x)(Js2Kg,S,f ), (π1h)Ew(π2p).

To see that this clause is not trivial, consider the case where for all x and w, f(x,w) is the

singleton set consisting of the identity function on De. (This permutation is w-admissible for

all w.) Under this assumption the clause will just reduce to

• λx. for all w ∈ DOX(x)(Js2Kg,S,f ), hEwp,

which as we saw above is not trivially satisfied. This simplifying assumption about f is very

strong, but the reader may readily verify that many less restrictive assumptions about f will

also yield the result that the property expressed is not trivially satisfied, so that 5 (and indeed

3 and 4) will have nontrivially true readings.33

Given the assumption that when names occur inside attitude reports, permutation pro-

nouns take them as arguments, the exact semantic values of names within a given equivalence

elements of De are treated as “contextually equivalent” to them, as the discussion in the main-text suggests.32The extra parameter w in f is needed to handle iterated attitude reports. When an attitude verb is

embedded in another intensional operator, the chosen permutation should be admissible relative to the worldsat which the inside attitude verb is assessed; it should not (oddly) look back automatically to the actual world.

33In n. 30 I noted that there was no particular motivation for using permutations rather than the general classof functions from De to De, but that I preferred the more restrictive use of permutations, and w-permutations.An incommensurable way of restricting the class of all functions from De to De would be to require that thevalues of f(x,w) be w-collapse functions, where a function κ : De → De is a w-collapse function if and onlyif for all x, y such that xEwy, κ(x) = κ(y). But there is a clear reason to reject this proposal, namely, thatit would rule out our earlier treatment of 3-5. Since JHesperusK)E@(JPhosphorusK), every @-collapse-functionκ has κ(JHesperusK) = κ(JPhosphorusK), so that given the syntax above 3 would be synonymous with “Platodidn’t know that Hesperus is Hesperus”, precisely the result our fine-grained semantics was designed to avoid.The restriction to permutations does not have this problematic result.

26

class of E@ no longer have real significance: these values are simply place-holders. Provided

“Hesperus” and “Phosphorus” have distinct semantic values, our permutations can map them

to (different) distinct values, and it is not important what these starting values were, so long

as they were distinct. Still, although formally there is nothing important about the exact

values we assign to names, it is a natural default assumption that the identity function will

typically be an element of f(x,w) for all x and w. If we make this assumption, then the choice

of semantic values for names does matter, at least in typical contexts.34

To produce a fully predictive theory given my semantics, we would need an account of

which permutations and which surrogates are salient in which contexts. This question is

extremely important, but I will not address it further here. My hope is that, once a semantics

which can deliver intuitive truth-conditions for the range of data I am interested in is available,

we can work backwards from this semantics to provide a metasemantic story about how the

relevant parameters are determined by context.

7 Solving the problems

In this section, I’ll show how the semantics introduced in the previous section solves the three

problems I described for the basic surrogatist theory (sections 7.1-7.3). I’ll then state more

formally how the examples constrain the theory I’ve developed (section 7.4). Sections 7.1-7.3

can be skipped without loss of continuity, especially by those familiar with the mechanics of

the CG-theory.

7.1 Beyond double vision

I suggested that on their most salient readings, 15 and 17 are true, while 16 and 18 are false.

(This is not to say that there are only true readings of 15 and 17 or only false readings of

34One might wonder how the theory handles sentences which involve quantification into sentence position,like:

22. John believes everything Mary believes.

I’ll show how by showing that we can extend the usual model theory to allow quantification over all of thevariable-type arguments of “believe”. (I set aside reference to world-pronouns for simplicity; adding it in ismechanical.) Let π be the type of permutations. Then as usual we have base types e, t for names and sentencesrespectively, and in addition π for permutations. (Note t is not the type of truth-values.) The simple variabletype is χ. The types are then the members of the smallest set containing e, t, π, χ, and such that if σ and τare members of the set, so is σ → τ . A simple abnormal type is anything of the form π1 → (...(πn → t))).Expressions of type χ → τ combine with an expression of a simple abnormal type to produce an expressionof type τ . For instance, the type of attitude verbs (again, ignoring the world-pronouns we had above) isχ → (e → t). 22 can then be regimented as ∀χ(λpχ. if Mary believes pχ then John believes pχ). We canassume a set W of worlds and let Dt be P(W ), De be an arbitrary set, and Π be the set of permutations onthat set. Domains for higher types are defined as usual, and booleans and the quantifiers can be interpreted inthe standard way, with quantifiers for the simple variable type ranging over all elements of domains for simpleabnormal types. Thanks to Peter Fritz here.

27

16 and 18; I can access both readings of all four.) In this section, I’ll show how my theory

accounts for this contrast.

In spelling out the predictions of my theory formally, I’ll call the equivalence classes

corresponding to each teacher A, B, and the elements of them corresponding to the four

pictures, a1, a2, b1, b2. I will assume that the relevant elements of A are exactly a1 and a2

and similarly that the relevant elements of B are exactly b1 and b2. This assumption is very

natural, given that we have not supposed that John knows about these individuals in any

other way than via the pictures, and this is all that is made salient about those individuals in

our vignette. Finally, I will also suppose that every @-permutation of the domain is salient

relative to John at the actual world (i.e. that f(John,@) is the set of all @-permutations.

This assumption is not strictly required to produce the results I’ll describe, but it is a natural

assumption and it is helpful to see how it gives rise to the contrast.

Relative to any choice of f and S, our lexical entry for “believe” predicts that on the most

natural syntax 15 expresses:

• λw. there is an x ∈ Sw such that for some π ∈ f(John, w), for all w′ ∈ DOX(John)(w),

π(x) is French at w′ and x is French at w.

Given our assumptions, about f and the domain of quantification, this proposition will be true.

Regardless of the choice of surrogate of B (whether it is b1 or b2), there is an @-permutation

which maps this surrogate to b2, which is French at John’s belief-worlds. Regardless of the

choice of surrogate of B, that surrogate is French at @ (since every element of B is). So the

surrogate of B witnesses the existential “there is an x ∈ Sw”.

But under the same assumptions, we predict that 16 will be false. Relative to any S and

f , our lexical entry for “believe” predicts that on the most natural syntax 16 expresses:

• λw. for every x ∈ Sw if some π ∈ f(John, w) is such that for all w′ ∈ DOX(John)(w),

π(x) is Italian at w′, then x is Italian at w.

Regardless of the choice of surrogate of B, there is a @-permutation which maps this surrogate

to b1. So the surrogate of B satisfies the antecedent of the conditional. But, again, regardless

of the choice of surrogate of B, that surrogate is French at @ (and hence not Italian at @).

So the surrogate of B is a counterexample to the universal “for every x ∈ Sw”, and the

proposition is false.

The reader may readily verify that 17 will similarly be predicted to be true, and 18 be

predicted to be false, under the same assumptions.

7.2 Problems with plural subjects

Here, I will work a simpler example than 19, though the morals for 19 will be clear from my

discussion. The running example will be:

28

22. Lois and Luthor know that Kal-El is a reporter.

The assumptions described above deliver the following syntax for this sentence:

Lois and Luthor

know

λp5

λs1

tp5 Kal-El s1is a reporter s1

I will assume that f returns a singleton set of permutations for both Lois and Luthor

relative to the actual world, and that there is no change of context throughout the vignette,

so that every occurrence of “Superman” has the same semantic value as every other, and

similarly for “Clark Kent”. Given these assumptions, 22 will be true relative to Monday at

noon (for example) if the permutation that is salient relative to Lois at the actual world maps

JKal-ElKg,S,f to JSupermanKg,S,f and the permutation salient relative to Luthor at the actual

world maps JKal-ElKg,S,f to JClark KentKg,S,f . Importantly, under the same specification of

f , the sentence would not be true at any earlier times on Monday morning: at those times,

Lois did not know or believe that Superman was a reporter, and Luthor did not know or

believe that Clark Kent was a reporter.35

The entry thus allows us to avoid the problem with 19. No element of De satisfies both

(i) and (ii), but 19 can be true in spite of this fact, because it may be that f(Lois,@) 6=f(Luthor,@) and that for every π ∈ f(Lois,@) and π′ ∈ f(Luthor,@), π(JKal-ElKg,S,f ) 6=π′JKal-ElKg,S,f ).

7.3 The bound de re

I now rehearse observations from Charlow and Sharvit [2014] showing how the proposal han-

dles 21. We assume the following syntax (abstracting from irrelevant world-pronouns and

abstraction over worlds, and grouping some abstractions for the sake of space):

35I’ve spoken of a sentence being true relative to Monday at noon as a weaselly way of not taking a standon whether a single proposition may be true or false at different times. Nothing important in my discussionhangs on how one settles that issue.

29

∃

λ3

John

believes

λp5 λp7 λs1

tp5 t3 is Jupiter s1and

tp7 t3 is Mars s1

The key point is that although the two occurrences of t3 are forced by the usual clause

for predicate abstraction to take the same value, different permutation pronouns take these

two occurrences of the variable as arguments. Recall that in the setup for this example, John

believes that Hesperus is Jupiter and Phosphorus is Mars. And it is easy to see how the

clause below “λs1” could express the proposition that Hesperus is Jupiter and Phosphorus is

Mars relative to an assignment. It will do so if the value of t3 relative to the assignment is the

denotation of “Hesperus”, the value of the first permutation pronoun on this assignment maps

the denotation of “Hesperus” to itself, and the value of the second permutation pronoun on

this assignment maps the denotation of “Hesperus” to the denotation of “Phosphorus”. Thus

our account can deliver the true reading of the sentence, since it allows different permutations

to map the same element of De to different elements of De.

Formally, relative to a g, S, f , assuming that relative to these parameters the denotation

of “Jupiter” is λw.j, while the denotation of “Mars” is λw.m, and simplifying away the

quantification over n, the clause below “John” will evaluate to:

• λx. there are π1, π2 ∈ f(x,w) such that for all w′ ∈ DOX(x)(w), π1(Jt3Kg,S,f )Ew′j and

π2(Jt3Kg,S,f )Ew′m.36

It is easy to see that this condition can non-trivially be satisfied, since π1 and π2 can vary

independently.

36This assumes also that the world-argument of “believe” has been saturated by a world-pronoun which isnot made explicit above.

30

7.4 Constraints

In this section I consider eight theories produced by varying three parameters of the official

theory, and show how the three examples uniquely pin down the official theory from among

these eight. Nothing I say in this section depends on the use of a fine-grained theory in the

background. If we replace “permutations” with “concept-generators”, the alternative theories

I present are alternatives to the CG-theory, and the arguments show that the CG-theory is

uniquely pinned down by the examples from these eight alternatives. The section thus shows

how the three examples – one new here, one due to Dorr, and one due to Soames [1989-90]

and Charlow and Sharvit [2014] – tightly constrain the CG-theory itself, independent of the

argument given in section 2 for a fine-grained theory. I won’t comment on this further, but will

leave the versions of the arguments as applied to the CG-theory as straightforward exercises

for the reader.

7.4.1 Type-simple vs. type-variable

A theory is type-simple if it assumes that there is only a single pronoun for permutations; it

is type-variable otherwise. To illustrate, here is one type-simple lexical entry for “believe”:

Type-Simple Believe

JbelieveKg,S,f = λw.λp.λx. for some π ∈ f(x,w), ∀w′ ∈ DOX(x)(w), p(π) = 1.

Here the quantification over n that appears in the official entry is no longer required: a single

abstraction over permutations is guaranteed to bind any number of occurrences of the single

pronoun for permutations. Type-simple theories allow the verb “believe” always to take an

argument of the same type. The official theory is type-variable.

Type-simple theories cannot accommodate a true reading of 21. Since they assume that

there is only one pronoun for permutations, they predict that in the appropriate version of

the syntax displayed in section 7.3, the same permutation pronoun occurs as sister to both

occurrences of the bound trace t3. Thus the clause below “John” in the syntax displayed

above would evaluate to:

• λx. there is an π ∈ f(x,w) such that for all w′ ∈ DOX(x)(w), π(Jt3Kg,S,f )Ew′j and

π(Jt3Kg,S,f )Ew′m.37

Since John was assumed to know that Jupiter and Mars are distinct, he does not satisfy this

condition: there is no single element of De which stands in Ew′ to Jupiter and to Mars at any

of his belief-worlds w′, never mind at all of them.

37Here I am assuming assuming the world-argument of “believe” has been saturated.

31

7.4.2 Insensitive vs. sensitive

A theory is insensitive if it takes the parameter f to be simply a function from worlds to sets

of permutations; it is sensitive if it takes the parameter to be a function from worlds and

individuals to sets of permutations. To illustrate, here is an insensitive, type-simple lexical

entry for “believe”.

Type-Simple Insensitive Believe

JbelieveKg,S,f = λw.λp.λx. for some π ∈ f(w), ∀w′ ∈ DOX(x)(w), p(π) = 1.

The official theory is, of course, sensitive.

Insensitive theories cannot accommodate a true reading of the sentence 19. On such

theories f is sensitive only to a world argument, so the same set of permutations will be used

for each attitude holder. If this set of permutations includes either one which maps JKal-

ElKg,S,f (w) to JSupermanKg,S,f (w), or one which maps JKal-ElKg,S,f (w) to JClarkKg,S,f (w),

then the proposition expressed by the complement clause of “learned” will fail condition (i):

either Lois or Luthor would have known it before. On the other hand, if the set of permutations

contains no permutations which either map JKal-ElKg,S,f (w) to JSupermanKg,S,f (w), or map

JKal-ElKg,S,f (w) to JClarkKg,S,f (w), then the proposition expressed by the complement clause

of “learned” will fail (ii), since neither person will know the relevant proposition on Monday

at noon.

7.4.3 Functionalist vs. existentialist

Functionalist theories assume that the range of f is singleton sets of permuations (or, equiva-

lently that the range of f is just the set of permutations, not the set of sets of permutations);

existentialist theories allow that non-singleton sets may be in the range of f . For example,

here is a (sensitive, type-simple) functionalist lexical entry for “believe”:

Type-Simple Functionalist Believe

JbelieveKg,S,f = λp.λx.λw. ∀w′ ∈ DOX(x)(w′), p(f(x,w))(w′) = 1.38

In this entry I’ve assumed that the values of f are just permutations, rather than singleton sets

of permutations (with the verb introducing existential quantification over the sole member).

The official theory of the paper is existentialist.

Under the natural assumptions described in section 7.1, functionalist theories (like Basic

Surrogatism) fail to predict the contrast between 15 and 16.39 They predict that 15 is true in

38A nice feature of functionalist proposals is that if extended to modals they would preserve the dualityof “must” and “might”; the proposal motivated in the next section fails to do this. Cian Dorr and JohnHawthorne brought this latter fact to my attention.

39Note that by contrast, they can predict the joint truth of 13 and 14, provided these are interpreted indifferent contexts. In this sense my example goes beyond the standard arguments based on double-vision.

32

a context if and only if 16 is true in that context, and that 17 is true in a context if and only if

18 is true in that context. Moreover, under the same assumptions, it predicts that 15 is true

in a context if and only if 17 is false in that context, and that 16 is false in a context if and

only if 18 is true in that context. So such theories fail to predict the contrast in acceptability

between these sentences.40,41

The following table summarizes these results. “TS” stands for “Type-simple” and “TV”

for “Type-variable”; “I” stands for “insensitive” and “S” for sensitive; “F” stands for “func-

tionalist” and “E” for “existentialist”. “TS, S, E” is thus the official theory.

21 (Bound de re) 19 (Dorr’s datum) 15 vs. 16 (Teachers)

TS,I,F x x x

TV,I,F√

x x

TS,S,F x√

x

TV,S,F√ √

x

TS,I,E x x√

TV,I,E√

x√

TS,S,E x√ √

TV,S,E√ √ √

8 Are names context-sensitive?

Millians take the semantic value of a use of a name to be what it names (or a constant

function on worlds which returns that entity at every world). This position rules out any

context-sensitivity in names. But as I have already discussed above (in section 5.1), in the fine-

grained setting it is open that uses of a single name may have different fine-grained semantic

values in different contexts, even when the name is used to name the same individual. In this

section I consider arguments that names are context-sensitive.

Consider the following case, analogous to the famous “Paderewski” case of Kripke [1979]:42

40As noted above (n. 26), it is no reply to those examples to say that different contexts are suggestedwhen “French” occurs in the complement clause of an attitude report, as opposed to when “Italian” occursin the complement clause of an attitude report, since if we simply substitute “is not Italian” for the relevantoccurrences of “is French” in 15 and 18, and substitute “is not French” for the relevant occurrences of “isItalian” in 16 and 17, the modified examples lead to the same pattern of judgments of acceptability andunacceptability.

41Schiffer’s famous “Madonna problem” [Schiffer, 1992, p. 507-8] could be handled by either a Sensitivetheory, or by an Existentialist one. Dorr’s example goes beyond the standard arguments based on Schiffer’sexample, by forcing a Sensitive one. See Moss [2012, p. 516] for discussion of an example which similarlysuggests a Sensitive theory.

42This case is taken verbatim from Goodman and Lederman [2018]. That case itself was based on one inDorr [2014], whose case was in turn based on one in Schiffer [1979].

33

Context Thelma, a German who doesn’t speak English, is traveling in New York when

Shorty steals her purse. She doesn’t get a good look at him, but she sees him limping

away. The next day the police round up some suspects and call Shorty in for a lineup.

Knowing that Thelma saw him get away, Shorty wisely shows up early. Thelma is

looking for someone who limps, but doesn’t know how to ask the police to make the

suspects walk around. So the lineup fails – she can’t pick anyone out. Later, as Shorty

celebrates his ill-gotten gains, Shorty’s friend is telling the story in the bar. “You won’t

believe how smart this guy is. Since the lady saw him getting away, she knew Shorty

limped, so Shorty got there early. His trick worked: she didn’t see him walk in, so she

didn’t know Shorty limped, and he got off scot-free!”

23. Thelma knew Shorty limped.

24. Thelma didn’t know Shorty limped.

The second of these sentences is the negation of the first, but both are used truly by the

accomplice, so it is natural to say that they are used in different contexts. In the present

semantics, we can allow for this this result if we hold that the name “Shorty” denotes the

same element of De in each context, but that different permutations are salient relative to

Thelma and the actual world in the two contexts (i.e. different fs are supplied by context).

A permutation salient relative to her and the actual world in the first context maps the

denotation of “Shorty” to an element of De corresponding to the way of knowing about him

associated with seeing him limp away after stealing her purse. But no permutation salient

relative to her and the actual world maps the denotation of “Shorty” to this value; perhaps

the only permutations salient in the second context map the denotation of “Shorty” to an

element of De corresponding to the way of knowing about him associated with seeing him

(say) third from left in the lineup.

Thus the official theory can handle these examples. But presented with just this example

on its own, and without the official theory of this paper in the background, it is more natural

for a fine-grained theorist to say that the name “Shorty” is context-sensitive and may denote

one element of De in one context, and a different element of De in a different context. And

in fact, we can give an argument that names should be taken to be context-sensitive in this

way even in the present theory. For suppose the accomplice continues his speech by saying:

25. In the lineup, the lady didn’t know that Shorty was Shorty.

This sentence has a true interpretation. But without postulating context-sensitivity in names,

the official theory cannot accommodate its non-trivial truth. The reason it cannot is exactly

parallel to the challenge for the CG-theory presented in section 2. On the official theory, this

sentence could only be true in contexts (if any) where no permutations are salient relative

34

to Thelma and the actual world. But in these contexts the sentence is trivially true, since

“Thelma doesn’t know that two plus two is four” would also be true. (Note that the official

theory theory does allow true non-trivial readings in a single context of “Thelma thought

Shorty wasn’t Shorty”; it is only the wide-scope negation that causes trouble.)

In the face of this example, it is natural for a fine-grained theorist to hold that names are

context-sensitive or ambiguous; different uses of the same name may have different elements

of De as their semantic values (though presumably all of them would belong to the same

equivalence class of E@). Someone who endorsed such a theory would then have a choice

about which tools to invoke in explaining the true readings of 23 and 24, whether the name

changes its semantic value between the two contexts or the verb supplies different permutations

for Thelma in them. But postulating this dimension of context-sensitivity or ambiguity in

names would not on its own account for the contrast between 15 and 16, for 19, or for 21, so

there would still be reason to adopt the official theory.

Some will choose to respond to this example in a different way, by taking 25 to be literally

false, and rejecting the claim that names are context-sensitive.43 This position is to some

degree in tension with the motivations for the fine-grained theory in the first place, since if we

are willing to reject speakers’ judgments about 25, we might also be willing to reject 3. But I

do not think the theory is unprincipled, and holding that names are not context-sensitive has

advantages in terms of predictive power. So while I think there is good reason for fine-grained

theorists of names also to hold that names are context-sensitive, I do not take this assumption

to be part of the official theory of the paper.44

43Richard [1990] makes this prediction.44There is a subtle question about how fine-grained theorists should understand the notion of context, and

its relation to the semantic values of names which name the same thing. In the main text, I have developedthe theory on the assumption that “Hesperus” and “Phosphorus” can have different semantic values in a singlecontext, and thus (*) “Plato knew that Hesperus rises in the evening, but did not know that Phosphorus risesin the evening” can be true in a single context. By contrast, on this theory, 23 and 24 cannot both be truein a single context. Similarly, 5 can be true in a single context but 25 cannot be. A different development ofthe theory would require that in any context, “Hesperus” and “Phosphorus” denote the same element of De.Indeed, Dorr [2014] argues for a theory of this kind, and against theories (like Richard’s and the one in themain text), on the basis that the latter kind of theory require a “split decision” in how they handle (e.g.) 5and 25. Dorr observes that if one postulates context-sensitivity to produce true readings of 23 and 24, then thevery same mechanism can produce a true reading of (*): there is no need to (in addition) hold that “Hesperus”and “Phosphorus” can have different semantic values in a single context. Similarly, if one claims that truenon-trivial readings of 25 require that the two occurrences of “Shorty” be interpreted in different contexts,then one should be open to claiming that there is a context-shift also within the complement clause of 5, sothat in that sentence “Hesperus” and “Phosphorus” are interpreted in different contexts. Dorr argues that amore economical theory would allow that “Hesperus” and “Phosphorus” are context-sensitive, but require thatthey have the same semantic value in every context. His positive view is in effect that there is a conventionto interpret the names “Hesperus” and “Phosphorus” in a correlated way in the same context, analogously tothe convention governing “strong” and “weak”.

Nothing in the main text (until this section) turned crucially on the claim that 5 was true in a single context.Given a suitable reinterpretation of the notion of context, the fine-grained semantics I’ve developed can beseen as friendly to Dorr’s picture. The main work of the paper is also still relevant to proponents of Dorr’stheory; I’ve shown how in such a theory one can handle quantification and give a full account of data like those

35

9 Conclusion

The semantics of this paper combines the virtues of a fine-grained theory with the virtues of

the CG-theory. Unlike the CG-theory, it allows intuitive true readings of 3-5. Unlike the usual

fine-grained theories it accommodates a range of complex examples, presented in section 5.

The theory uses impossible worlds, but in a highly constrained form, which means that

it does not lose much by comparison to ordinary “possible worlds” theories in the way of

strength.

In this concluding section I will discuss two sources of potential dissatisfaction with my

theory, and consider the prospects for addressing them.

The first source of dissatisfaction stems from the fact that my theory has two extra param-

eters by comparison to the CG-theory. On my theory, which element of De is denoted by a

name can change from context to context, as can which surrogate domain restriction is in play.

These extra parameters lead to some hard metasemantic questions. For instance, if I assert

“Hesperus is bright”, what proposition or propositions have I asserted? What does it take

for a listener to come to believe what I intended to convey? The use of fine-grained semantic

values leads to many possible asserted propositions, and makes it harder to understand how

speakers and hearers could coordinate on a single proposition, or even a set of them. Vari-

ability in surrogate domain-restrictions leads to similar questions about quantified sentences

such as “Some planet is bright”. The Millian CG-theory has neither of these parameters, and

so raises no such questions.

I am tempted by each of two incompatible responses to this problem. The first is to reject

the theory I’ve developed and instead to amend the CG-theory so that there is not a single

set set of concept-generators which is salient relative to an individual and a world, but rather

a sequence of sets of concept generators. Using f as a function from individuals to worlds to

natural numbers to sets of concept-generators, we would then have:

considered in section 5 (which Dorr does not attempt to do).I’ve preferred to present the theory in the main text as I have, mainly because I think it is easier to understand,

since the notion of context it employs is more familiar. But I also think the style of theory I have developedmay be preferable to Dorr’s, for two reasons. First, the fact that Dorr’s theory would be more economical doesnot make it true, and in fact the more economical theory misses out on important contrasts in the data. It isnot possible to utter 23 and 24 “all in the same breath” and hear them as true. There must be some interveningmaterial to clue the hearer in to what is meant. By contrast, (*) requires no such intervening material. Thisdistinction between these examples warrants holding that cases like 23 and 24 cannot be true in a single contextwhile allowing that (*) can be true in a single context. Similarly, 25 requires a setup which makes clear how thedifferent names will be used differently in its complement clause; such a setup is not needed for 5. (Dorr mayof course respond that our knowledge of the background story about Hesperus and Phosphorus provides thecues needed to suggest the relevant changes in context, but if those cues are conventionalized, why are they notpart of the conventional meaning of the expressions?) Second, Dorr’s positive view of the context-sensitivity ofnames seems to me to blur an important distinction between “Hesperus” and “Phosphorus” and expressionslike “strong” and “weak”. While the convention to interpret “strong” and “weak” in the same way is readilyacknowledged by speakers, the corresponding putative convention for “Hesperus” and “Phosphorus” is alieneven on reflection.

Still, as I’ve said, nothing in this paper turns crucially on the difference between the two styles of theory.

36

CG-Believes (extended) JbelievesKg,f = λp.λx.λw. for some n > 0, there areG1 ∈ f(x)(w)(1), ..., Gn ∈f(x)(w)(n) such that for all w′ ∈ DOX(x)(w), p(G1)...(Gn)(w′) = 1.

Provided that f(Plato)(@)(1) is in some contexts disjoint from f(Plato)(@)(2), this lexical

entry will allow for non-trivial true readings of 3-5. Since the theory preserves the Millianism

of the CG-theory, it does not face the challenges about the asserted content of assertions of

unembedded sentences I have just described. But the theory does face a different kind of

metasemantic challenge, namely, to provide an account of how a sequence of sets of concept-

generators are made salient in context. The idea that such a sequence is supplied by context

is on its face considerably less intuitive than the idea that the names themselves have distinct

semantic values. But in some moods I am sufficiently moved by the challenges of providing

an intuitive account of the asserted content of sentences that this issue about sequences of

sets of concept-generators seems comparatively unimportant.

The second response is to hold on to my theory and develop an account of what is asserted

by typical utterances of sentences that does not face the problem just described. For instance,

one might hold that, typically, those who assertively utter “Hesperus is bright” or “Something

is bright” assert every proposition that these sentences could denote relative to different

contexts. For a speaker to communicate successfully, the hearer must merely come to believe

one of these propositions. On this picture, it is only in special contexts (or in embedded

reports, where the different contextual resolutions can matter to the truth of the sentence)

that speakers and hearers bother to narrow down the available contextual resolutions of names

and surrogate domain restrictions.

As in the case of giving a metasemantic account of which sequences of concept-generators

are salient relative to an individual in a given context, there is a great deal of work to be done

here to develop a full story about assertion and communication given my fine-grained theory.

But it is not obvious to me that the challenges faced by the fine-grained account are more

difficult to meet than those faced by the extended CG-theory. I hope that future work will

help to address these questions.

A second source of potential dissatisfaction with my theory (which extends also the CG-

theory) concerns the complexity of the type-variable lexical entry for attitude verbs. Here, I

will to lay out an alternative version of the main theory, which does away with permutation

variables altogether, and show how, though it is attractive in some ways, it faces challenges

which I have not been able to resolve. A proposition p′ is a w-variant of a proposition p if

and only if for all for all w′ such that wRw′, p(w′) = p′(w′). Consider:

Propositional Believe λw.λp.λx. for some p′ a w-variant of p that is salient relative to x

is such that ∀w′ ∈ DOX(x)(w), p′(w′) = 1.

This entry is the lexical entry of Richard [1990], transposed to the present unstructured setting.

The entry can accommodate all of the data we have considered to this point, and has the

37

great advantage over the official theory of not requiring a complex syntax with permutation

variables.45 This Richardian theory allows us to use the simple syntax of Basic Surrogatism;

the arguments of attitude verbs are also straightforwardly propositions.46

But there is an important problem for this simpler theory: as it stands it allows very

many readings which are not observed. Suppose that if a person is female, they are neces-

sarily female, and that John mistakenly believes that Queen Elizabeth is male. Given these

assumptions, the theory allows a true reading of “John believes 2 + 2 = 5”. For provided the

proposition that Queen Elizabeth is male is salient relative to John, that proposition would

be a proposition which is true at all the same possible worlds (i.e. none) that 2 + 2 = 5 is.

This prediction seems absurd: a mistake about Queen Elizabeth’s sex does not amount to a

mistake about simple mathematics.

So while I am attracted to this variant of Richard’s theory, the theory would require further

constraints on w-variants for it to be a viable, predictive alternative to the official theory. I

confess that I hope a version of this simpler theory will work out, but for the moment I don’t

see how to make it more predictive, so in our present state of knowledge, I recommend the

official theory as our best option.

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45Its way of accommodating 21 is perhaps less intuitive than that of the official theory: that sentence canbe true on the present theory only if John has no genuinely possible worlds as belief-worlds (though he mayhave impossible worlds as belief-worlds).

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A Reinterpretations of the Model Theory

In this appendix I present two ways of eliminating impossible worlds and elements of De in

favor of more familiar model-theoretic ideas. The first uses interpretations, and the second

uses individual concepts.

A.1 Interpretations

Assume there is a special class of mental representations which correspond to mental repre-

sentations of individuals. These might be “names” in a “language of thought” (Fodor [1975]),

if one thinks mental representations are sufficiently language-like to have a syntactic category

of this kind. But they might also be understood in different ways, so long as we can identify

a category of mental representations corresponding to individuals.

We begin by taking as given a set of individuals X, a set of possible worlds S, and a

set De, the set of mental representations of individuals. Given these ingredients we can

construct a model in the class of models I introduced above: we let I be the set of functions

f : De → X, which map mental representations of individuals to individuals. If one works

with the language of thought idea, these can be thought of as “interpretations” of the names

in the language of thought. We then let W be S × I, and say that 〈s, i〉R〈s′, i′〉 just in case

i = i′. (This specification of W is similar to the models in Cumming [2008].) Finally, we

define E by the condition that aE〈s,i〉b just in case i(a) = i(b), or as we might say on the

“language of thought” interpretation of the models, these names in the language of thought

are interpreted by the same individual.

A great deal more would have to be said to make this model plausible. Here is one obvious

issue. If public-language names are to be assigned elements of De then the mental represen-

tations should be “had” by every individual. On many theories of mental representations,

however, different individuals never possess the same mental representations. To use this

class of models, proponents of these theories would have to take as given a primitive notion

of synonymy among different agents’ mental representations, and think of the elements of De

as equivalence classes of mental representations which are related by synonymy.

The class of models induced by this kind of construction would be sufficiently rich to do

everything I’ve done in the main text.

A.2 Descriptivism

A second way of thinking about impossible worlds may be more attractive to those familiar

with the ideas behind the CG-theory.

We begin again with a primitive set of individuals X and a nonempty set S of worlds.

Once again, we will use these tools to construct a model which belongs to the class of models

40

introduced earlier in this section. This construction will have the advantage over the previous

one that we do not need to take a further set, De, as primitive. Let the set of individual

concepts of X in S be I = XS . A set of individual concepts C is a conceptual cover of X in S

just in case for every x ∈ X, and every s ∈ S, there is exactly one f ∈ C such that f(s) = x.

(This notion is taken from Aloni [2005].) Let C be the set of conceptual covers of X in S. We

then let W = S×C, and say that 〈s, c〉R〈s′, c′〉 just in case c = c′. We define De as the subset

of IC consisting of those functions which satisfy the constraint that if f ∈ De then f(C) ∈ Cfor all C ∈ C. Finally we define E so that aE〈s,C〉b just in case a(C) = b(C).

The class of models induced by this kind of construction would again be sufficiently rich

to do everything I’ve done in the main text.

B Aloni

In this appendix, I will compare my model theory to that of Aloni [2005]. Every model in

Aloni’s class of models can be transformed into a model in my class of models. A subclass

of my class of models can be transformed into a model in Aloni’s class of models, and that

subclass is sufficiently rich to do everything I’ve done in the paper. In that sense, the present

paper can be seen as giving a new argument for Aloni’s theory, and arguing that the theory

should be supplemented with aspects of the CG-theory. But I will argue that the move to the

more general class of models I use in this paper is conceptually significant.

B.1 Formal comparisons

Aloni is happy to countenance impossible worlds, so in comparing her theory to mine I will

assume given a set of impossible worlds W . Instead of having a primitive domain De with

individuals taken to be equivalence classes of them, Aloni takes as primitive a set of individuals

X, and takes the denotations of names to be individual concepts of X in W (i.e. functions

from W to X). In her basic theory, “surrogatist” domain restrictions are given by a conceptual

cover of X in W , i.e. by a set of individual concepts C such that for every x ∈ X, and every

w ∈W , there is exactly one f ∈ C such that f(w) = x. It is fairly easy to see that every model

of Aloni’s can straightforwardly be transformed into one of mine (by letting De be the set of

individual concepts, and defining aEwb iff a(w) = b(w)). This mapping won’t preserve the

truth of every sentence, but the differences are immaterial. In the reverse direction, however,

things are not as straightforward: not every model of mine can be transformed into one of

Aloni’s, since I have not required that there be elements of De which correspond to each

individual concept; there may be no “covers” at all in my models. But consider the following

richness condition on my models: for every function f : W →⋃

w∈W Iw such that f(w) ∈ Iwthere is an x ∈ De such that for every w, x ∈ f(w). Every model which satisfies this condition

41

can be transformed into a model like Aloni’s.

B.2 Individuals in Aloni’s theory

This relationship between the two kinds of model theory might make it seem that there is little

to choose between in the two models. My class of models, and my notion of surrogate domain

restriction may be less restrictive than Aloni’s (more on the latter in a moment), but since the

generality is not essential for predictions about English data, one might be led to prefer Aloni’s

setup. But there is an important conceptual issue which Aloni’s model theory obscures. Aloni

works in a first-order language, assumes that names denote arbitrary individual concepts, and

takes variables to have their denotations fixed relative to a conceptual cover. She takes the

denotations of simple predicates in the first instance to be functions from worlds to individuals

to truth-values. Although these denotations don’t take individual concepts as arguments, they

can compose with the denotations of names (i.e. individual concepts) once the world-argument

of these functions have been saturated, to produce an individual. This way of defining the

denotations of predicates makes it seem that the individuals in Aloni’s model theory are

primary, and that the individual concepts are in some sense secondary (and one might be

attracted to this feature of her theory as opposed to my use of an abstract De). But in fact

all that matters to the truth-conditions of any expression in her system is the behavior of the

predicates as applied to individual concepts. The fact that in the model theory we started from

a set of individuals and defined the denotations of predicates on those individuals is formally

irrelevant to the use of these models in giving a theory of English. This shows that the idea

that the individuals are primary belongs to a metaphysical interpretation of the models, not

to the use of them in making predictions about English sentences.

What are the merits of this metaphysical picture? Interestingly, the very fact that in

Aloni’s theory names do not in general denote individuals undermines the motivation for the

idea that simple predicates apply in the first instance to individuals. One might have tried

to motivate this idea by saying something like “John, that very person, is happy, not some

concept of him”. But on the theory Aloni presents, the meaning of “John” is an individual

concept so this speech does not ensure that we are talking about an individual rather than

an individual concept. More generally, according to Aloni herself, we can’t use English to

articulate any motivations for this way of assigning meanings to simple predicates, since we

don’t talk about individuals, only concepts of them.

Moreover, if we consider extending Aloni’s theory to allow for predicate abstraction, we see

that the most natural way of doing so would yield an odd and unmotivated type-distinction

between the denotations of simple predicates like “is red” and the denotation of λ-abstracts.

Consider λx. John believes x is happy. There are three natural options for thinking about

the denotation of this abstract: (a) it takes individuals as its arguments directly (like the

42

denotations of primitive predicates); (b) it is sensitive to the choice of a conceptual cover,

but takes a suitable element of the cover as its argument; or (c) it takes arbitrary individual

concepts as its arguments. (c) is the choice made in my theory; unlike the other two options

it yields the attractive result that “(λx. John believes x is happy)(n)” is equivalent to “John

believes n is happy” and in general that β-equivalent terms are equivalent. But notice that

it is only option (a) which preserves the idea, embodied in Aloni’s treatment of the simple

predicates, that predicates denote functions which in the first instance apply to individuals.

The problem is that in the context of Aloni’s theory this proposal is conceptually very strange:

if the constant individual concepts have a privileged role in handling abstraction, it would be

natural for them also to have such a privileged role in handling quantification. But the whole

point of Aloni’s theory is not to give them such a privileged role in handling quantification,

and to use flexible conceptual covers instead.

In short: Aloni’s use of individual concepts is motivated primarily by a metaphysical

picture that individuals are in some sense primary. But this position is unmotivated given her

theory of the semantics of names (since according to her we never talk about those individuals,

as opposed to concepts of them). Morevoer, the theory requires an unattractive asymmetry

between the denotation of simple predicates and λ-abstracts.47

B.3 Surrogate domain restrictions vs. conceptual covers

One can define the notion of a surrogate domain restriction in Aloni’s setting, as a function

S : W → I (where I is the set of individual concepts of X in W ) such that for every x ∈ Xand every w ∈ W there is exactly one i ∈ S(w) such that i(w) = x. Unlike conceptual

covers, surrogate domain restrictions have a world-argument. Even the value of a surrogate

domain restriction on a world w differs from a conceptual cover (by not requiring that its

members cover the individuals at worlds other than w. Here I first consider the difference

between the basic theories which use surrogate domain restrictions and covers (without using

permutations), and then compare extended versions of the theories.

Unlike conceptual covers surrogate domain restrictions are functions on worlds. But I

think there is reason, even for those who use conceptual covers to want to make the choice of

cover sensitive to a world-argument:

Context John is looking at three pictures, a, b, and c. He knows that they are pictures of

exactly two people, but he doesn’t know which pictures represent distinct people.

• John knows there is an x and a y such that x 6= y and (x = a or y = a) and (x = b or

y = b) and (x = c or y = c).

47One final, separate misgiving: the use of individual concepts in Aloni’s theory suggests – although thissuggestion is looser than what I have drawn out to this point – a form of descriptivism about names. It is anattractive feature of my model theory that it is clearly neutral on substantive questions about the semanticsof names.

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Of course this “data sentence” isn’t really a data sentence, but it seems natural to want it to

be able to be true. But no single conceptual cover can deliver a true interpretation of this

sentence (when the quantifier is interpreted as “opaque” or de dicto, and we use lexical entries

in the style of Believe (Provisional)). John has three different ways of thinking about these

two people, and his beliefs are undecided about which two of these three ways of thinking

about them are the ones that represent the very same person. No single cover can capture

this feature of John’s thought, since it would have to select exactly two concepts for the

two individuals. If the choice of cover is made sensitive to a world-argument, however, this

problem would disappear: the relevant cover could then change from one knowledge-world of

John’s to another.

Now on to the second kind of difference, between surrogate domain restrictions at a world,

and conceptual covers. (The problems in this paragraph and the next are recognized by

Aloni herself and are discussed at length by Holliday and Perry [2014].) Relative to a single

conceptual cover, Aloni’s theory cannot deliver a true reading of: “there are two people that

John thinks are identical” (i.e. there are x, y such that x 6= y and John thinks x = y).

Elements of a cover which produce distinct entities at the actual world are constrained also

to produce distinct entities at non-actual worlds. This problem for Aloni is not a problem

for Basic Surrogatism. Elements of De which belong to different equivalence classes at the

actual world can belong to the same equivalence class at other worlds, so this sentence poses

no problem for the basic semantics which uses surrogate domain restrictions.

There is however a related problem, which causes problems both for Basic Surrogatism

and for Aloni. Neither theory can produce a true reading of 21 (“There’s a planet John thinks

is Jupiter and is Mars”). There can only be one surrogate (one element of a cover) of each

planet in the domain of the quantifier, and unless John is incoherent it cannot be identified

with both Jupiter and with Mars (provided, as in the setup of that sentence, John knows that

they are distinct).

In the official theory, I solved the second problem by appeal to permutations. Interestingly,

if we supplement Aloni’s theory by adding permutations we could solve not only to solve the

second problem, but also the first. This shows that in fact, there is more reason for Aloni

to incorporate elements of the CG-theory than there was for me. But interestingly, the

permutations one must use to deliver true readings of sentences like “there are two people

John thinks are identical” would have the global effect of mapping covers to surrogate domain-

restrictions at a world. (Not all permutations are like this; some might map covers to covers.)

This formal fact makes the use of covers in the first place seem unnatural.48

48Aloni solves the first two of the above problems by proposing that different variables may be interpretedrelative to different covers. She solves the third by proposing that different variable-occurrences can be asso-ciated with different covers. But both of these proposals come at a significant loss in predictive power (andleads to the need for a complex pragmatic theory about when covers will shift). The use of permutations seemsto me preferable. Holliday and Perry [2014] offer a different, partial solution which simply allows variables

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Why then have I used my model theory and the surrogate domain-restrictions in the

main text as opposed to Aloni’s model theory and conceptual covers? I argued above that

my model theory is to be preferred on grounds of perspicuousness to Aloni’s (it is also, I

think, easier to work with). Given that model-theory, it is not guaranteed that there will

be surrogate domain-restrictions which correspond to conceptual covers, and the richness

condition that would ensure that there are conceptual covers is a substantive, unmotivated

assumption. For these reasons, although one could impose the relevant richness assumption,

and then work with covers as opposed to surrogate domain-restrictions throughout the main

text, it is conceptually more natural to use the definitions I have used in the main text.

C In Scope Existentialism

This appendix is dedicated to an intriguing piece of data from Charlow and Sharvit [2014]

that the official theory does not account for. Charlow and Sharvit present the following case,

to be assessed in the context of 15-18:

26. John believes every teacher is Italian.

27. ?John believes no teacher is French

28. John believes both teachers are Italian.

29. ? John believes neither teacher is French.

They claim that 26 and 28 are naturally interpreted as true, while 27 and 29 are naturally

interpreted as false. My informants have almost universally rejected these judgments. Some

report something of a contrast between 28 and 29, but almost none reported that contrast for

26 and 27. I am therefore not particularly concerned about the fact that the official theory

does not account for these data. Further work needs to be done to see whether there is a

genuine contrast here. But in case further work does bear out the contrast, I will show in this

appendix how the official theory could be extended to predict the contrast.49

To predict the contrast, I propose altering the lexical entries for non-upward monotone

quantifiers, for instance:

to range over all individual concepts directly. But their theory if taken at face value would lead straight tothe problem with 6 in section 4, and they don’t say how they propose to resolve the problem. They suggestsomewhat loosely that context will supply a restriction on which individual concepts are considered, but theydon’t consider problems this will lead to with generalized quantifiers. The official theory avoids these problems,and accommodates the problematic data without requiring the kind of pragmatic story Aloni requires.

49Cable [2018] develops an account designed to predict the contrast between these in-scope data. His accountof that contrast is very elegant. Unfortunately, his proposal has several undesirable features. Here are two.First, it predicts that in any context in which “Plato thought that Hesperus rose in the evening and Phosphorusrose in the morning” is true, “Plato knew that Hesperus rose in the evening and Plato did not know thatHesperus rose in the evening.” will also be true. (Note the main clause negation in the second conjunct here.)Second, Cable’s theory cannot accommodate the data discussed in section 5.2.

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Surrogatist No (Final)

JnoKg,S,f = λw.λF.λG. no x ∈ Sw is such that

for some n > 0 there are π1 . . . πn ∈⋃

x∈De f(x,w) such that F (π1) . . . (πn)(x) = 1, and

for some m > 0 there are π1 . . . πm ∈⋃

x∈De f(x,w) such that G(π1) . . . (πm)(x) = 1.

As before, we take “F (π1) . . . (π0)” to abbreviate “F”. Here the determiner existentially

quantifies over salient salient permutations. Whereas the arguments of the verb were functions

from permutations...to permutations to propositions, here the arguments are functions from

permutations....to permutations to extensions. When working with attitude verbs we assumed

that different permutations were salient for different individuals. But here, since determiners

do not have individuals as arguments, we must quantify over a set of permutations which are

salient simpliciter. There are various ways one might operationalize this idea, but in the entry

above the permutations which are salient simpliciter are defined as those such that there’s

some individual relative to whom they are salient at that world.

This entry is designed to work with a syntax like the following:

John

believes

noλp4

2

t2 tp4teacher

λp53

t3 tp5is French

Here the binder λp5 is produced beneath “no teacher” and the binder λp4 is produced below

“no”. We assume that even with simple predicates like “is a teacher” there is a λ-abstract

produced by movement.

The key result is that provided the syntax above, with its different scope of the quan-

tifier over permutations with respect to “no”, our predictions for 27 will make it naturally

interpreted as false. The transparent reading of that sentence relative to an S and f (and

assuming natural indexing of world-pronouns not displayed above) will now express:

• λw. ∀w′ ∈ DOX(John)(w), no x ∈ Sw is such that for some π ∈⋃

x∈De f(x,w) π(x) is

a teacher at w, and for some w-admissible π π(x) is French at w′.

Given this entry, assuming that all w-permutations are salient, 26 would be true, and 27

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false.50

I’ve assumed that the only altered entries are for non-upward monotone determiners. One

way of motivating this restriction is as follows. It is natural to think that the truth-conditions

of the transparent reading of:

30. John thinks some interior planet rises in the evening,

are the same as those of:

31. There’s an interior planet John thinks rises in the evening.

If the quantifier over permutations in the first of these sentences is only available below the

verb, we will achieve this desirable result. If however it can also be produced below “some”

in that sentence, then it would also scope below the quantification over worlds. The first

sentence would thus be true (while the second sentence would be false) in a situation where

John thought that Hesperus and Phosphorus were distinct planets, and said “exactly one of

Hesperus and Phosophorus rises in the evening”.51

50Charlow and Sharvit suggest that either attitude verbs are ambiguous between a “universal” and an“existential” entry (where the universal has a universal quantifier over permutations), or that attitude verbsalways have the universal entry, but that the only non-singleton restrictions arise when non-upward-monotonequantifiers are embedded in the attitude report. The second of these options cannot predict the contrastbetween 15 and 16, since no non-upward monotone quantifiers occur embedded in attitude reports in thesesentences. The first of these theories is supplemented by the idea that the “universal” entry tends to bepreferred when the attitude report features a non-upward monotone quantifier. If this idea is understood insuch a way that 18 is supposed to suggest a universal interpretation of the attitude verb, the theory would befalse: for under the universal interpretation, it would be true that there is no one that John thinks is French,and hence true that no one John thinks is French, is French. Charlow and Sharvit might therefore hold that theuniversal interpretation is suggested only when the non-upward-monotone quantifier occurs inside the scope ofthe attitude verb. But the proposal was already somewhat ad hoc and the fact that this restriction is neededmakes it even more so.

Note, moreover, that the present theory explains some further data which puzzle Charlow and Sharvit andwhich pose problems for their own theory (see Charlow and Sharvit [2014, pg. 37 example 72]).

51There is no formal reason why, in the lexical entries for attitude verbs in the main text, we could not havestipulated that the quantifier over permutations scopes under the universal quantification over worlds. Theproblem is that this theory (as Charlow and Sharvit note) makes questionable predictions. Consider:

Context Mary has two pictures of Martin. She thinks they are different people. She says: “exactly one ofthese people is French”, pointing to the two photos.

• Mary thinks Martin is French.

Charlow and Sharvit think this is intuitively false. My consultants go different ways on it. But I’ve preferredthe theory which rejects it, since such a theory is stronger, and even if accepted the data are middling.

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