## 1. Brief History



We will attempt only the briefest history of the topic, focusing on
key episodes rather than on a comprehensive survey.



It is difficult to find in the writings of Plato or Aristotle a clear
endorsement of propositions in our sense. Plato's most
challenging discussions of falsehood, in *Theaetetus*
(187c-200d) and *Sophist* (260c-264d), focus on the
puzzle (well-known to Plato's contemporaries) of how false
belief could have an object at all. Thinking that Theaetetus flies
would seem to require thinking the non-existent flying Theaetetus.
Were Plato a propositionalist, we might expect to find Socrates or the
Eleactic Stranger proposing that false belief certainly has an object,
i.e., that there is something believed in a case of false
belief--in fact, the same sort of thing as is believed in a case
of true belief--and that this object is the primary bearer of
truth-value. But it seems no such proposal is seriously considered. In
both dialogues, it is suggested that thought is a kind of inward
dialogue carried on in the mind itself (*Theaetetus*
189e-190a and *Sophist*263e), and that judgment results
when the two inward voices affirm the same thing. Plato is standardly
understood as explaining false belief (*doxa*) in terms of the
assertion of a false statement (*logos*). But it is far from
clear that he takes the objects of belief to be statements rather than
simply the ordinary concrete objects (e.g., Theaetetus) and forms
(e.g., *flying*) which the statement is about, and still less
clear that he takes statements to be *sharable* between minds.
Statements, for Plato, might simply be tokens of inner speech, as
Nuchelmans (1973, p. 21) suggests.



Aristotle expends great energy in investigating what in reality makes
true statements true, but less investigating the nature of
truth-bearers themselves. In his most significant discussions of truth
and falsehood, he seems not to take a clear stand on the question of
propositions. In *On Interpretation* 1 16a, for instance,
Aristotle remarks that falsity and truth require combination and
separation, whether of names and verbs in speech, or of elements in
thought. However, it is unclear whether the resulting combination of
thought elements is anything other than a token thought, as opposed to
something which is the content of the token thought and which could be
thought by others, could be denied, asserted, etc.



Arguably, the first employment in the western philosophical tradition
of the notion of proposition, in roughly our sense, is found in the
writings of the Stoics. In the third century B.C., Zeno and his
followers, including Chrysippus especially, distinguished the material
aspects of words from that which is said, or *lekta*. Among
*lekta*, they distinguished the complete from incomplete (or
deficient), the latter corresponding roughly to the meanings of
predicates, the former to the meanings of sentences. Among complete
*lekta* they included *axiomata*, or the meanings of
declarative sentences. For the Stoics, only *axiomata*, and not
the words used to articulate them, were properly said to be true or
false. *Axiomata* were therefore the proper subject matter of
Stoic logic.



*Lekta* posed a problem for Stoic materialism, according to
which everything real is corporeal. For the Stoics, the real was
limited to that which can act or be acted upon, and therefore to the
bodily. *Lekta*, however, were thought to be incorporeal.
Seneca explains:



> 
> For instance, I see Cato walking; the sense of sight reveals this to
> me and the mind believes it. What I see is a material object and it is
> to a material object that I direct my eyes and my mind. Then I say
> 'Cato is walking'. It is not a material object that I now
> state, but a certain affirmation about him... (Epistulae morales,
> 117, 13)
> 



The notion of a proposition can also be found in the works of Medieval
philosophers, including especially Abelard (1079-1142) and his
followers, but also among later scholastic philosophers in England,
including Adam Wodeham (d. 1358) and Walter Burleigh
(1275-1344).



Abelard distinguishes between *dicta* or what is said and acts
of assertion (or thinking), the former being the fundamental bearers
of truth-value. While Abelard himself seems to have had little to say
about the nature or identity conditions of *dicta*, his
successors took up the subject with vigor (Nuchelmans 1973, pp.
162-3). Are *dicta* particular acts of thinking, concrete
events or facts, or entities having the same sort of being as
universals? Each of these views is considered and evaluated in the
treatise *Ars Meliduna*, of unknown authorship.



A similar debate raged among the English scholastics in the fourteenth
century. Against Ockham's nominalistic account, under which the
object of assent is a complex token mental sentence, Adam Wodeham, for
example, maintained that the object of assent is not any sort of
mental entity, nor even a *thing* at all, properly speaking,
nor of course a *nothing* but rather a *being the case*
(see Wood 2003, and Nuchelmans 1996, IV for further discussion of
Wodeham and his contemporaries).



One complicating factor for the contemporary reader in examining
Medieval (and later) work on the topic is that the term
"propositio" was standardly used, following Boethius, to
refer to sentences, mental as well as written or spoken (*oratio
verum falsumve significans*, i.e., speech signifying what is true
or false). Propositions in our sense were what was signified by these
*propositiones* if they signified at
 all.[2]



When we turn to the early modern period, it is not easy to find, at
least in the writings of major philosophers, an unabashed assertion of
the reality of propositions. Unsurprisingly, one looks in vain in the
writings of the British empiricists. As for Descartes, particular acts
of judgments serve as the primary bearers of truth-value (although
there is considerable debate about the status of his eternal truths).
Leibniz's *cogitato possibilis* have some of the
characteristics of propositions. These *possible* thoughts seem
to play the role of thought-contents and the fundamental bearers of
truth-value. However, it is a matter of debate whether they are
accorded real ontological status.



Propositionalists were by no means rare in the 19th century, Gottlob
Frege being the best known example. The Czech philosopher and
mathematician Bernard Bolzano also deserves special mention. In his
*Wissenschaftslehre*, or *Theory of Science*, published
in 1837, he argued for the existence of what he called
'*Satze an sich*,' or sentences in themselves,
which he clearly distinguished from linguistic items or mental
phenomena. They are the fundamental bearers of truth and falsity, and
the objects of the attitudes. It is the goal of every science,
including mathematics, to state the fundamental true sentences in
themselves pertaining that subject matter. (This marks a clear
departure from the psychologizing approaches of many of
Bolzano's contemporaries.) Like Frege after him, Bolzano
conceived of propositions as complexes composed of wholly abstract
mind-independent constituents (*Vorstellungen an sich*).
Bolzano's work has had a profound influence on Husserlian
phenomenology and the development of modern logic.



Arguably, the three figures whose work has most shaped the framework
for contemporary Anglophone work on propositions are Gottlob Frege,
G.E. Moore, and Bertrand Russell. We will give short summaries of
their thought on the matter.



In 1892, Frege published his classic paper "On Sense and
Reference". This paper contains his first formulation of the
distinction between sense (*Sinn*) and reference
(*Bedeutung*). Roughly speaking, the sense of an expression is
the mode of presentation of its referent, or the cognitive value of
its referent. Expressions were said to *express* their senses.
Sentences, too, had both referents and senses, according to Frege. The
referent of a sentence is its truth-value. Its sense is a thought
(Beaney 1997, p. 156), not a token thought, but a thought in the sense
of a proposition: a sharable content. Thus, in Fregean jargon,
meaningful sentences express thoughts.



Frege conceived of thoughts as structured complexes of senses. The
thought expressed by 'The evening star is bright' consists
of the sense of 'the evening star' and the sense of
'is bright'. (It should be noted that this claim about
structure does not strictly follow from the fact that sense is
compositional, i.e., that the sense of a whole expression is fixed by
the senses of its constituent parts and their syntactic mode of
arrangement.) In his late masterpiece, "The Thought"
(1922), Frege is explicit about the nature of thoughts. They are not
part of the outer realm, which consists of those entities perceivable
by the senses. This Frege thinks is obvious. Nor are they part of the
inner realm, which consists of ideas. Unlike ideas, thoughts do not
require an owner (i.e., they exist even if not present in any mind),
and can be present to more than one mind. A third realm must be
recognized, he tells us--a realm of abstract eternal entities
which we can *grasp* by virtue of our power of thinking.
However, Frege is explicit that thoughts do act:



> 
> Thoughts are not wholly unactual but their actuality is quite
> different from the actuality of things. And their action is brought
> about by a performance of a thinker; without this they would be
> inactive, at least as far as we can see. And yet the thinker does not
> create them but must take them as they are. They can be true without
> being grasped by a thinker; and they are not wholly unactual even
> then, at least if they *could* be grasped and so brought into
> action (Beaney 1997, p. 345).
> 



This is perhaps the *locus classicus* for platonism in the
modern sense of that term, that is, for the doctrine that there exist
mind-independent abstract entities.



In their early writings, Russell and Moore endorse propositionalism.
In his 1903 book *The Principles of Mathematics*, Russell
affirms the existence of propositions, taking them to be complexes of
ordinary concrete objects (the referents of words) rather than of
Fregean senses (p. 47). Propositions so conceived are now standardly
called *Russellian*, and propositions conceived as complexes of
senses or abstract entities are called *Fregean*. In his 1899
paper, "The Nature of Judgment," Moore affirms the
existence of propositions, taking them to be broadly Fregean in nature
(in particular as being complexes of mind-independent Platonic
universals which he calls concepts).



Russell and Moore later grow suspicious of propositions (although
Russell seems to have accepted them later as a kind of derived or
immanent entity). Interestingly, Moore's thinking on the matter
seems to have changed dramatically during the winter of 1910-11,
as his published lectures *Some Main Problems of Philosophy*
reveal. Before Christmas, Moore claims:



> 
> In the one case *what* is apprehended is the meaning of the
> words: Twice two are four; in the other case *what* is
> apprehended is the meaning of the words: Twice four are eight...
> Now by a proposition, I mean the sort of thing which is
> *apprehended* in these two cases.... I hope it is plain
> that there certainly are such things as propositions in this sense.
> (p. 73)
> 



After Christmas, Moore is more skeptical. While the theory of
propositions is admittedly simple and natural (p. 286), there are good
reasons to reject it. He specifies two problems, both having to do
with *facts*, a topic he avoided in his earlier lectures. The
first is that the theory of propositions suggests the
"primitivist" theory of truth, previously held by Moore
and also Russell, according to which truth is a simple unanalyzable
property of propositions. Primitivism, Moore now claims, requires the
claim that facts consist in the possession by a proposition of the
simple property of truth. This Moore now finds unacceptable. The
second problem is simply that the theory seems intuitively false:



> 
> ...if you consider what happens when a man entertains a false
> belief, it doesn't seem as if his belief consisted merely in his
> having a relation to some object which certainly *is*. It seems
> rather as if the thing he was believing, the *object* of his
> belief, were just *the* fact which certainly is
> *not*--which certainly is not, because the belief is
> false. (p. 287)
> 



Russell echoes similar sentiments in essays after *Principles*.
In 1910 he writes that "we feel that there could be no falsehood
if there were no minds to make mistakes" (Slater 1992, p. 119),
and in the 1918 he remarks that a person with "a vivid instinct
as to what is real" cannot "suppose that there is a whole
set of false propositions about " [Russell 1956, p. 223).



These doubts led Russell (1912) to propose a multiple relation theory
of judgment, to replace the standard two-place relational theory
(which is discussed at length in section 3.1). To use Russell's
example, in judging that Desdemona loves Cassio, Othello stands, not
in a binary relation to a proposition, but rather in a multiple or
many-placed relation to Desdemona, loving, and Cassio. Othello's
judgment is true when there is a fact of Desdemona loving Cassio and
otherwise false. This theory, and its contemporary incarnations, is
discussed in a supplementary document.



Moore's doubts led him to postulate what appear to be merely
possible facts as the objects of the propositional attitudes. When a
subject believes that x is F and x is not F, the object of belief is
the non-existent but possible fact that x is F. See section 9 below
for further discussion of possible facts and their relations to
propositions.


## 2. Roles for Propositions: Modality



If there are propositions, they would appear to be good candidates for
being the bearers of alethic modal properties (necessary and possible
truth), as well as the relata of *entailment*. And if
propositions stand in entailment relations, then there would seem to
be maximal consistent sets of them. Prima facie, such sets seem to be
good candidates for possible worlds (Adams 1974; 1981). A proposition
will be true in a possible world (at a maximal consistent set of
propositions) iff it is a member of that world.



If possible worlds are understood in this way, however, it is
important to distinguish two meanings for talk of 'the actual
world'. This may refer either to the totality of what exists, to
what Lewis calls "I and all my surroundings", or to the
maximal consistent set which includes all the true propositions. The
latter is part of I and all my surroundings, but only a proper
part.


## 3. Roles for Propositions: Semantics


### 3.1. The Relational Analysis



By our stipulation, 'proposition' is used to pick out the
objects of the attitudes and the bearers of truth and falsity. One
would therefore expect that if there are propositions, they would
figure importantly in the semantics of attitude- and
truth-ascriptions. One would expect, in particular, that in
'\(S\) believes that \(p\)', and in 'that \(p\) is
true', the *that*-clauses would refer to
 propositions.[3]



One might doubt whether *that*-clauses could really
*refer*, if reference is understood on the model of proper
names. For, *that*-clauses are not proper names, nor are they
noun
 phrases.[4]
 Still, because propositions are the objects of the attitudes and the
bearers of truth, mustn't they somehow be semantically
associated with ascriptions of attitudes and of truth? Following
Jeffrey King (2002), we will use the term 'designate' as a
catch-all covering any sort of semantic association between a
linguistic item and an entity. We follow standard terminology in using
the word 'express' to pick out the relation between a
predicate and the property which is its sense or semantic content.



More carefully, then, the propositionalist will find it natural to
accept the following account of attitude-ascriptions:



*The Relational Analysis of Attitude Ascriptions*:
 An attitude ascription '\(S\) \(V\)s that \(p\)' is
true iff '\(S\)' designates a person who stands in the
attitude relation expressed by '\(V\)' to the proposition
designated by 'that \(p\)' (and false iff
'\(S\)' designates a person who doesn't stand in
such relation to such a proposition).


Analogously, there is:



*The Property Analysis of Truth-Ascriptions*:
 'That \(p\) is true' or 'it is true that
\(p\)' is true iff the proposition designated by 'that
\(p\)' has the property expressed by 'true'.


One of the great advantages of these analyses--the combination of
which we will simply call *The Relational Analysis*--is
the smooth explanation of the validity of certain inferences.
Consider, for example:



Charles believes everything Thomas said.
  

Thomas said that cats purr.
  

So, Charles believes that cats purr.



Something Barbara asserted is true.
  

Nothing John denied is true.
  

So, something Barbara asserted John did not deny.



John believes that every even is the sum of two primes.
  

Goldbach's Conjecture is that every even is the sum of two
primes.
  

So, John believes Goldbach's Conjecture.



These inferences are valid if they have the following simple logical
forms:



For all \(x\) such that Thomas said \(x\), Charlie believes \(x\).
  

Thomas said \(A\).
  

So, Charlie believes \(A\).



Some \(x\) such that Barbara asserted \(x\) is true.
  

No \(x\) such that John denied \(x\) is true.
  

So, some \(x\) such that Barbara asserted \(x\) is such that John did
not deny \(x\).



John believes \(A\).
  

Goldbach's Conjecture is \(A\).
  

So, John believes Goldbach's Conjecture.



We will discuss problems for the Relational Analysis in Section
 5.[5]


### 3.2. Meanings of Sentences



Propositions are also commonly treated as the meanings or, to use the
more standard terminology, the *semantic contents* of
sentences, and so are commonly taken to be central to semantics and
the philosophy of language. However, there is room for doubt about
whether propositions are the right sort of entity for the job (Lewis
1980). Here is why. Note that a sentence would appear to contribute
the same content regardless of whether it occurs as a proper part of a
larger sentence. So, a sentence such as 'in the past, Reagan was
president' would seem to be true depending on whether the
content of 'Reagan is president' is true at some past
time. But this would seem to imply that this content must lack
temporal qualification--that it can change in its truth-value
over time. Similarly, it seems there are locative sentential operators
'in Chicago, it is raining'. If so, then by a similar
argument, it would seem that the content of 'it is
raining' would have to lack spatial qualification. The problem
is this: it seems *propositions*, being the objects of belief,
cannot in general be spatially and temporally unqualified. Suppose
that Smith, in London, looks out his window and forms the belief that
it is raining. Suppose that Ramirez, in Madrid, relying on
yesterday's weather report, awakens and forms the belief that it
is raining, before looking out the window to see sunshine. What Smith
believes is true, while what Ramirez believes is false. So they must
not believe the same proposition. But if propositions were generally
spatially unqualified, they would believe the same proposition. An
analogous argument can be given to show that what is believed must not
in general be temporally unqualified.



If these worries are well-taken, then the meanings or contents of
sentences are not in general propositions.



Appealing to recent work in linguistics, Jeffrey C. King (2003)
presents evidence against one of the crucial assumptions of the above
arguments, that there are no genuine locational or temporal operators
in English. King claims that 'somewhere' and
'sometimes' are better regarded as quantifiers over
locational and temporal entities (i.e., either locations and times
themselves or locational or temporal properties of events). Thus,
'somewhere, it is raining' would have the logical form
'there is some location \(L\) such that it is raining at
\(L\)'. King further argues that tenses are best analyzed as
quantifiers over times rather than temporal operators. 'John
flunked chemistry', thus, would have the form 'there is
some time \(t\) within \(I^\*\) such that John flunks chemistry at
\(t\)', where the interval \(I^\*\) is contextually supplied.
These analyses, of course, require the controversial claim that
predicates like 'is raining' and 'flunks '
include extra argument places for locations and times.



King emphasizes that his argument is thoroughly empirical. It relies
on results from empirical linguistics. If King is right, however, the
view that the contents of sentences are propositions can be
maintained.



For other criticisms of Lewis's argument, see Richard (1982),
Salmon (1989) and Cappelen and Hawthorne (2010). Brogaard (2012)
provides a defense of the temporalist view of
 propositions.[6]


## 4. Arguments for Propositions


### 4.1 One over Many



One familiar argument for propositions appeals to commonalities
between beliefs, utterances, or sentences, and infers a common entity.
Thus, it has been suggested, less in print perhaps than in
conversation, that propositions are needed to play the role of being
what synonymous sentences have in common, what a sentence and its
translation into another language have in common, etc.



Arguments of this sort are typically met with the following reply:
commonalities do not necessarily require common relations to a single
entity. Two red things have something in common, in that they are both
red, but it does not *follow* that they bear a common relation
to a single entity, the universal of redness. Similarly, two
sentences, in virtue of being synonymous, can be said to have
something in common, but that fact alone does not entail they are
commonly related to a proposition. When a relation \(R\) is symmetric
and reflexive with respect to a certain domain, it may be useful to
speak of the things in the domain which bear \(R\) to one another as
"having something in common", but nothing of ontological
significance follows. Thus, the conclusion is drawn: we need an
argument for thinking that commonalities require common relations to a
single entity.


### 4.2 Metalinguistic Arguments



One standard sort of argument for propositions is metalinguistic.
Thus, many argue that we think of *that*-clauses as designating
expressions if we are to explain how certain argument patterns (such
as those considered in Section 2) are valid and in fact have sound
instances (Horwich 1990, Higginbotham 1991, Schiffer 1996, Bealer
1998). Since some of these sound argument instances contain as
premises sentences attributing truth to the designata of
*that*-clauses, those designata must be bearers of
truth-values. Similarly, premises of some of these sound instances
ascribe attitudes toward the designatum of a *that*-clauses,
these designata would seem to be objects of attitudes. In brief, in
order to explain these facts about validity and soundness, it seems
*that*-clauses must not only designate but must designate
entities fitting the propositional role.



Whether propositions are needed for the semantics of natural language
is a matter of continuing dispute. For more on these matters, see the
entry on
 theories of meaning.


### 4.3 The Metaphysics 101 Argument



Our focus here will be on a different sort of argument. Here is a
speech the basic character of which should be familiar to
undergraduate students of metaphysics:



> 
> When someone has a belief, we can distinguish *what she
> believes* from *her believing it*. I have a belief that
> Homer wrote *The Iliad*, for example. We can distinguish
> *what I believe* in believing that Homer wrote *The
> Iliad*--the content of my belief--from *my believing
> that Homer wrote* The Iliad. What I believe in believing this is
> something you believe, too. What we both believe is the proposition
> that Homer wrote *The Iliad*. This same proposition may be
> asserted, doubted, etc. And, in fact, this proposition is true: Homer
> wrote *The Iliad*. So, there are propositions, and they are the
> contents of beliefs and other attitudes and they are the bearers of
> truth and falsity.
> 



One might attempt to regiment these remarks, somewhat artificially, to
take the form of an argument, which we will dub the *Metaphysics
101* argument:



> 
> 1. With respect to any belief, there is *what is believed* and
> *the believing of it*, and these are distinct.
> 2. What is believed is something that may be rejected, denied,
> disbelieved, etc. by multiple subjects, and is something that may be
> true or false.
> 3. There are beliefs.
> 4. So, there are propositions (i.e, sharable objects of the attitudes
> and bearers of truth-values).
> 
> 
> 



Further tinkering might improve the argument in certain ways. Our
concern, however, is whether the argument goes seriously awry.



The Metaphysics 101 Argument is not metalinguistic. It does not rely
on premises about English. This can be verified by noting that the
argument looks just as good after it is translated into other
languages. Nevertheless, it might be claimed that the argument derives
its apparent force from a seductive mistake about how English (and
other languages) function. Perhaps this is another case of what
Wittgenstein called "language on
 holiday."[7]


## 5. Linguistic Problems?



How might one reply to the arguments for propositions just discussed?
One might reply, of course, by arguing for the opposite conclusion.
Thus, many have argued, on broadly naturalistic grounds, that we ought
not accept propositions. Any such argument will involve controversial
claims about the nature and status of propositions. These issues are
discussed in section 7. However, one increasingly popular reply to
arguments for propositions is to argue, (1), that they presuppose the
Relational Analysis, and (2), that the Relational Analysis does a poor
job of accounting for certain linguistic data.


### 5.1 The Substitution Problem



The problem here is quite simple. If, as the Relational Analysis
entails, attitude-ascriptions of the form '\(S\) \(V\)s that
\(p\)' assert relations to propositions, then we should be able
to replace 'that \(p\)' with 'the proposition that
\(p\)' without affecting truth-value. But in general we
can't do this. Therefore, the Relational Analysis is false. Here
are some examples of failed substitutions:



1.
I insist that it will snow this year. (TRUE)
\*2.
So, I insist the proposition that it will snow this year.


3.
I imagine that it will snow this year. (TRUE)
4.
So, I imagine the proposition that it will snow this year.
(FALSE)


5.
I remember that combustion produces phlogiston. (FALSE)
6.
I remember the proposition that combustion produces phlogiston.
(TRUE).


The class of attitude verbs for which substitution problems
arise--the "problematic" attitude verbs--can be
divided into two subclasses: one consisting of verbs which do not
grammatically tolerate substitutions (e.g., intransitive verbs such as
'insist', 'complain', 'say', and
VPs of the form 'Aux Adj', such as 'is
pleased', 'was surprised'); the other consisting of
verbs which grammatically tolerate substitutions but for which
truth-value is not necessarily preserved (e.g., 'expect',
'anticipate', 'bet', 'gather',
'judge', 'claim', 'maintain',
'hold', 'feel', 'remember',
'know', 'recognize', 'find').



Friederike Moltmann (2003) dubs this problem the *Substitution
Problem*. (See also Vendler 1967, Prior 1971, Parsons 1993, Bach
1997, McKinsey 1999, Recanati 2000, King 2002, Moffett 2003, Harman
2003.)


### 5.2 The Objectivization Effect



Closely related to the Substitution Problem is what Moltmann (2003, p.
87) calls the *Objectivization Effect*, or objectivization.
Substitutions in some cases seem to force a new reading for the verb,
an *object* reading rather than a *content* reading.
Thus, in 'I imagine that it will snow this year,'
'imagine' has the content reading (this is, by
stipulation, what the content reading is!), whereas in 'I
imagine the proposition that it will snow this year,'
'imagine' takes an object reading--it expresses the
same relation that holds between subjects and garden variety objects
such as those designated by NPs like '19th-century Wessex'
and 'my college roommate'.



The problem here can be described as follows. If the Relational
Analysis is true, then propositional attitudes are relations to
propositions; but then it seems very odd that we should be unable to
retain the content meaning by substituting 'the proposition that
\(p\)' for 'that \(p\)'.


### 5.3 Defensive Responses



*Defensive Response #1.* The above arguments against the
Relational Analysis prove too much. Similar problems arise for the
appeal to facts (as distinct from true propositions), properties, and
events in semantics. Here are several examples of substitution
failures.



\(S\) found that the room was a mess.
  

So, \(S\) found the fact that the room was a mess. 



Freedom is on the march.
  

So, the property of freedom is on the march. 



I jumped a jump.
  

So, I jumped an event (of jumping). 



A difficulty for Defensive Response #1 is that it seems to spread a
problem around rather than solve it. One might argue that relational
analyses invoking propositions, facts, properties, and events all make
the same mistake of reading too much ontology into English.



*Defensive Response #2*. From '\(S\) believes that
\(p\)' we *can* infer '\(S\) believes the
proposition that \(p\)' and '\(S\) believes a
proposition.' And the same goes for 'reject',
'assert', 'deny', and many other attitude
verbs. If we concede that these sentences assert relations to
propositions, then we are conceding that there are propositions.



Apart from such defensive replies, though, the relationalist might
attempt to solve the problems. We will discuss several approaches.


### 5.4 The Syntax Response



Next, following Jeffrey King (2002), the propositionalist might give a
purely syntactic answer to the problems. King (pp. 345-6)
claims, first, that there is a very simple syntactic explanation for
the substitution failures that produce ungrammaticalities: such verbs
don't take NP complements at all, and so don't take
nominal complements, which are NP complements. (A verb can take
*that*-clause complements without taking NP complements,
because *that*-clauses are not NPs.) One might say something
similar, for example, about why we cannot substitute descriptions for
names in apposition (e.g., 'The philosopher Plato believed in
universals' is true but 'the philosopher the teacher of
Aristotle believed in universals' is not true.) King claims,
second, that the other class of failures are explained by shifts in
verb meanings (i.e., because of objectivization). These shifts are due
to syntactical matters, in particular the syntactic category of the
verb complement. If the complement is an NP, the verb has an object
meaning. If it is a *that*-clause, it has the content meaning.
King recognizes the need for qualifications: verbs in the problematic
class can have the content reading with certain special NPs, e.g.,
quantifiers ('everything Bill holds, Bob holds'), and
anaphoric pronouns ('I hold that, too'.). In the final
analysis, King claims only that all the syntactic properties of the
complement (and not just its general syntactic category) determine the
verb's meaning when taking that
 complement.[8]


### 5.5 Semantic Responses



The relationalist might respond by making claims about the semantics
of *that*-clauses, 'the proposition that \(p\)', or
some combination of these. We discuss two such proposals here.



First, the relationalist might claim *that*-clauses are
ambiguous, and in particular that they pick out different kinds of
entities depending on which attitude verb they complement. How do we
tell what kinds of entities are picked out? We look at substitution
failures. Thus, it might be argued the truth of '\(S\) remembers
that \(p\)' requires that the subject bear the remembering
relation to a fact, rather than a proposition. After all,
'remember' shows substitution failures for 'the
(true) proposition that \(p\)' but not for 'the fact that
\(p\)'.



However, there are obstacles to this response. For one thing, some
attitude verbs seem not to permit substitutions no matter which
nominal complement is chosen. King (2002) gives the example of
'feel'. What sorts of entities, then, do
*that*-clauses designate when they complement
'feel'? No answer is possible. Is the Relational Analysis
therefore false of such verbs? Perhaps even more damaging, there are
verbs which are near synonyms of 'believes', at least in
attitude ascriptions, and which grammatically take NP complements, but
which exhibit substitution failures and objectivization.
'Feel' is one example, as are 'maintain',
'hold', 'judge', 'expect', and
'suspect'. How could 'believes' designate a
relation to propositions in attitude ascriptions but these verbs not?
Consider also the near-synonyms 'assert' and
'claim'.



Even if the ambiguity hypothesis cannot provide the propositionalist
with a general solution to the *Substitution Problem* and the
*Objectivization Effect*, it may help in explaining other
linguistic phenomena, such as the distributional differences between
various nominal complements ('the fact that \(p\)',
'the proposition that \(p\)', 'the possibility that
\(p\)', etc.). (See Vendler 1967 and Moffett 2003.)



Nebel (2019) proposes an alternate strategy. He maintains the
traditional view that *that*-clauses designate propositions,
but argues that 'the proposition that \(p\)' does not.
Call phrases of the form 'the proposition that \(p\)'
*proposition descriptions*. Proposition descriptions, on this
view, denote *propositional concepts*--functions from
situations to propositions. This is motivated by a puzzle from Partee
(1974):



The number of insect species on Earth is increasing.
  

The number of insect species on Earth is 5.5 million.
  

Therefore, 5.5 million is increasing.



To explain this argument's invalidity, Montague (1973) argued
that 'the number of insect species' does not denote a
number, but an individual concept--a function from situations
(world-time pairs) to individuals (in this case, a number). The copula
in the second premise specifies, rather than equates, the value of the
individual concept relative to this situation.



Nebel presents an analogous puzzle involving a proposition-like
description:



The evidence that vaccines cause autism is that vaccines contain
thiomersal
  

The evidence that vaccines cause autism is scant.
  

Therefore, that vaccines contain thiomersal is scant.



To explain the invalidity of this argument, Nebel claims that
'the evidence that \(p\)' does not denote a proposition,
but a propositional concept--a function from situations to the
proposition that provides evidence for \(p\) in that situation. The
'is' of the first premise again specifies the proposition
that is the value of the propositional concept in that situation; it
does not state an identity between 'the evidence that
\(p\)' and 'that \(q\)'. In general, all proposition
descriptions are said to denote propositional concepts. In the case of
'the proposition that \(p\)', the propositional concept is
a constant function that designates the same proposition in every
situation.



Nebel supports this view by noting particular uses of proposition
descriptions. Compare the following pairs of statements:



1.


a.
The teacher explained the cause of World War I.
b.
The teacher explained the assassination of Franz Ferdinand.

2.


a.
Sally explained that Fido barks.
b.
Sally explained the proposition that Fido barks.



The members of each pair have different truth conditions, despite the
assassination of Franz Ferdinand being the cause of WWI, and the
proposition that Fido barks being the denotation of 'that Fido
barks'. To explain this, Nebel appeals to the notion of a
*concealed question;* in certain contexts--for instance,
when the complement of 'explains' is a noun
phrase--the meaning of the noun phrase is given by an
interrogative clause. Thus, (1a) means that the teacher explained
*what caused World War I*. In the same way, the proposition
description in (2b) conceals a question, although it is a murkier, and
often context-sensitive, matter exactly which question is concealed.
Nebel suggests that Sally explained *what the proposition that Fido
barks is, means, or involves*.



If proposition descriptions sometimes function as concealed questions,
then it is plausible that they share a semantics with interrogative
clauses. Interrogative clauses have been taken to denote *question
intensions*, functions from situations to propositions that truly
answer the question in that situation. If this is correct, then
question intensions are just propositional concepts. Nebel takes this
to provide evidence for his view: If proposition descriptions denote
propositional concepts (and not propositions), then we should predict
that proposition descriptions can be used as concealed questions in
contexts which permit interrogative complements, which is what we
find.



Since 'that \(p\)' and 'the proposition that
\(p\)' denote different entities, Nebel's proposal seems
able to explain the substitution failures that result from replacing
proposition descriptions for *that*-clauses. It would seem,
however, that on his view inferences from 'S believes that
\(p\)' to 'S believes the proposition that \(p\)'
will be invalid. Nebel gives a tentative response that
'believes' may be polysemous. Compare the following:



3.
Sally believes that Fido barks.
4.
Sally believes the proposition that Fido barks.
5.
Sally believes her mother.


In (3), 'believes' takes a proposition as argument and
returns a predicate that is true of Sally iff she believes that
proposition. In cases like (3), 'believes' takes a
non-propositional entity (her mother) as argument and forms a
predicate that is true of Sally iff she believes some
contextually-salient proposition that is associated with her mother.
Nebel proposes that (2) is like (3); in this case, the
contextually-salient proposition associated with the propositional
concept is that Fido barks. Thus, (1) and (2) have the same truth
conditions, despite the *that*-clause and proposition
description denoting different entities.



One may object that many descriptions which denote proposition-like
entities (statements, rumors, claims, etc.) can take predicates that
don't apply to abstract objects like propositional concepts. For
example, in the sentence 'the rumor that Jim consumes peyote is
vicious,' the description 'the rumor that Jim consumes
peyote' is said to denote the function from situations to the
proposition rumored at that situation. But it seems to be a category
mistake to say that a propositional concept (or even a proposition) is
vicious. Similarly, van Elswyk (2022) appeals to points made by
Moltmann (2013) that certain descriptions permit causal predicates, as
in 'the statement that durian is pungent caused
astonishment'. On Nebel's view, 'the statement that
\(p\)' denotes a propositional concept. But if propositional
concepts are abstract, then they cannot enter into causal relations.
On a more natural reading, the description designates an act of
stating (or perhaps its product, as Moltmann maintains), which can be
a cause.



Finally, we may ask whether this view can explain the Objectivization
Effect. If proposition descriptions denote propositional concepts, and
these are functions from situations to propositions, then why do we
get the object readings with proposition descriptions? For 'the
number of insect species is increasing' we do not get an object
reading for the NP, but a "structural" reading that makes
sense if 'the number of insects' denotes an individual
concept. The same applies to 'the evidence that vaccines cause
autism is scant'. However, in 'John fears the proposition
that a bear is behind the tree', we do not get a structural
reading. John does not fear the function itself, nor any structural
feature of it. We get an objectual reading of the sort King
predicts.


### 5.6 Substitution and Objectivization Problems for Everyone?



Although the dominant view in the literature is that the
*Substitution Problem* and the *Objectivization Effect*
are problems principally for defenders of the Relational Analysis
(e.g., Prior 1971, Bach 1997, Recanati 2000, Moltmann 2003; 2004), it
is intriguing to ask whether some version of these problems arise for
*everyone*--friend or foe of the Relational Analysis,
friend or foe of propositions.



As noted above, there are near-synonyms (e.g., the verbs
'assert' and 'claim') which are alike in
taking nominal complements but which differ with respect to
substitutions. This seems to be a fact that everyone must explain. It
seems likely that the substitutional differences must be explained in
terms of shifts in verb meaning. Because substitution does not affect
the meaning of 'assert', it must affect the meaning of
'claim', and, intuitively, it does. This does leave the
question of how the *Objectivization Effect* itself is to be
explained. But one might hope that a broadly syntactic
solution--perhaps like King's--would be available to
anyone, regardless of one's stance on propositions.



If these problems are problems everyone faces, some heat is taken off
the relationalist, and the propositionalist generally.



That said, the relationalist may have to take account of other
linguistic puzzles. She will need to explain why it sounds so
peculiar, e.g., to talk of "my believing what you desire, or my
dreading what the thermometer indicated." And, even with purely
cognitive attitude verbs, similar puzzles arise: the mild peculiarity
of "I doubt/assert what you contemplate/entertain," for
example, will require explanation. (For more on these matters, see
Vendler 1967 and Harman 2003.)


### 5.7 Modifying/Replacing the Relational Analysis



Let us suppose, for the sake of argument, the linguistic problems
discussed above undermine the Relational Analysis. Can a
propositionalist dissociate herself from that analysis, and its
linguistic difficulties, while still endorsing the arguments we
discussed for propositions in section 5.1?



Some modifications of the Relational Analysis do not avoid the
linguistic problems. For instance, it is not enough to claim that
attitude verbs designate *three*-place relations between
subjects, propositions, and modes of presentation.



One possibility is to deny that attitude verbs designate relations
when complemented by *that*-clauses, and to claim that they
rather make a syncategorematic semantic contribution. Under one
approach, *that*-clauses in attitude ascriptions designate
propositions which serve to "measure" attitudes conceived
of as mental particulars (Matthews 1994). It is not clear that this
view will be immune to substitution and objectivization problems. See
Moltmann (2003) for further discussion.



Another possibility is to abandon the Relational Analysis altogether,
in favor of a version of Bertrand Russell's "multiple
relation" theory. Following Russell (1911; 1913; 1918), Newman
(2002) and Moltmann (2003; 2004), have recently argued that
*that*-clauses in attitude ascriptions do not designate
propositions but rather provide a number of entities as terms of a
"multiple" attitude relation. These philosophers
nonetheless do accept propositions, and use them to explain sentences
in which 'proposition' explicitly occurs, e.g.,
('Some proposition that John believes is true',
'John believes the proposition that snow is white'). The
basic idea is that there are propositions, but they have the status of
"derived objects"--derived from our attitudes, which
themselves are not relations to propositions. It is an interesting
question whether a Russellian is positioned to endorse the arguments
for propositions given in section 4. (For more on the Russellian
theory, see the supplementary document:



> 
> The Multiple Relation Theory
> 



An alternate proposal which abandons the Relational Analysis takes
*that*-clauses to be predicates. Van Elswyk (2020) argues that
this explains why *that*-clauses can compose with nouns, as in
'the belief that snow is white', as well as why
*that*-clauses can follow the adverb 'now', as in
'now that Giannis will be named MVP, Giannis will be offered a
supermax contract'. In the first case, the *that*-clause
specifies the content of the attitude denoted by the noun phrase (e.g.
'the belief'). In the second case, the use of
'now' contributes the information that the event \(e\_1\)
described in the main clause occurs after the event \(e\_2\) following
'now'. The *that*-clause serves as a predicate that
is satisfied by \(e\_2\). Even rejecting the Relational Analysis, van
Elswyk finds a need for propositions as meanings of sentences and the
things designated by certain names (e.g. 'logicism'),
proposition descriptions, and propositional anaphors, such as
'so', 'yes', and 'no'.



Trueman (2021) rejects the Relational Analysis in favor of a
*prenective* view of attitude reports inspired by Prior (1971).
Whereas the Relational Analysis treats the attitude verb \(V\) in
ascriptions of the form '\(S\) \(V\)s that \(p\)' as
contributing a dyadic relation between \(S\) and the proposition
designated by 'that \(p\)', this view treats V as
prenective, meaning that it acts as a predicate at one end and a
sentential connective at the other. So, the prenective view denies
that 'that \(p\)' is a singular term, instead parsing our
ascription as '[\(S\)] \(V\)s that [\(p\)]', where
'\(p\)' is a sentence that expresses the proposition
content of S's attitude. In denying that *that*-clauses
are singular terms, Trueman avoids reifying propositions, and instead
identifies propositional contents as truth-conditions of sentences.
Thus, to believe the proposition that \(p\) is to stand in the
believing relation to the truth-condition of '\(p\)'.



One might worry that the prenective parsing of belief reports clashes
with the syntactic data that motivated treating *that*-clauses
as singular terms in the first place. After all, instead of
'Simon believes that Sharon is funny', we may say
'that Sharon is funny is what Simon believes', where the
complementizer 'that' moves with 'Sharon is
funny' rather than staying put with 'believes'.
Trueman responds in two parts. First, the mere fact that
*that*-clauses are syntactic units does not imply anything
semantic about them--viz., that they are singular terms.
(Hofweber 2016 gives a sustained defense of this point.) Second, he
modifies the proposal from Prior's original parsing; rather than
'[\(S\)] \(V\)s that [\(p\)]', attitude ascriptions are
parsed as '[\(S\)] \(V\)s [\(p\)]'. The complementizer
'that' is semantically vacuous, but functions to indicate
that 'Sharon is funny' is a complement of
'believes' rather than occurring as a standalone sentence.



## 6. The Metaphysics 101 Argument: Deep or Shallow?



We have suggested that the most promising arguments for propositions
are the metalinguistic arguments and the Metaphysics 101 argument. The
former arguments are plainly theoretical: they appeal to the
explanatory power of semantical theories invoking propositions. To
resist them, there is no need to explain away their intuitive appeal,
because they do not and are not intended to have intuitive appeal.
This is not true of the Metaphysics 101 argument. It is thoroughly
intuitive, and so resisting the argument requires giving a story about
how and why intuition goes wrong. In this section, we will consider
one general strategy for doing this.



The Metaphysics 101 argument can seem Janus-faced: its premises seem
utterly shallow, and yet its conclusion seems to resolve a deep
ontological debate. One is apt to think, "Sure, what I believe
is different from my believing it. And so we can distinguish the
content of a belief from the attitude of belief. These contents are
propositions. Fine, but now it seems there must be a domain of
entities here, whose nature remains to be investigated. How could that
be?" One might suspect some sort of equivocation or ambiguity is
at work, some oscillation between a shallow and a deep
interpretation.


### 6.1 The Internal/External Distinction



Rudolf Carnap's (1956) distinction between internal and external
questions may prove relevant here. For Carnap, an internal question is
a question that is asked within a particular linguistic framework.
Internal questions are answered by invoking the rules of the framework
together with logic and the empirical facts. Not all such questions
are trivial, but questions about the existence of the sorts of
entities definitive of the framework are. Carnap in fact thought that
the traditional metaphysician aimed to ask a framework independent
question, an external question, failing to realize that external
questions are best seen as non-cognitive practical questions about
which framework to adopt and at worst meaningless. (See the link to
Weisberg 2000, in the Other Internet Resources section).



Relying on Carnap's distinction, within certain linguistic
frameworks, such as that presupposed by the Metaphysics 101 argument,
it is almost trivial that there are propositions. All it takes is
something as superficial as the Metaphysics 101 argument, or the
following even less enlightening argument, "The proposition that
snow is white is true; therefore, some proposition is true; therefore,
there are propositions." The traditional metaphysician, however,
aims to ask a non-trivial question about the reality of the
propositions outside such frameworks. Such questions have no cognitive
content.



One of the chief difficulties for Carnap is to explain the truth of
internal statements. If 'there are propositions' is true,
even within a framework, what does its truth consist in? If truth in a
framework is explained in terms of truth *given the axioms of the
framework*, we will want to know about the truth-value of the
axioms themselves. If they are true, what makes them true? If they are
not true, why can't we conclude that there really are no
propositions?



Even if we must reject Carnap's internal/external distinction,
perhaps some form of "Neo-Carnapian" ambiguity hypothesis
can help explain away the appeal of the Metaphysics 101 argument.



A number of questions arise for the Neo-Carnapian. First, how are the
internal and external readings to be distinguished? Second, how
pervasive is the ambiguity? are there different readings not only for
quantified sentences but for attitude- and truth-ascriptions as well?
Third, what is the status of the Metaphysics 101 argument, given the
two readings? The argument must be unsound when understood externally,
but must it be invalid, or is it a valid argument with a false
premise? If so, which is false? Fourth, how could philosophers
regularly miss the internal/external ambiguity?



We will briefly describe two Neo-Carnapian accounts.


### 6.2 Fictionalism



One possibility is to explain the internal/external distinction by
reference to fictions. Internal statements are statements made within
or relative to a fiction, and they are to be assessed as true or false
relative to the fiction.



However, any fictionalist interpretation of the internal/external
distinction would have to explain why the fiction of propositions,
like the fictions of properties and numbers, is not a mere game, but
can be used for describing reality. We will briefly discuss a kind of
fictionalism designed to do just this: *figuralism*. (For
discussion, see Yablo (2000, 2001), Yablo and Rayo (2001), Yablo and
Gallois (1998), and for a similar view, Balaguer 1998a and 1998b).



Relying on pioneering work by Kendall Walton (1990), Yablo argues that
pretense can serve serious practical and theoretical purposes. To use
Walton's example, by pretending that Italy is a boot, I can
easily convey to you the location of the Italian town of Crotone. Here
I am, in effect, using a pretense to convey information about the real
world. Literally, Italy is not a boot, but my interest is not in
speaking the literal truth, but in conveying a rather complicated fact
to you as effectively as I can. Similarly, Yablo and Gallois claim,
one may pretend there are certain entities in order to better convey
certain facts (1998, 245-8). One might pretend there are
directions in order to facilitate communication of facts about which
lines stand in which geometric relations to which other ones. Perhaps
one could do the same with propositions?



However, Yablo (2001) emphasizes that the figuralist need not be
*committed* to any psychological thesis about making-believe.
We may not consciously pretend that there are propositions when we say
that what we believe is true, just as we may not consciously pretend
that there are such things as stomach butterflies when we say we have
butterflies in our stomach. Figuralism requires only that there is a
semantical distinction between literal content and figurative content,
and that by asserting sentences with certain false or at least highly
doubtful literal contents, we may also express genuine facts, which
would be well nigh impossible to express literally. (See Balaguer
1998a and 1998b on the concept of representational aids)



Figuralism makes it possible to diagnose the failure of the
Metaphysics 101 argument as follows. If its steps are interpreted
literally, the argument is unsound but valid. If its steps are
interpreted figuratively, it is sound. Why are we fooled, then? One
promising suggestion is that it can be very difficult to distinguish
figurative from literal content, particularly when the figures
employed have little presentational force.



If we accept this diagnosis, we are committed to thinking that every
belief-ascription is literally false. This is a bitter pill to
swallow, though it may seem less bitter the less importance is placed
on literalness in communication (See Yablo 2001, p. 85).


### 6.3 Two Readings for Quantifiers



Some philosophers have suggested that ordinary English quantifiers are
susceptible to multiple readings, or different readings in different
contexts of use. Thus, Hilary Putnam (1987, 2004) has argued that
there is no single meaning associated with the vocabulary of
quantification, and that, depending on context, an assertion of
'there are \(F\)s' might be true or false. For example,
the Polish mereologist, in certain contexts, might be able to speak
truly in asserting 'any objects compose a further object',
whereas an assertion of the negation of this sentence might true in
different contexts. (Note that Putnam is clear that the phenomenon he
is describing isn't mere quantifier-restriction.)



The acknowledgement of different meanings for the quantifiers is not
enough by itself to explain away the intuitiveness of the Metaphysics
101 argument. As we mentioned earlier, what is needed is an account of
the apparent oscillation between a shallow and a deep interpretation.
There could, in principle, be a plurality of interpretations of the
quantifiers even if none of the readings differed with respect to
metaphysical depth.



Recently, Thomas Hofweber (2005, 2016) has claimed to have found the
required pair of readings. A quantifier, he claims, may have either a
*domain-conditions* or *inferential role* reading. The
domain-conditions reading is just the familiar reading we know from
first order semantics: 'there are \(F\)s' is true iff
there exists an entity in the relevant real domain which satisfies
'\(F\)'. This reading is therefore ontologically
committing and so *deep* (and thus external). The inferential
reading, by contrast, brings with it no ontological commitment, and so
is shallow (and thus internal).



Hofweber explains that the inferential role reading serves an
important function. It enables us the easy expression of partial
information. For example, I might not recall a name or unique
description of Fred's favorite detective, but if I want express
the partial information I have, I can do this by saying "Fred
admires some detective.". Now, on the domain-conditions reading,
what I express is false, and so I have misinformed my audience. What
we need, to achieve the desired end, is a reading for 'there is
an \(F\)' which validates existential generalization, regardless
of whether the names occurring in the premise refer to an entity. This
is what the inferential role reading provides. Thus, we say
"Fred admires some detective--yes, it's Sherlock
Holmes!"



Hofweber points out that these two readings are not like the two
readings for 'bank'. They validate many of the same
inferences (e.g., 'there is an \(F \amp G\), therefore, there is
an \(F\) and there is a \(G\)') and, within discourses lacking
empty singular terms, they validate all of the same inferences.



Now for the relevance to the Metaphysics 101 argument. On either
reading of the relevant quantifiers in the Metaphysics 101 argument
(those in steps 1, 2, and 4), the argument is valid. But on the
domain-conditions reading, premise 1 (at least) is, if not false, then
at least dubious--a piece of controversial ontology. On the
inferential-role reading, all the problems go away, and the argument
appears completely shallow. The Janus-faced character of the argument
comes from oscillating between the two readings. Moreover, given the
close relations between the two readings, it is understandable that
the metaphysician fails to realize her mistake in thinking that the
argument establishes the existence of propositions.



For an account like Hofweber's to succeed, it must be possible
for attitude- and truth-ascriptions to be true even if
*that*-clauses do not designate. For if they designate, then
the domain-conditions reading of 'there is something \(S\)
believes' would be true.


## 7. The Nature and Status of Propositions


### 7.1 Easy Arguments: Mind-Independence and Abstractness



Reflection on the proposition role leads many propositionalists to
rather dramatic answers to questions about the nature and status of
propositions. Below is one standard line of argument, versions of
which can be found in Bealer (1998) and Schiffer (2003). (See also
Cartwright (1962) and Soames (1999).)



The proposition that there are rocks, which we denote \(\ltb\)there
are rocks\(\gtb\), does not entail the existence of any beings that
have or are capable of having mental states. It entails this neither
in a strictly or broadly logical sense. That is, it is
*possible* in the broadest sense for \(\ltb\)there are
rocks\(\gtb\) to be true in the absence of all mental states. But now,
if this proposition is possibly true in the absence of mental states,
then it possibly exists in the absence of all mental states, and so is
mind-independent. This is an easy argument for the mind-independence
of at least some propositions.



A parallel "easy argument" can be given for the
abstractness of at least some propositions. \(\ltb 2+2=4\gtb\) does
not entail the existence of concrete entities. So it is possible for
it to be true (and so to exist) in the absence of concrete entities.
Thus, it is possibly abstract. Assuming, contra Linksy and Zalta
(1996), that abstractness is, necessarily, an essential feature of
abstract entities, then it follows that \(\ltb 2+2=4\gtb\) is in fact
abstract. One might want to extend such arguments to contingent
propositions. Consider \(\ltb\)there are trees\(\gtb\). This
proposition is false in a world without concrete entities. But if it
is false in such a world, it must exist in that world, and so is
possibly, and so actually abstract.



Similar arguments can be constructed for properties. If properties are
what we *assert of* objects and what is *true/false of*
objects, then there are simple arguments for the conclusion that at
many properties are mind-independent and abstract.



It is dangerous to generalize these sorts of "Easy
Arguments" to *all* propositions (particularly singular
propositions). But even if they cannot be fully generalized, they
threaten to show that propositions would be mind-independent abstract
entities. Now, given that propositions *de jure* are sharable
objects of attitudes, it is antecedently unlikely that they should
turn out to be, say, token utterances. But one might have thought that
propositions could be identified with natural language sentence types
(as in Quine 1960), or with sentence types in the language of thought.
But if the Easy Arguments succeed, it seems that to accept
propositions, we must accept Platonism. *Conceptualism* about
propositions seems ruled out.



Many philosophers deny that there are propositions precisely because
they accept the validity of these Easy Arguments (and the truth of
certain attitude ascriptions). There are familiar problems besetting
the believer in abstract entities. The two "Benacerraf
problems," in particular have received much attention in the
literature: the epistemological problem and identification problem.
The epistemological problem for abstract propositions, roughly, is
this: how can we know about abstract propositions, given that we
cannot causally interact with them? The identification problem
requires a bit more explanation. If propositions are abstract, then
there will be many distinct candidates for propositions which seem to
play the proposition role equally well. If certain entities, the
\(F\)s, are candidates for being propositions, why won't the
entities consisting of an \(F\) paired with the number 1 count as
adequate candidates as well, so long as we reconstrue predicates for
propositions in such a way as to make the number 1 irrelevant? But
propositions cannot be both \(F\)s and these new entities, because
these new entities are not \(F\)s. Is it simply indeterminate what
propositions are? See the entry on
 platonism in metaphysics.
 (See also J. Moore 1999.)



The Easy Arguments can appear suspicious. How can the seemingly
obvious acknowledgement that there are propositions--i.e., that
beliefs have sharable objects which bear truth-values--commit us
to there being mind-independent abstract entities? We will discuss two
sorts of reply found in the literature. Both are objections to the
*inference* from there being propositions to the claim that
propositions have the surprising features. We are putting aside
objections to the claim that there are propositions.


### 7.2 Reply #1: Truth *in* a World vs. Truth *at* a World.



The Easy Arguments rely on an assumption about entailment and truth,
namely:



(Assumption A)
If a proposition \(\ltb p\gtb\) fails to entail a proposition
\(\ltb q\gtb\), then it is possible for \(\ltb
p\gtb\) to be true while not-\(q\).


This assumption is needed to reason from premises about propositions
failing to entail other propositions about there being mental states
or being concrete entities to the possible truth of those propositions
in the absence of mental states and concrete entities.



But how could (A) fail? If a proposition fails to entail that \(q\),
doesn't it follow that there is a possible world in which the
former is true and not-\(q\)?



Some philosophers (Pollock 1985, King 2007) have argued that
principles like (A) have two readings, one clearly acceptable but
useless to the Easy Arguments and the other useful to those arguments
but false. The two readings correspond to two ways of understanding
talk of truth with respect to possible worlds. One way for something
to be true with respect to a world requires the truth-bearer to exist
in the world and be true there. Another way is for the truth-bearer to
"correctly describe" the world, where this does not
require existing in the world. Pollock gives the example of a picture
depicting the non-existence of all pictures. The picture could
correctly depict a situation even though the situation it depicts is
one in which the picture itself does not exist. Similarly, the
Medieval philosopher Jean Buridan discusses the example of an
utterance of 'there are no negative utterances'. This
utterance correctly describes a certain possible situation even though
that situation is one in which the utterance would not exist.
Following Adams (1981), we may call the former way of being true with
respect to a world *truth in a world* and the latter *truth
at a world*. The conceptualist may claim that propositions can be
true at worlds without being true in them, by analogy with the
examples from Pollock and Buridan. A proposition like \(\ltb\)there
are no propositions\(\gtb\) is true at certain possible worlds but
true in none. Since we do not want to say that such propositions are
necessary, we must understand necessity as truth *at* every
possible world. Correspondingly, to preserve the connections between
entailment and necessity, we must understand entailment in terms of
the entailed proposition being true at every world at which the
entailing proposition is true. Given all this, we can distinguish two
readings for Assumption A:



(Reading 1)
If a proposition \(\ltb p\gtb\) fails to entail a proposition
\(\ltb q\gtb\), then there is a possible world \(W\) such that \(\ltb
p\gtb\) is true *in* \(W\) and not-\(q\) at \(W\).


(Reading 2)
If a proposition \(\ltb p\gtb\) fails to entail a proposition
\(\ltb q\gtb\), then there is a possible world \(W\) such that \(\ltb
p\gtb\) is true *at* \(W\) and not-\(q\) at \(W\).


Given the understanding of entailment in terms of truth at a world,
the conceptualist will claim that Reading 1 is false, while Reading 2
is true but useless to the Easy Arguments. Thus, the conclusions of
those arguments are blocked.



The plausibility of this response depends on having a good account of
what truth at a world amounts to. But this, in turn, depends on issues
in the metaphysics of modality.



If worlds are concrete particulars ("I and all my
surroundings"), as they are for David Lewis (1986), then we
could say that a proposition is true *at* a world if the
proposition is about the entities that are parts of that world and is
true, and true *in* a world if true at a world and also part of
that world. There may well be difficulties of explaining how a
proposition could be part of more than one concrete world (and why it
would only be part of some concrete worlds but not all), but this
framework seems to make conceptual room for the possibility
propositions being true at worlds without being true in them.



Suppose, however, that worlds were conceived as world stories, i.e.,
as maximal consistent sets of propositions (see Section 2). How, then,
might truth at a world be understood? One approach, favored by Adams
(1981), is to explain truth at a world in terms of truth in a world,
understanding the latter to amount to truth were the world actual
(were all its members true). On this approach, we would understand
what is true at a world in terms of what is true in it, together with
certain facts about the actual world. However, the conceptualist
cannot abide this approach. For, on this approach, the members of any
world are true in that world. But since the members of any and every
world are propositions, it would follow that, contrary to
conceptualism, that it is necessary that there are propositions. A
more conceptualist-friendly approach is to reverse the order of
explanation, to explain truth in a world in terms of truth at a world
+ existence in that world. How could truth at a world be understood? A
natural proposal is to understand it as membership in a world
story.



Difficulties emerge with this proposal when we face the question of
how to understand consistency of world stories. There are maximal sets
of propositions that are not possible worlds because they are not
*consistent* in the relevant sense. But the relevant sense is
not easily defined. Following Adams (1981), we might wish to use the
concept of possibility to gloss the notion of consistency: a set of
propositions is consistent if and only if those propositions could all
be true together. This returns us to the problem noted in the previous
paragraph: it again would turn out that necessarily there are
propositions (even in mindless worlds).



The conceptualist might hope to take the relevant notion of
consistency as primitive and reject the gloss in terms of joint
possible truth. Still, we should ask about the broader implications of
denying the joint possible truth of consistent world stories.
Consider, for instance the notion of actuality. Only one of the many
possible worlds is actual, although each is actual relative to itself.
The actual one, on the world story view, is the one all of whose
members are true. But if this is what actuality for worlds amounts to,
then assuming possible worlds are possibly actual, it would follow
that for each possible world all its members could be true together.
Ought we to deny that possible worlds are possibly actual?



The conceptualist might hope to avoid these problems, without falling
back on Lewis's concrete realism about possible worlds, by
understanding worlds in terms of properties or states of affairs,
rather than propositions. Following Stalnaker (1976), one might think
of worlds as properties which are ways things could have been.
Following Plantinga (1974) and others, one might think of worlds as
maximal consistent states of affairs, where these are thought of as
distinct from propositions.



However, this retrenchment may end up only shifting the Platonist
worries elsewhere. To distinguish the *ways* that are possible
worlds (or possible world-states) from those which are not, it is
difficult to avoid appealing to a gloss in terms of being possibly
instantiated: the possible worlds are not only maximal but they could
be instantiated. Taking this line would require conceding that in
every world there are properties. Something similar holds for the
conception of possible worlds as maximal consistent states of
affairs.



One might think, however, that Platonism about properties is less
problematic than Platonism about propositions. The former do not
represent the world, whereas the latter, as truth-bearers, do (Jubien
2001, King 2007). However, properties can apply or fail to apply to
objects, and can be said to be true or false of objects, and so it is
not clear that worries about representation clearly gain more traction
for propositions than for properties. Similar considerations apply to
states of affairs.



Despite these worries, the conceptualist might be encouraged by the
example of singular propositions. Hasn't the truth in vs. truth
at distinction been useful in dealing with the modality of singular
propositions? For example, consider any singular proposition about
Socrates, e.g., the proposition that Socrates was a philosopher. Such
propositions, plausibly, depend for their existence on the object they
are directly about. One might therefore think that no singular
proposition about Socrates could exist unless Socrates existed.
Consider, then, the proposition that Socrates does not exist. It is
clearly contingent that Socrates exists; things could have been
otherwise. But then the proposition that Socrates does not exist would
appear to be possible without being possibly true. Unlike the examples
from Pollock and Buridan, however, we cannot understand such
possibility without possible truth in terms of expressing a possibly
true proposition while not being possibly true itself. Propositions do
not express propositions, of course, and so we cannot understand their
possibility without possible truth in this way (Plantinga 1981). What
is it, then, for such a singular proposition to be possible but not
possibly true? Answering this question was one of the key motivations
in the development of the distinction between truth in and truth at a
world. But while Adams and others attempted to do this by thinking of
truth at a world as determined by what is true in that world together
with a certain set of facts about the actual world, the conceptualist
hopes to kick aside the ladder of truth in a world altogether. Whether
this hope is reasonable or not is an important issue in contemporary
work on propositions. (Key recent discussions include King 2007,
Soames 2010, and Merricks 2015).


### 7.3 Reply #2: Deflationism to the Rescue?



Another response to the Easy Arguments is, so to speak, to deflate
their significance by deflating propositions. The Easy Arguments
succeed, but their success marks no great philosophical discovery and
raises no hard questions of the sort that have traditionally bothered
metaphysicians of a nominalist bent.



We will here discuss only Stephen Schiffer's (2003) theory of
"pleonastic
 propositions."[9]



Propositions exist, for Schiffer, but unlike rocks or cats, there is
nothing more to them than what our concept of a proposition
guarantees. One may call them "abstract entities," if one
likes, but this label should not encourage the thought that our minds
can reach beyond the physical world to make contact with denizens of a
Platonic universe. We know about propositions, not by interacting with
them, as we do with rocks and cats, but by being participants in
certain sorts of linguistic or conceptual practice. It's because
we speak or think in certain ways that we are able to know about
propositions.



Schiffer argues, in effect, that given our proposition-talk and
thought, propositions are, in D. M. Armstrong's phrase, a kind
of "ontological free lunch." That is, the key
"axioms" of our proposition-talk and thought are
guaranteed to be true. These include the instances of the equivalence
schema (E) for propositions: *The proposition that \(p\) is true
iff \(p\).* Given the truth of such axioms, it follows that
propositions exist and have the features attributed to them by our
axioms. Moreover, because these axioms are constitutive of the concept
of a proposition, it follows that, by possessing that concept, we can
know the truth of these axioms.



One might concede to Schiffer that the axioms are constitutive of our
concept of a proposition. But why think those axioms are true?
Schiffer stresses that we do not make the axioms true by saying,
thinking, or "stipulating" that they are true. The
mind-independence of propositions, after all, is implicit in those
axioms.



Schiffer's argument for pleonastic propositions is of a piece
with his argument for pleonastic entities generally, including
fictional entities, events, and properties. A pleonastic entity, for
him, is an entity that falls under a pleonastic concept. The latter is
the key notion and is defined as follows.



*Definition*: A concept \(F\) is pleonastic iff it implies true
something-from-nothing transformations. 



A SFN (something-from-nothing) transformation (about \(F\)s) is a
statement that allows us to deduce a statement about a kind of entity
F, from a statement that involves no reference to \(F\)s. (61) SFN
transformations assert a kind of *supervenience* condition on
\(F\)s: if the relevant non-\(F\) conditions obtain, \(F\)s exist and
have the relevant features. (E.g., if snow is white, then the
proposition that snow is white exists and is true.)



If the concept \(F\) is pleonastic, then there are \(F\)s. We need to
know how to tell if a concept is pleonastic. Here is Schiffer's
test:



> 
> *Test*: A concept \(F\) is pleonastic (and so implies true
> something-from-nothing transformations) iff adding it to any theory
> yields a conservative extension of that theory. (57)
> 



Schiffer's final formulation of the conservativeness test
is:



> 
> For any theory \(T\) and sentence \(S\) expressible in \(T\), if the
> theory obtained by adding to \(T\_{/{\sim}F} \ltb\)the theory resulting
> from restricting quantifiers in \(T\) to \({\sim}F\)s\(\gtb\) the
> concept of an \(F\), together with its something-from-nothing
> \(F\)-entailment claims, logically entails \(S\_{{\sim}F}\ltb\)the
> sentence resulting from restricting quantifiers in \(S\) to
> \({\sim}F\)s\(\gtb\), then \(T\_{/{\sim}F}\) logically entails
> \(S\_{{\sim}F}\). (p. 57)
> 



One might think the conservativeness test is overly complicated, and
that all that matters is that the new entities not interfere with the
empirical world. If so, then the test would mention only empirical
theories not all theories. But, as Matti Eklund (2007) points out, two
kinds of entity that are individually non-interfering with respect to
the empirical world might interfere with one another. Schiffer is
aware of this problem (see his discussion of anti-fictional entities,
pp. 55-6), and this is why he turns to the more complicated
account.



Schiffer's picture is this. If a concept satisfies the
conservativeness test, then its instantiation would be unproblematic
because it would interfere with nothing else. Its instantiation comes
for free. If a concept doesn't meet this test, it doesn't
come for free.



Although Schiffer's view of propositions can be described as
deflationary in one sense (because it attempts to deflate questions
about the existence and nature of propositions), the meta-ontology
underlying Schiffer's approach is, if anything, inflationary:
all "non-interfering" kinds of entity are
instantiated.



Schiffer's, and other deflationist theories, must, at a minimum,
answer the following two questions, in addition to the questions
facing all propositionalists:



(1)
Why would the non-interference of \(F\)s be evidence for their
existence?


Even if \(F\)s would be non-interfering in Schiffer's sense, the
postulation of \(F\)s logically conflicts with some consistent
theories, e.g., 'There are no \(F\)s'. Schiffer places
severer constraints on the denial of entities than on the acceptance
of them. Suppose \(F\)s would be non-interfering. Then adding them
would not add information about non-\(F\)s. But suppose also that
denying \(F\)s would not add information about non-\(F\)s. Why
isn't this a reason to deny \(F\)s? So, in this sense, the
theory denying \(F\)s passes a corresponding conservativeness
test.



(2)
How can the deflationist explain how these propositions have
truth-conditions?


If the proposition that snow is white is a simple, necessary and
eternal object, why does its having a property (truth) have anything
to do with concrete snow's having a property (whiteness)? Do
instances of the T-schema simply state brute necessary connections
between abstract objects and concrete ones? Or do these necessary
connections somehow derive from our practices, and if so, how?


### 7.4 Reply #3: Propositions as Types



Another reaction one might have to the Easy Arguments is to accept
their conclusions but to give an account of the nature of propositions
which will make these conclusions palatable. One promising line of
thinking, in this regard, is to think of propositions as types, the
tokens of which are mental or linguistic acts or events, and in
particular the acts that would be thought to *express* the
proposition. Such views have been developed in recent years by Dummett
(1996), Hanks (2011, 2015), and Soames (2010, 2014a, 2015). We focus
here on the recent proposals put forth by Hanks and Soames.



The type view is motivated by its answers to otherwise puzzling
features of traditional Platonist views of propositions (e.g. Frege
(1984)). On this view, belief and other attitudes are understood as
relations to already-existing propositions which represent things as
being a certain way. The truth or falsity of an individual's
belief or other cognitive state is explained by the truth or falsity
of the proposition which is the object of that state. If truth
consists in a representation's being accurate, then a
proposition is true just in case it accurately represents things as
being a certain way. Thus, on the traditional view, thinking subjects
represent things as being a certain way (either in thought or
language) by standing in appropriate relations to propositions which
fundamentally represent things as being a certain way.



Two problems arise for the Platonist's position. First, how do
cognizers come to be acquainted with such propositions? Second, what
explains how propositions represent things as being a certain way?
Platonists appear to have no answer to the epistemic question, and
presumably accept representation as a primitive feature of
propositions. Type theorists, however, explain the relation between a
cognizer and a proposition simply as an instance of the general
relation between type and token. Consider, as Dummett (1996, p. 259)
does, one's humming of a tune. The tune is a species or type of
musical performance capable of having multiple performances at
differing times or locations, while the humming of it is a token act
belonging to that type. One might then see the relation of a
proposition to a mental or linguistic act as one between the type of
act performed and the performance of the act.



What type of acts should one identify with propositions? For both
Hanks and Soames, propositions are types of *predicative* acts.
The notion of predication here is simply, for atomic propositions, one
of an agent's representing an object \(o\) as having property
\(F\). (Hanks (2015, p. 64) characterizes predication as
*categorization*, or the sorting of things into groups
according to a rule. We will take this to be a form of
representation.) Since representation is primarily something done by
cognitive agents, according to Hanks and Soames, one might wonder
whether the proposition itself is representational, and so possesses
truth-conditions, on the type view. Both theorists respond to this
concern by claiming that propositions are representational in a
secondary, derivative sense. There are many examples of types that
inherit features of their tokens (a sonata (type) can be discordant in
virtue of performances of it being discordant; a movie can be
frightening in virtue of its tokens being so, etc. See the entry on
 types and tokens.)
 Just as an *act* can be described as intelligent in order to
communicate that the *agent* acted intelligently in performing
the act, type theorists will claim that a proposition represents \(o\)
as \(F\) in a similarly derivative sense wherein any agent who
performs the act of predicating \(F\) of \(o\) will thereby represent
\(o\) as \(F\). One question that arises for such a view is whether
propositions are genuinely representational entities with
truth-conditions, or whether the claim that a proposition represents
things as being a certain way is simply a convenient manner of
speaking indirectly about the actual and possible representational
acts of thinkers.



As we have seen, the type view reverses the traditional order of
explanation concerning the nature of predication, representation, and
truth-conditions. On the traditional, Fregean picture, propositions
exist as objective, mind-independent entities "waiting" to
be entertained, judged or asserted, so to speak. On this view, for a
subject S to predicate \(F\) of \(o\) is for S to entertain the
proposition that \(o\) is \(F\); for S to represent \(o\) as \(F\) in
thought or language is to have have a thought or utterance with the
primarily representational proposition *that o is F* as its
content, etc. On the type view, a proposition's representational
and predicative properties are derived from the fundamentally
representational and predicative acts of agents.



A concern for the type view is whether there will be "missing
propositions"--truths or falsehoods which have never been
entertained. One drawn to the type view may allow for the existence of
uninstantiated types to account for the existence of these
propositions. However, given that propositions are claimed to derive
their representational features from their tokens, such uninstantiated
types would lack representational features, and so lack
truth-conditions. Hanks suggests dealing with such propositions
counterfactually. Even if no one had ever predicated eloquence of
Clinton, the proposition that Clinton is eloquent is true iff Clinton
is eloquent because if someone *were* to predicate eloquence of
Clinton, the token would be true iff Clinton is eloquent. Predicative
types, then, inherit their representation features from both their
actual and possible tokens. This response, however, leaves us with the
question of truths for which there are not even any merely possible
tokens--for example, mathematical truths that are too complicated
for any finite mind to grasp. What, if anything, provides the
truth-conditions of these propositions?



Hanks (2015, p. 27) allows that propositions are mind-independent and
objective entities which do not depend for their existence on having
any tokens, just as one might think about a difficult type of dive
that has never been performed. Thus, while Hanks' view appears
to be a rejection of a traditional Platonism about propositions, it
seems nevertheless to accept a Platonism about types by untethering
their existence from their tokens. (Compare to Dodd's (2007)
defense of Platonism about types.) Soames (2014a,b) also allows for
untokened types, but only those whose constituents have been referred
to or predicated in other propositions. For Soames, a proposition
\(p\) may exist in \(w\) even if no token of \(p\) has been performed
in \(w\). For Soames, if in \(w\) a predicative event has occurred in
which an agent predicates \(n\)-place property \(R\) of \(n\) objects,
and in \(w\) events of referring to or thinking of objects \(o\_1,
\ldots, o\_n\) have occurred, then the proposition that is the type of
act of predicating \(R\) of \(o\_1, \ldots, o\_n\) exists (even if \(R\)
has never been predicated of \(o\_1, \ldots, o\_n\) in \(w)\). Still, it
would seem that there can be truths in a world about objects that have
never been thought of or referred to in that world. In response to
this, Soames claims that a proposition need not exist in a world \(w\)
in order to be true in \(w\). In support of this, Soames appeals to
other, albeit controversial, cases in which an object can have a
property despite not existing. For instance, Socrates can have the
properties of *being referred to* or *being admired*
despite no longer existing. Thus, Soames' accommodation of our
intuitions concerning propositions that have never been thought
appears to involve a rejection of Actualism.



The type view has been argued to provide solutions to several
traditional problems for propositional thought, including
Frege's puzzle, first-person belief, Kripke's puzzle about
belief, and the problem of empty names. In responding to these
problems, Soames invokes "Millian modes of presentation,"
or ways of cognizing an object in thought which do not affect the
representational content of the act, to preserve a non-Fregean,
Millian view of semantic content for names and natural kind terms
while individuating propositions finely enough to solve traditional
problems in the philosophy of language. Hanks, by contrast, invokes
distinct types of referential and expressive acts as the constituents
of propositions. On this view, each use of a name falls under several
different reference types which differ in their fineness of grain,
each associated with a different proposition.



As we have seen, the type view is motivated in large part by the
perceived need to explain how propositions represent things as being a
certain way on the grounds that a view which accepts primitively
representational propositions is objectionably mysterious. Some
question, however, whether the representational properties of
propositions can (or need to) be explained at all (McGlone 2012,
Caplan, et al. 2013, Merricks 2015). Merricks, for example, argues
that we should accept that there are fundamentally representational
entities, but that we have no reason to favor mental states (such as
beliefs) over propositions as being the fundamental bearers of
representational properties. For if, e.g., beliefs are fundamentally
representational, then it is either a primitive fact about them that
they represent what they do, or it is a feature capable of
explanation. If it is a primitive fact about them, then the view
appears just as mysterious as one which accepts that propositions are
primitively representational. If it is a fact capable of explanation,
as the type theorists contend, then it is presumably explained in
terms of an agent's ability to predicate properties of objects.
But unless there is some explanation of how an agent can engage in
predication, predication must itself be a primitive representational
ability, and the theory has not made any genuine progress on what was
to be explained.



A final question worth considering at this stage is whether
propositions are representational entities at all. Richard (2013) and
Speaks (2014), for instance, each develop views of propositions which
deny that they are. Consider the view defended by Richard. Sentences,
beliefs, and the like represent things as being a certain
way--snow as being white, for example. Put another way, the
sentence 'Snow is white' represents snow's being
white, where this is simply a way for things to be--a state of
affairs or property that is either instantiated or not (but does not
represent things as being any way, just as properties are not in
general representational). On this approach, the proposition expressed
by the sentence is identified with the way that things are represented
as being, not as something which has representational properties
either primitively or in need of explanation by more fundamental acts
of predication. If an approach along these lines is correct, the type
view appears to lose one of its central motivations.


## 8. The Individuation of Propositions



Some philosophers, notably W.V.O. Quine, recognize the existence of
certain sorts of abstract entities but not others at least partly on
the basis of concerns about identity conditions. Quine granted the
existence of sets, in part because they obey the extensionality axiom:
sets are identical iff they have the same members. When it came to
properties, relations and propositions, however, he found no such
clear criterion of identity. The property of being a creature with a
heart, he noted, is distinct from the property of being a creature
with a kidney, even if all the same things exemplify the two
properties.



It is a controversial matter whether Quine was right to demand such
rigorous criteria of identity as a condition for acceptance of a class
of entities. However, even if Quine asks too much, any good theory of
propositions ought to have something to say about when propositions
are identical and when they are distinct. Developing theories which
give such accounts in a way that fits well with intuitive data
concerning propositional attitude ascriptions would enhance our
reasons to accept propositions.



The question of identity conditions for propositions is importantly
related to the question of whether propositions are structured
entities. Propositions are structured if they have
*constituents*, in some broad sense, and the order of the
constituents matters. Order matters only if there could be two
structured propositions sharing all the same constituents, but which
are distinct due to differences in the way under which those
constituents are "united" in the proposition. E.g., if the
proposition that \(a\) loves \(b\) is the ordered triple
\(\ltb\)*loving*, \(a, b\gtb\), it is distinct from the
proposition that \(b\) loves \(a\), which would be the ordered triple
\(\ltb\)*loving*, \(b, a\gtb\).



If propositions are structured entities, then sameness of constituents
and sameness of order will entail identity. There are, of course,
dangers, in regarding propositions as structured. Prima facie, one
would rather not claim that the proposition that \(x\) is triangular
is identical to the proposition that \(x\) is trilateral, since a
subject might believe one but not the other. It will be important,
then, not to individuate propositions too coarsely. However, one might
worry, in the opposing direction, about overly fine individuations of
propositions. Is the proposition that John loves Mary different from
the proposition that Mary is loved by John? For more on structured
propositions, see the entry on
 structured propositions.[10]



Any theory that construes propositions as structured entities would
seem to face the problem of the *unity* of the proposition. It
is not entirely straightforward to say what this problem or set of
problems is. But at the very least, there are at least two problems
here. There is the problem of explaining why one sort of structured
whole, a proposition, can be true or false, while the set of its
constituents is not. A list isn't true or false, and a
proposition with the same constituents is; why is this? Second, there
is a general problem of explaining how two distinct things could have
all the same constituents. For a thorough discussion of the history of
philosophical work on the unity of the sentence and the proposition,
the reader should consult Gaskin (2008).



Some hold that propositions lack constituents altogether, and so are
unstructured. If propositions are unstructured, then if they are sets,
they inherit the identity conditions for sets: sameness of members.
Thus, if a proposition is the set of worlds in which it is true (as in
Stalnaker 1976), then \(P=Q\) iff \(P\) and \(Q\) have the same worlds
as members iff \(P\) and \(Q\) are true in the same worlds. As is
well-known, this theory leads to a very coarse individuation of
propositions, too coarse, arguably, to handle propositional attitudes.
(See Soames (1987) for a discussion of this theory as well as the
theory of propositions as sets of concrete situations or facts.



If propositions are unstructured and distinct from sets, there are
several possibilities for explaining their identity conditions. First,
identity conditions might be specified in terms of possible attitudes.
One possibility is this: \(P=Q\) if, necessarily whoever believes
(asserts, denies, etc.) \(P\) believes (asserts, denies, etc.) \(Q\),
and vice versa. Second, proposition identity might be reduced to
property identity in the manner of Myhill (1963) and Zalta (1983).
Thus, Zalta (1983, 72) offers the following definition of proposition
identity: \(\ltb p\gtb =\ltb q\gtb\) if and only if the property of
being such that \(p\) is identical to the property of being such that
\(q\). A third proposal, not incompatible with the second, is to
explain proposition identity in terms of the "free
generation" of propositions from a stock of certain
non-propositional entities, e.g., individuals, properties and
relations, by algebraic operations (Bealer 1982, Menzel 1986, Zalta
1983 and
 1989).[11]
 Although propositions on this approach are unstructured, each
proposition may be represented by its "construction
sequence." To avoid identifying \(\ltb\)Hesperus is
beautiful\(\gtb\) with \(\ltb\)Phosphorus is beautiful\(\gtb\), the
relevant inputs cannot simply be Hesperus (Phosphorus) and the
property of being beautiful. A well-known strategy to cope with this
problem, due to Frege, is to appeal to different modes of presentation
associated with the different names, each contributing something
different to the proposition expressed. However, these modes need not
be understood as complex properties uniquely exemplified by referent
of the name. For instance, Bealer (1998) invokes what he calls
"non-Platonic" modes of presentation. Whether these
non-Platonic modes of presentation are understood as words, as causal
chains of word use, or in some other way, the important point is that
the mode associated with 'Hesperus' will be different than
that associated with 'Phosphorus'. Zalta (1989) introduces
propositions with abstract constituents to do the work of these modes.
On Zalta's view, such singular propositions are built out of
abstract individuals that encode the cognitive content of names. Since
these abstract individuals encode this cognitive content, there is no
need for the referent of the name to instantiate it, and a fortiori no
need for the content to be a property uniquely instantiated by this
referent. For more on encoding vs. instantiating, see section 6 of the
entry on
 existence.
 Thus, these theorists hope to use the metaphysical tools of these
algebraic accounts to accommodate some of the key Fregean intuitions
about differences in propositions expressed while avoiding
difficulties with the Fregean doctrine of sense.



For a recent criticism of the notion of propositional constituency,
see Keller (2013); for a positive account of propositional
constituency, see Gilmore (2014).


## 9. Propositions, Facts, and States of Affairs



Frege famously wrote, "'Facts, facts, facts' cries
the scientist if he wants to bring home the necessity of a firm
foundation for science. What is a fact? A fact is a thought that is
true." (1918, p. 25)



Is a fact just a true proposition? There are metaphysical and
linguistic arguments to the contrary. Here is a standard metaphysical
argument. The fact that snow is white couldn't exist if snow
wasn't white, but the true proposition would (only it would be
false). Therefore, the fact isn't the true proposition (See
Moore 1953, p. 308). Facts might be, still, in *some* sense,
derivative from true propositions, even if the identity claim fails.
Following Moore (1953, pp. 261-2) and Slote (1974, p. 99), Kit
Fine (1982, pp. 52-3) suggests that facts may be conceived as
concretizations of true propositions. Thus, the fact that \(p\) is the
truth of \(\ltb p\gtb\). However, so construing facts makes them poor
candidates for truthmakers: the truth of \(p\), presumably, is not
what makes \(\ltb p\gtb\) true.



One well-known linguistic argument against identifying facts with true
propositions is closely related to the Ambiguity Response to The
Substitution Problem, considered in Section 5.4. Substitution of
'the fact that \(p\)' for 'the true proposition that
\(p\)', or vice versa, produces peculiarities such as
"John believes the fact that Obama is president", or
Harman's (2003) "The true proposition that fires are hot
makes it the case that fires are hot." If facts were true
propositions, so it is argued, one would expect the substitutions to
preserve truth.



Nonetheless, there are other uses of 'fact' that support
the identification:



> 
> Snow is white. That's a fact. But it wouldn't have been a
> fact if snow were not white. So, some things that are facts might not
> have been facts.
> 



Used in this way, 'fact' seems to apply to entities that
resemble propositions, in that they have two modes of being: existence
and something akin to truth (e.g., obtaining) (see McGrath
 2003).[12]



One option, in the face of apparently conflicting uses of
'fact', is to posit an ambiguity. (Fine 1982, p. 54) There
are two kinds of entity associated with different uses of
'fact': one kind has one mode of being (it simply exists),
the other has having two modes of being (it may exist without
obtaining). "Bipolar" facts correspond, roughly, to what
some philosophers call possible states of affairs.



However, some philosophers would want to distinguish even such bipolar
facts from propositions. Bipolar facts, the argument goes, are states
of affairs, rather than true propositions. Clearly, not all
propositions can be possible states of affairs, because there are
propositions that are not possibly true, whereas possible states of
affairs must obtain in at least some possible world. We might wish to
extend the notion of a state of affairs to include impossible ones.
Whether states of affairs, understood in this extended sense, are
propositions clearly depends on the answers to questions about their
identity conditions. See the entry on
 states of affairs,
 as well as Richard (2013) for a recent view identifying propositions
with states of affairs.



King (1995, 2007, 2014) argues that all propositions are facts,
although not the ones that we might expect. The proposition that Mary
loves John is not the fact that Mary loves John but rather (to a first
approximation) the following fact: Mary, loving, and John being the
semantic values of linguistic items standing in a certain syntactic
relation (represented by a phrase marker tree) which encodes
instantiation. King argues that his account has many virtues. It helps
solve the problem of the unity of the proposition (see the previous
section), insofar as the structure of a proposition derives from the
syntactic structure of a corresponding sentence. It requires
relatively minimal ontological commitments: if one accepts that there
are languages with expressions designating objects and properties and
in which certain syntactic relations encode instantiation, then one
will accept King-propositions. The account also provides for finely
individuated propositions: differences in syntactic structure of
sentences will carry over to differences in the propositions
expressed. Given that the existence of King-propositions seems to
depend on their being language-users who use language in certain ways,
King is a conceptualist about propositions. (See section 7.2
above).


## 10. Sparse and Abundant Conceptions of Propositions



In discussing the question of whether there are properties, D. M.
Armstrong (1989) distinguishes sparse from abundant conceptions of
properties. Following standard terminology, let us say that when a
predicate has a property as its semantic content, the predicate
*expresses* that property. (For simplicity, we will assume that
sentences can have propositions as semantic contents.) Under an
abundant conception of properties, whether a predicate expresses a
property depends only on its broadly syntactic facts about it. The
simplest abundant conception holds that every well-formed predicate
expresses a property. According to sparse conceptions, not every
syntactically well-formed predicate expresses a property.



A similar distinction may be applied to conceptions of propositions.
Abundant conceptions will impose only broadly syntactic restrictions
on the expression of propositions. Sparse conceptions will deny that
having the relevant syntactic properties is sufficient for the
expression and designation of propositions. Abundant conceptions of
propositions face the threat of paradox. For more, see the discussion
on
 the Russell-Myhill Paradox
 in the entry on Alonzo Church.


### 10.1 Expressivism and Moral Propositions



One motivation for accepting a sparse conception of propositions is
expressivism in metaethics. "Old-fashioned" expressivists
(e.g., Ayer and Stevenson) claimed that moral sentences are
non-cognitive. We cannot believe that lying in politics is wrong, nor
can we have any broadly cognitive attitudes (e.g., disbelief) of the
form '\(A\)-ing that \(p\)' where '\(p\)'
contains moral terms. If we cannot have such attitudes, then
presumably there are no moral propositions. (If there were such
propositions, why wouldn't there be possible cognitive attitudes
having them as contents?). And if there are no moral propositions,
then moral sentences do not express propositions, and so lack
truth-value.



We certainly talk and think as if we have moral beliefs, as if we
believe moral propositions. For the old-fashioned expressivist, then,
many of our apparently sincere ordinary claims will have to be
rejected. Endorsing such a sparse conception of propositions thus
leads to the surprising consequence all moral sentences lack
truth-value.



Some contemporary expressivists (Blackburn 1998, Horwich 1993, Stoljar
1993) are less averse to moral propositions, moral properties and
moral facts. But they take these commitments as
 shallow.[13]
 They accept an abundant conception of propositions, properties, etc.,
but combine it with a generous dose of deflationism. There are moral
propositions, but they are mere shadows of moral declarative
sentences. (Even if they are shadows of our sentences in some sense,
they are not shadows in another sense, at least if the Easy Arguments
for mind-independence and abstractness are successful: what is
mind-independent and abstract is, in a clear sense, not merely a
shadow of sentences.)



At least three important questions can be asked about the combination
of expressivism and deflationism about moral propositions. First, if
the expressivist accepts moral propositions, what is the difference
between expressivism and realism? Second, by accepting deflationary
moral propositions, can the expressivist avoid the familiar problems
for moral realism (and cognitivism) which helped motivate expressivism
in the first place? Third, can the realist avoid these familiar
problems equally well by accepting deflationary moral
propositions?



The first question is examined in the entry on
 moral cognitivism vs non-cognitivism.
 We will briefly discuss the other two.



Consider, for example, the Humean argument facing realism, a crude
version of which is as follows. If there are moral propositions, then
moral judgments are beliefs in moral propositions. But moral judgments
are intrinsically motivational states, whereas beliefs are not. So,
there are no moral propositions. Of course, this argument may be
criticized as relying on an overly strong internalism, or a
simple-minded speculative psychology. But even when improved, it is
not immediately clear how accepting deflationism about moral
propositions will help the expressivist solve the problem. The moral
propositions exist, and so why can't they be believed
independently of having any intrinsically motivating states? How can
their deflationary character help defuse this question? Moreover,
suppose that deflationism did help the expressivist cope with this
problem. Why couldn't the realist follow suit with her own
appeal to deflationism?



Blackburn's supervenience argument is a second argument against
realism. Blackburn formulated the argument in terms of moral
properties, as follows. If there are moral properties, then they
supervene on non-moral properties as a matter of conceptual necessity.
That is, in every conceptually possible world, if two things share all
non-moral properties, they share all moral properties. But if there
are moral properties, the pattern of supervenience is not itself
conceptually necessary. So, even if all \(P\)s are \(M\)s in fact,
there is some conceptually possible world in which there is a \(P\)
which isn't an \(M\). Blackburn's question is this: if
moral properties can come apart from non-moral properties
*across* worlds, why can't they come apart from them
*within* worlds? That is: what explains the "ban on mixed
worlds"? A similar problem can be formulated for truth as a
feature of moral propositions. What explains the ban on conceptually
possible worlds in which one moral proposition \(\ltb x\) is \(M\gtb\)
is true, while another moral proposition \(\ltb y\) is \(M\gtb\) is
false, but in which all relevant non-moral propositions \(\ltb x\) is
\(P\gtb\) and \(\ltb y\) is \(P\gtb\) are alike in truth-value? What
is not immediately clear is, first, how deflationary moral
propositions will prove useful to the expressivist in answering this
question, and second, how, supposing they do prove useful, why they
won't prove equally useful to the realist.



What the expressivist seeks is a conception of propositions (and of
truths, facts, and beliefs) substantive enough to explain and validate
our ordinary realist-seeming discourse but deflationary enough to
avoid the traditional problems for realism. Whether it is possible to
navigate the two is the subject of intense scrutiny in contemporary
metaethics.