## 1. Setting Up the Problems



Intuitively, given that a sentence expresses a structured proposition,
the proposition will have parts or constituents that are the semantic
values of words or subsentential complex linguistic expressions
occurring in the sentence; and the proposition will have a structure
similar to the structure of the sentence. For example, assuming that
the semantic value of a name is its bearer and that the semantic value
of a transitive verb is a relation, a structured proposition theorist
will likely hold that the sentence


* (1) Jason loves
Patty



expresses a proposition consisting of Jason, the loving relation and
Patty, bound together in some way into a unity. Letting
'*j*' stand for Jason, '*p*' for
Patty and '*L*' for the loving relation, we can
represent the proposition in question as follows:


* (1a) [*j*[*L*[*p*]]]



Thus (1a)'s structure is very close to that of (1); and (1a) has
as constituents the semantic values of the words occurring in (1).
Indeed, in the case of (1) and (1a), all and only semantic values of
words in the sentence are constituents of the proposition. But a given
account of structured propositions may not hold that this is the case
in general for any one of at least three reasons. First, one might
hold that certain words as they occur in phrases in sentences do not
contribute their semantic values to the propositions expressed by
those sentences because the semantic values of these words instead
partially determine the semantic values of the phrases in which they
occur, where these latter semantic values are contributed to the
proposition. For example, one might hold that in the sentence


* (2) Colin is a tall
young man.



the phrase 'is a tall young man' contributes to the
proposition expressed by (2) the property of being a tall young man,
which is its semantic value. Thus, though the semantic value of the
word 'tall' partly determines the semantic value of the
phrase 'is a tall young man', the proposition expressed by
(2) contains no constituent that is the semantic value of the word
'tall' alone. Second, one might hold that a sentence may
express a proposition (in a context), where the proposition has
constituents not contributed by any syntactic constituent of the
sentence, let alone any word in the sentence. For example, Mark
Crimmins [1992] claims that an utterance of the sentence


* (3) It's
raining



expresses a proposition to the effect that it is raining at a
particular time and place. The present tense manages to somehow
contribute the time of utterance to the proposition. But no syntactic
constituent of the sentence contributes the place to the proposition,
though Crimmins claims it is a constituent of the proposition
 expressed.[4]
 Third, one might hold that certain words simply have no semantic
values, and so make no contribution to propositions. So-called
neoplanastic 'ne' in French might be thought to be an
example of this.



But even if, for one of the above reasons or some other reason, a
sentence does not express a proposition whose constituents are
precisely the semantic values of words in the sentence, we can still
say that structured proposition theorists hold that sentences
expresses propositions, where many (and likely most) constituents of
the proposition are semantic values of words or phrases occurring in
the sentence. So in the case of (1) and (1a), the constituents of the
proposition are precisely the semantic values of the words in (1). In
the case of (2) and (2a) (given the assumptions made above), the
constituents of (2a) are precisely the semantic values of the name
'Colin' and the verb phrase 'is a tall young
man'. And in the case of (3), the proposition it expresses has
three constituents, two of which are contributed by
'raining' and the present tense construction.



Thus, ignoring, or at least not dwelling on, the qualifications just
made, we can say that structured proposition theorists hold that
sentences express propositions that are complex entities (most of)
whose constituents are the semantic values of expressions occurring in
the sentence, where these constituents are bound together by some
structure inducing bond that renders the structure of the proposition
similar to the structure of the sentence expressing it.



This highlights an important feature of structured proposition
accounts that distinguishes them from the other main competing account
of propositions, namely the account of propositions as sets of
possible worlds (to be discussed below). Because structured
propositions have as parts the semantic values of expressions in the
sentences expressing them, the semantic values of those expressions
are recoverable from the semantic values of the sentences (i.e. the
propositions).



It is perhaps worth noting that one could have a theory according to
which the semantic values of expressions in a sentence are recoverable
from the proposition expressed by the sentence, even though the
semantic values of the expressions are not (mereological or set
theoretic) parts of the proposition. For example, George Bealer [1993]
formulates what he calls an algebraic conception of propositions (see
also Bealer [1982]). Bealer associates with each proposition a
"decomposition tree." This decomposition tree shows how a
given proposition is the result of the application of logical
operations to individuals, properties, relations or other propositions
(e.g. the application of the logical operation of negation to a
proposition *P* yields a proposition that is true iff *P* is
false; the application of the logical operation of singular
predication to an item and a property yields a proposition that is
true iff the item possesses the property, etc.). In general, a
sentence will express a proposition such that the semantic values of
expressions in the sentence will occur on the decomposition tree
associated with the proposition. Thus, the semantic values of
expressions in a sentence will be recoverable from the proposition
(together with its decomposition tree) expressed by the sentence.
However, Bealer denies that these semantic values are in any sense
set-theoretic members or mereological parts of the proposition. Bealer
appears to hold that the proposition is metaphysically simple and has
no parts at all. As the term is used here then, Bealer's is not
an account of structured propositions for this reason. We will see
below that others hold similar "algebraic" conceptions of
propositions, where the propositions are complex entities consisting
of constituents bound together in certain ways and so are structured
propositions.



Since the structured proposition expressed by a sentence has a
structure similar to that of the sentence and has as constituents
semantic values of expressions occurring in the sentence, the theory
of structured propositions allows for distinct necessarily equivalent
propositions. For example, the propositions expressed by
'Bachelors are unmarried' and 'Brothers are male
siblings' presumably are both necessarily true and hence are
necessarily equivalent. But clearly the propositions expressed by
these sentences have different constituents and so are distinct. The
proposition expressed by the former presumably contains the semantic
value of 'bachelor' (perhaps, the property of being a
bachelor), whereas the proposition expressed by the latter
doesn't. And the proposition expressed by the latter contains
the semantic value of 'brother', whereas the proposition
expressed by the former doesn't. This is an important virtue of
the structured proposition view. The fact that it has this feature and
that its main competitor, the possible worlds account of propositions
(discussed below), doesn't is one of the reasons many favor the
structured proposition view.



In discussing recent accounts of structured propositions below, it
will be shown how, on those accounts, sentences that are necessarily
equivalent may express distinct propositions; and how the semantic
values of expressions in a sentence are recoverable from the
proposition expressed by the sentence.


## 2. From Possible Worlds to Structured Propositions



Because the structured proposition view arose in large part due to
dissatisfaction with the then prevailing view of propositions,
discussing this other account of propositions will help to illuminate
structured proposition views. The late 1950s and 1960s saw the
development of a new sort of model theory, "possible worlds
semantics", for systems of modal logic. In the framework of
possible world semantics, linguistic expressions are assigned
extensions "at" possible worlds. Thus, e.g. names, n-place
predicates and sentences are assigned individuals, sets of
*n*-tuples of individuals, and truth values, respectively, at
different possible worlds. Intuitively, possible worlds are to be
thought of as "ways things could have been", and the
assignment of (possibly different) extensions to expressions at
different possible worlds is part of capturing this intuition. Thus
there might have been more or fewer cows, and this is reflected in the
fact that the extension of 'cow' (intuitively, the set of
things that are cows) can vary from possible world to possible
world.



Because we wish the extensions of expressions to vary from possible
world to possible world (at least in some cases), it is natural to
associate with each expression a function from possible worlds to
extensions appropriate to that sort of expression. Thus we associate
with names, functions from possible worlds to individuals; with
n-place predicates functions from possible worlds to sets of
*n*-tuples; and with sentences, functions from possible worlds to
truth values. Such functions from possible worlds to extensions of the
appropriate sort are often called intensions of the expressions in
question, and the term 'intension' shall be used this way
throughout the present
 work.[5]
 Now since most think that the extensions of sentences are truth
values, as indicated above, the intension of a sentence is a function
from possible worlds to truth values. Intuitively, it maps a world to
true if the sentence is true at that world. Thus the intension of a
sentence can be seen as the primary bearer of truth and falsity at a
world: the sentence has the truth value it has at the world in virtue
of its intension mapping that world to that truth value. Further,
modal operators were typically construed as operating on the
intensions of the sentences they embed, and so those intensions could
plausibly be thought of as possessing modal properties. Since
propositions were traditionally held to be the primary bearers of
truth and falsity and the bearers of modal properties, it was natural
for possible world semanticists to identify propositions with
functions from possible worlds to truth values (sentential
intensions), or equivalently, sets of possible worlds (the set of
possible worlds at which the sentence in question is true). Indeed,
this identification was thought by many to vindicate the previously
mysterious notion of a
 proposition.[6]
 Possible worlds were apparently needed for the model theory of modal
logic anyway; why not build propositions out of them?



Current structured proposition accounts arose largely out of
dissatisfaction with the idea that propositions are sets of possible
worlds (or functions from worlds to truth values). In fact, there were
at least two quite distinct motivations for abandoning the view of
propositions as sets of worlds and adopting the structured proposition
account.



The first had to do with the way propositions are individuated on a
possible worlds account. The view that propositions are sets of
possible worlds does not individuate propositions very finely. For
example, consider any pair of sentences that express metaphysically
necessary propositions, say 'Bachelors are unmarried' and
'Brothers are male siblings'. Since these propositions are
true in all possible worlds, each must be the set of all possible
worlds. But there is only one such set. Thus there is only one such
proposition! Hence these two sentences express the same proposition.
(The view also predicts that all true sentences of mathematics express
the same (necessary) proposition, that any two necessarily equivalent
sentences express the same proposition, that the conjunction of any
sentence *S* with a necessarily true sentence expresses the same
proposition as *S*, and so on.)



This should make clear that the account of propositions as sets of
worlds is not a structured proposition account. For, as we saw, on a
structured proposition account, the semantic values of expressions in
a sentence are recoverable from the proposition expressed by the
sentence, since those semantic values are constituents of the
proposition. This is why on such an account, 'Bachelors are
unmarried males' and 'Brothers are male siblings'
express distinct propositions: the propositions have different
constituents. But on the possible worlds account, the property of
being a bachelor is in no sense recoverable from or a constituent of
the proposition expressed by 'Bachelors are unmarried'.
For the latter proposition is just the set of all possible worlds. How
could the property of being a bachelor be "recovered" from
this set? Similarly, the property of being a brother is not
recoverable from the proposition expressed by 'Brothers are male
siblings.' Again, the latter proposition is just the set of all
possible worlds.



Further, if propositions are sets of possible worlds, belief is
construed as a relation between individuals and propositions and
sentences of the form '*A* believes that *P*'
assert that the individual *A* stands in the belief relation to
the proposition expressed by '*P*', then for any
necessarily equivalent sentences '*P*' and
'*Q*', '*A* believes that *P*'
and '*A* believes that *Q*' cannot differ in
truth value. This means that, for example, if '*A* believes
that 1+1=2' is true, so is '*A* believes that there
is no greatest natural number'. These consequences of the view
that propositions are sets of possible worlds were appreciated early
on; and theorists made a variety of attempts to make these
consequences seem less unpalatable. Despite these valiant efforts,
many philosophers viewed these consequences as a sign that there was
something very wrong with the view that propositions are sets of
possible worlds. Thus, philosophers were open to an account of
propositions that individuated propositions more finely than the
possible worlds account. As we have seen, the structured proposition
account is just such an account.



In order to make clear the second motivation for abandoning the view
of propositions as sets of worlds and adopting the structured
proposition account, we must discuss the notions of rigid designation
and direct reference. A rigid designator is an expression that
designates the same individual in all possible circumstances or
worlds. In the early 1970's, Saul Kripke argued in *Naming and
Necessity* that ordinary proper names are rigid designators. Kripke
claimed that when we consider a sentence containing an ordinary proper
name, such as



Aristotle was a great philosopher



and ask whether it would have been true or false in various
counterfactual circumstances, it is the properties of the very same
man, Aristotle, in those circumstances that are relevant to the truth
of the sentence. So, 'Aristotle' designates the same man
in these various counterfactual circumstances; it is a rigid
designator.



At around the same time, David Kaplan argued that indexicals (e.g.
'I', 'here', 'now') and
demonstratives (e.g. 'that', 'you',
'he') are directly referential. Concerning directly
referential expressions, Kaplan wrote:



> 
> For me, the intuitive idea is not that of an expression which turns
> out to designate the same object in all possible circumstances, but an
> expression whose semantical rules provide directly that the referent
> in all possible circumstances is fixed to be the actual referent. In
> typical cases the semantical rules will do this only implicitly, by
> providing a way of determining the actual referent, and no way of
> determining any other propositional component. (Kaplan [1977] p. 493)
> 



Thus, a directly referential expression is a rigid designator: its
associated semantic rules determine the actual referent of the
expression (in a context) and when evaluating what is said by the
sentence containing the expression (in that context) in other possible
circumstances, this same referent is always relevant. To illustrate,
if John utters



I ski.



at the present time and we want to evaluate whether what John said by
means of that utterance is true or false in other possible
circumstances, it is John's properties in those other
circumstances that are relevant. Thus, 'I' is rigid: when
evaluating the truth or falsity of what is said by an utterance of a
sentence containing 'I' in counterfactual circumstances,
it is the properties of the person whom 'I' referred to in
the utterance (the actual utterer) that are relevant.



Kaplan intended to contrast directly referential expressions with
expressions such as definite descriptions, which, though designating
particular individuals, do so by means of descriptive conditions being
expressed by the description and satisfied by the designated
individual. Thus Kaplan wrote that directly referential expressions
"refer directly without the mediation of Fregean Sinn as
meaning". (Kaplan [1977] p. 483) The designation of definite
descriptions is mediated by something like a Fregean sense (i.e. their
associated descriptive conditions).



Of course, even if descriptions are not directly referential, some are
rigid designators. For example, 'the successor of 1'
designates the same individual (2) in all possible worlds. So, though
all directly referential expressions are rigid designators, some rigid
designators are not directly referential. As was mentioned above, in a
possible worlds semantics linguistic expressions are associated with
intensions, functions from possible worlds to appropriate extensions.
In the case of expressions designating individuals, these intensions
will be functions from possible worlds to individuals. Note that all
rigid designators (whether directly referential or not) will have
intensions that are constant functions: they will be functions that
map all possible worlds to the same individual. Thus possible worlds
semantics tends to blur the distinction between directly referential
expressions and rigid non-directly referential expressions (e.g. rigid
definite descriptions). To make the distinction between directly
referential expressions and rigid non-directly referential expressions
more vivid, Kaplan invoked the notion of structured propositions:



> 
> 
> If I may wax metaphysical in order to fix an image, let us think of
> the vehicles of evaluation--the what-is-said in a given
> context--as propositions. Don't think of propositions as
> sets of possible worlds, but rather as structured entities looking
> something like the sentences which express them. For each occurrence
> of a singular term in a sentence there will be a corresponding
> constituent in the proposition expressed. The constituent of the
> proposition determines, for each circumstance of evaluation, the
> object relevant to evaluating the proposition in that circumstance. In
> general the constituent of the proposition will be some sort of
> complex, constructed from various attributes by logical composition.
> But in the case of a singular term which is directly referential, the
> constituent of the proposition is just the object itself. Thus it is
> that it does not just turn out that the constituent determines the
> same object in every circumstance, the constituent (corresponding to a
> rigid designator) just is the object. There is no determining to do at
> all. On this picture--and this is really a picture and not a
> theory--the definite description
> 
> 
> * (1) The *n*[(snow
> is slight & *n*2=9) [?] (~snow is slight &
> 22=*n*+1)]
> 
> 
> 
> would yield a constituent which is complex although it would determine
> the same object in all circumstances. Thus, (1), though a rigid
> designator, is not directly referential from this (metaphysical) point
> of view. (Kaplan [1977] p. 494-495)
> 
> 
> 



(Kaplan goes on to attribute this "metaphysical picture"
of structured propositions to Russell.) Adopting this structured
proposition account makes it simple to distinguish between directly
referential expressions and other expressions, rigid or not. Directly
referential expressions contribute their referents (in a context) to
the propositions expressed (in that context) by the sentences
containing them. Non-directly referential expressions contribute some
complex that may or may not determine the same individual in all
possible circumstances. Thus the desire to distinguish clearly between
directly referential expressions and other rigid designators prompted
Kaplan to re-introduce the Russellian notion of a structured
proposition into the philosophical literature (see the discussion of
Russell below). However, Kaplan [1977] tends to treat the notion of a
structured proposition as a heuristic device. He repeatedly calls it a
picture, explicitly says that it is not part of his theory, and in his
formal semantics he adopts the possible worlds account of propositions
(contents of formulae), taking them to be functions from worlds (and
times) to truth values.



Many current direct reference theorists take the structured
proposition account much more seriously. It is part of their theory in
the sense that when they say that an expression is directly
referential they are literally saying that it contributes its referent
to propositions expressed by sentences containing it, (e.g. see the
discussion of Salmon and Soames below).


## 3. Some Recent Accounts of Structured Propositions



Having discussed structured proposition accounts in a general way, the
best way to further illuminate these accounts of propositions is to
discuss some recent work on structured propositions. In so doing, we
shall see various respects in which accounts of structured
propositions can differ. Three caveats before proceeding. First, as
was mentioned above, structured proposition accounts, unlike possible
world accounts of propositions, allow for distinct necessarily
equivalent propositions, and thus individuate propositions more finely
than possible worlds accounts. There are other accounts of
propositions, or things that are intended to do the work of
propositions, as in the previously mentioned example of Bealer [1993],
that are not structured proposition accounts (given the way that term
is used here), but that allow for distinct necessarily equivalent
propositions or things that are to do the work of propositions.
Another example is the interpreted logical form account defended by
Larson and Ludlow [1993]. Though such accounts will not be discussed
here, the reader should be aware of them and that they are motivated
by many of the considerations that motivate structured proposition
theorists. In particular, they attempt to individuate propositions (or
things that do the work of propositions) more finely than possible
worlds accounts of propositions. Second, discussing a sampling of
recent work on the view that propositions are structured will not (and
is not intended to) exhaust the versions of structured proposition
approaches that there are. Rather, only some of the main issues and
current approaches will be highlighted. To that end, three broad
approaches to structured propositions will be discussed; these are the
Neo-Russellian Approach, the Structured Intensions Approach, and the
Algebraic Approach. In discussing each approach, a number of authors
who adopt the approach will be mentioned, but for definiteness, only a
representative of each approach will be highlighted in explaining it.
The reader should be aware that these groupings are somewhat loose,
and that there may be important differences among authors who are
grouped together. Third, though questions will be raised here and
there, criticisms of the various approaches discussed will be left
aside. The task at hand is simply that of introducing the reader to
approaches to structured propositions; criticizing the various
approaches is a task for another day.


### 3.1 The Neo-Russellian Approach



In a series of papers and a book, Scott Soames [1985, 1987, 1989] and
Nathan Salmon [1986a, 1986b, 1989a, 1989b] have laid out what is
probably the best known current theory of structured propositions.
There are some differences of detail between Salmon and Soames, but
both shall be treated here as holding the same view. Though some of
their contributions will be discussed separately, the main account
followed will be that laid out in Soames [1987].



First, Soames [1985,1987] produced what many take to be a devastating
attack on the view of propositions as sets of possible worlds. Soames
showed that even when one tries to get more fine-grained
propositions-as-sets-of-worlds by allowing metaphysically impossible
worlds (e.g. worlds in which George Bush is identical with Ronald
Reagan), inconsistent worlds (in which a thing can both possess and
lack a property), and incomplete worlds (where some purported
"matters of fact" are simply not settled), the resulting
view, when combined with other independently plausible assumptions, is
riddled with overwhelming difficulties. These difficulties all stem
from the fact, noted earlier, that on the worlds view, sentences with
very different syntactic structures and containing words with
different semantic values may express the same proposition. Soames
[1987] concludes that we ought to give up the view that propositions
are sets of worlds of any sort, and embrace an account of propositions
according to which propositions are structured entities, with
individuals, properties and relations as constituents. Soames called
these structured Russellian propositions. If the syntactic structures
of sentences and the semantic values of words occurring in them are
reflected in the structures and constituents of propositions they
express, sentences with different syntactic structures and containing
words with different semantic values, whether true in all the same
worlds or not, may express different propositions. It is perhaps worth
noting that having sentences with different syntactic structures and
containing words with different semantic values express different
propositions doesn't require one to hold that propositions
themselves are structured and contain the semantic values of the words
as constituents. Still, it is a natural way of accounting for why
sentences with different syntactic structures and containing words
with different semantic values that are true in all the same worlds
express different propositions. Soames [1987] sketches a formal theory
of structured propositions, including an assignment of structured
propositions to the sentences of a simple formal language, and a
definition of truth relative to a circumstance for structured
propositions.



Soames and Salmon are direct reference theorists, holding that names
(as well as indexicals and demonstratives) have their referents as
their semantic values and so contribute them to the propositions
expressed by sentences containing them. Further they hold that
predicates and intransitive verbs have properties as their semantic
values; and that transitive verbs have relations as their semantic
values. Thus they hold that sentences such as


* (4) Scott
runs.
* (5) Scott saw
Nathan.



express the propositions


* (4a) < < *o* >,
*R* >
* (5a) < < *o*,
*o*' >, *S* >



where *o* is Scott , *o*' is Nathan, *R* is the
property of running, and *S* is the relation of seeing. The
negation of (4) expresses the proposition


* (4b) < NEG,
< < *o* >,
*R* > >



where NEG is the truth function for negation. And the conjunction of
(4) and (5) (in that order) expresses the proposition


* (5b) < CONJ< 
< < *o* >, *R* >,
< < *o*, *o*' >,
*S* > > >



where CONJ is the truth function for conjunction. Similar remarks
apply to sentences formed with other truth functional connectives.
Further a sentence such as


* (6) Something
runs.



expresses the proposition


* (6a) < SOME,
*g* >



where SOME is the property of being a nonempty set and *g* is the
function from individuals *o*' to the proposition
< < *o*' >,
*R* >, (where, as before, *R* is the property of
running).



It should be easy to imagine the definition of truth relative to a
circumstance for structured propositions of the sort mentioned above.
For example, (5a) will be true at a circumstance *c* iff
< *o*, *o*' > is in the extension
of the relation *S* at *c*. (5b) will be true at *c*
iff CONJ maps the truth values of
< < *o* >, *R* > and
< < *o*, *o*' >,
*S* > at *c* to truth. And (6a) will be true at
*c* iff there is an individual in *c* that *g* maps to
a proposition that is true in *c*, (in that case the set of
individuals in *c* that *g* maps to propositions true in
*c* possesses SOME).



It should be clear that on this account of propositions sentences that
are necessarily equivalent may express distinct propositions, and that
the semantic values of expressions in a sentence are recoverable from
the proposition it expresses. For example, 'All bachelors are
unmarried' and 'All brother are male' are both true
in all possible worlds. But on the present view, the former expresses
a proposition that has as a constituent a propositional function
mapping an object to the proposition that that object is unmarried;
the latter does not. Further, e.g. the semantic value of
'runs' as it occurs in sentence (4) is recoverable from
the proposition (4) expresses in that it is a constituent of that
proposition. Similar remarks apply to 5/5a and 6/6a (except that in 6a
the semantic value of 'runs' is encoded in *g*: that
is, *g* maps individuals *o* to the proposition that
*o* runs, which in turn has the semantic value of
'runs' as a constituent).



Note that this account of propositions (including the commitment to
names being directly referential) entails that sentences that differ
only with respect to coreferential names express the same proposition.
Thus



Mark Twain is Samuel Clemens.



and



Samuel Clemens is Samuel Clemens.



express the same proposition on this view. Many have found this result
incredible, since it would appear that the one sentence could be
informative and the other not. Salmon and Soames also hold that
'believes' expresses a relation between individuals and
propositions, so that 'Scott believes that Mark Twain is Samuel
Clemens' expresses a proposition to the effect Scott stands in
the believes relation to the proposition expressed by 'Mark
Twain is Samuel Clemens'. But then it follows that 'Scott
believes that Mark Twain is Samuel Clemens' and 'Scott
believes that Samuel Clemens is Samuel Clemens' express the same
proposition (since the embedded sentences in both belief ascriptions
express the same proposition) and so cannot diverge in truth value.
Many have found this consequence of the Salmon-Soames view of
propositions (and belief ascriptions) hard to swallow as well.



Salmon [1986] is largely an extended defense of these two consequences
of the Salmon-Soames view. It is beyond the scope of the present work
to explain Salmon's defense and the interested reader should
consult that work
 directly.[7]
 Soames [2002] deals with these issues, among others, as well.



In the formal semantics offered by Salmon and Soames, propositions are
ordered *n*-tuples (or concatenations of *n*-tuples), as are
(4a), (5a), (5b) etc. above. But since Salmon and Soames say nothing
explicitly about the matter, it is unclear whether these
*n*-tuples and concatenations merely represent propositions in
the formalism, or whether Soames and Salmon take them to be
propositions. If the former, then the Salmon and Soames view is
incomplete and we need to be told what propositions really are, and
more specifically what it is that really holds propositions together
(i.e. what the corner brackets in (4a), (5a) etc. stand for). If the
latter, then the view at least seems to have trouble accounting for
some of the properties possessed by propositions. Propositions have
truth conditions: they are true or false, depending on how the world
is. So if some ordered *n*-tuples are propositions, some ordered
*n*-tuples have truth conditions. But ordered *n*-tuples
don't seem to be the kinds of things that have truth conditions.
Indeed, presumably many ordered *n*-tuples have no truth
conditions, (e.g. < 1,2,3 >). So how/why did those
*n*-tuples that are propositions come to have truth conditions?
Similar remarks apply to modal properties. Propositions are necessary,
contingent, and possible. These, again, don't seem to be
properties of *n*-tuples. Finally, if propositions are ordered
*n*-tuples, that is, set theoretic constructions, it is hard to
see why a particular set theoretic construction is the proposition in
question (and so has truth conditions, modal properties, etc.) as
opposed to some other set theoretic construction that seems equally
well suited to the task. For example, we said that the sentence


* (4) Scott
runs.



expresses the proposition/set theoretic construction


* (4a) < < *o* >,
*R* >



But the following set theoretic construction seems equally suited to
be the proposition (4) expresses:


* (4b) < *R*,
< *o* > >



So why it is that (4a), instead of (4b), is the proposition (4)
expresses, and has modal properties and truth conditions? 



These questions as to what holds structured propositions together and
gives them their structure, and how/why proposition have truth
conditions turns us to other recent work within the neo-Russellian
approach. While adopting more or less the same view as Salmon and
Soames on the semantic values of different kind of words (though
claiming to be strictly neutral on the question of what the semantic
values of names and predicates are), Jeffrey C. King [1995, 1996,
2007, 2009] develops a view as to what binds the constituents of
propositions together and how/why propositions have truth conditions.
He holds that propositions are not *n*-tuples and that a complex
relation binds together the constituents of a proposition and provides
the proposition with its
 structure.[8]
 Further, King is motivated by the idea that propositions cannot be
the kinds of things that by their very natures and independently of
minds and languages have truth conditions. Hence, a radical feature of
King's view is that we speakers of natural languages endow
propositions with their truth conditions, as a result of which he
calls his account a naturalized account of propositions.



In order to explain what complex relation King claims binds the
constituents together, consider the sentence 'Dara swims'
and, idealizing considerably for the sake of exposition, assume that
its syntactic structure at LF is as follows:



![Dara swims diagram](fig1.png)

Figure 1.




Call the syntactic relation between 'Dara' and
'swims' here R. King sometimes calls *R* the
sentential relation of the sentence 'Dara swims'. Among
the reasons that the English sentence in Figure 1 is true iff Dara
swims is that the sentential relation *R* is interpreted by
English speakers in a certain way. We interpret it as
*ascribing* the semantic value of 'swims' to the
semantic value of 'Dara'. As King points out, this is a
contingent matter. There might have been a language containing the
sentence 'Dara swims' the speakers of which took the
sentence to be true iff Dara fails to possess the property of
 swimming.[9]
 The difference in truth conditions of the sentence 'Dara
swims' in these two languages is due to the speakers of the
languages interpreting the syntactic concatenation in the sentence
differently. And of course we English speakers interpreting *R*
in the way we do (described above) is not an isolated matter. In
general we interpret syntactic concatenation by composing semantic
values of the concatenated lexical items in certain
 ways.[10]
 King sometimes puts this by saying that we interpret syntactic
concatenation as instructing us to compose semantic values in certain
ways. The fact that *R* in Figure 1 is interpreted by English
speakers as ascribing the semantic value of 'swims' to the
semantic value of 'Dara' is expressed by saying that in
English, *R* encodes
 ascription.[11]
 It is the fact that *R* encodes ascription in English that makes
the English sentence 'Dara swims' have truth conditions
rather than being a list of Dara and the property of
 swimming.[12]



Returning to the main theme, we are trying to say what relation holds
together Dara and the property of swimming in the proposition that
Dara swims on King's view. King claims that we ought to be sure
that we pick a relation such that there are good independent grounds
for thinking that Dara and the property really do stand in that
relation, so that the proposition in question exists. Given that
'Dara' has Dara as its semantic value and that
'swims' has the property of swimming as its semantic
value, then in virtue of the existence of the English sentence
'Dara swims', here is a two-place relation that Dara and
the property of swimming stand in:



**(Relation)**
  

*there is a language L, a context c and lexical items a and b of L
such that a and b occur at the left and right terminal nodes
(respectively) of the sentential relation R that in L encodes
ascription and \_\_\_ is the semantic value of a in c and \_\_\_ is the
semantic value of b in c.*



Following King, let's call an object possessing a property, or
*n* objects standing in an *n*-place relation, or an object
standing in a relation to a property, or *n* properties standing
in an *n*-place relation and so on a fact. Then since Dara stands
in the above relation to the property of swimming, the following is a
fact:



**(Fact)**
  

*there is a language L, a context c and lexical items a and b of L
such that a and b occur at the left and right terminal nodes
(respectively) of the sentential relation R that in L encodes
ascription and Dara is the semantic value of a in c and the property
of swimming is the semantic value of b in c.*



That the English sentence 'Dara swims' exists, that
'Dara' has as its semantic value (in any context) Dara and
that 'swims' has as its semantic value (in any context)
the property of swimming jointly suffice for the existence of this
fact. Equally, that the German sentence 'Dara schwimmt'
exists (and that the words in the sentence have the semantic values in
context that they do) and that the English sentence 'I
swim' taken in a context in which Dara is the speaker exists
each suffices for the existence of this fact as well. Without the
existence of any such sentences, the fact in question wouldn't
exist.



(Fact), or what is the same thing, Dara standing in (Relation) to the
property of swimming, is almost what King claims is the proposition
that Dara swims. To see what more needs to be added, note that there
is no reason to think that (Fact) has truth conditions and so is
either true or false. But consider again (Relation), which relates
Dara and the property of swimming in (Fact). Since Dara stands in
(Relation) to the property of swimming in the proposition that Dara
swims, call (Relation) the propositional relation of the proposition
that Dara swims. Now if this propositional relation encoded
ascription, as does the sentential relation R that is a component of
the propositional relation, the proposition would have truth
conditions. For in that case, the propositional relation would be
interpreted as ascribing the property of swimming to Dara and so the
proposition would be true iff Dara possesses the property of
 swimming.[13]
 Hence, King claims that the following fact is the proposition that
Dara swims, where we now include as part of the fact/proposition that
the propositional relation in it encodes ascription: *there is a
language L, a context c and lexical items a and b of L such that a and
b occur at the left and right terminal nodes (respectively) of the
sentential relation R that in L encodes ascription and Dara is the
semantic value of a in c and the property of swimming is the semantic
value of b in
 *c*.*[14]
 Since Dara does possess the property of swimming, there is also the
fact of her possessing this property. But note that this fact is quite
distinct from the fact that King claims is the proposition that Dara
swims. Still, the former makes the latter true. But had there been no
fact of Dara possessing the property of swimming, the fact that is the
proposition that Dara swims would still have existed and sadly would
have been
 false.[15]



King claims that his account has several significant
 virtues.[16]
 First, on his account it is hard to deny that propositions exist
given fairly minimal assumptions; and there is no mystery about what
they are. Second, his theory is naturalized, in the sense that it is
something *we do* that endows propositions with truth
conditions. Third, and related to the previous point, we can give some
explanation as to how and why propositions have truth
 conditions.[17]
 On the proposed explanation the representational powers of sentences
and their users are explanatorily prior to those of propositions.



In more recent work, King has emended his account of propositions in
various ways. On King's [2007] view, because of the role the
syntax of a sentence plays in the propositional relation expressed by
the proposition it expresses, sentences with any difference in their
syntactic structures express different proposition. However, in both
King, Speaks, & Soames [2014] and especially in King [2018], King
formulates a version of his view that allows sentences with quite
different syntactic structures, whether in the same or different
languages, to express the same proposition. In King, Speaks, &
Soames [2014], King gives his most explicit account to date of how it
is that propositions have truth conditions and so represent the world
as being a certain
 way.[18]




Finally, we turn to a discussion of a view of propositions recently
championed by Scott Soames [2010a, 2010b]. Soames follows King [2007,
2009] in rejecting the view that propositions are things that are
representational, and so have truth conditions, independently of minds
and languages on the grounds that such a view is ultimately mysterious
and unintelligible. Again following King, Soames thinks that the fact
that propositions are representational must ultimately be explained in
terms of the representational capacities of agents. However,
Soames' positive account of how/why propositions have truth
conditions differs in important ways from King's.



Soames begins with the notion of the mental act of predication, which
he takes to be primitive. However, by way of illustration, if an agent
perceives an object *o* as red, and so has a perceptual
experience that represents *o* as being red, the agent
*predicates* redness of *o*. Similarly, if an agent
"thinks of" *o* as
 red[19],
 or "form[s] the nonlinguistic perceptual *belief* that
*o* is
 red".[20]
 For Soames, predicating redness of *o* does not amount to
*believing* that o is red. To believe that *o* is red, one
must predicate redness of *o* and do something like endorse the
predication. It is hard to say precisely what *predicating*
amounts to since the notion is primitive for Soames. An agent
predicating redness of *o* is an event token. Of course there may
well be many event tokens of agents predicating redness of some object
*o* by an agent perceiving it as red, an agent thinking of it as
red and so on. Soames claims that the proposition that *o* is red
is the event *type* of an agent predicating redness of
*o*. Other more complex propositions are identified with events
types of agents performing *sequences* of primitive mental
 acts.[21]
 Soames doesn't say what he takes events (types or tokens) to
be. But since he thinks that propositions are structured entities with
constituents, he must think that event types are structured entities
with constituents. Presumably, the proposition that *o* is
red--the event type of an agent predicating redness of
*o*--has *o* and redness as constituents. 



Like King, Soames grounds the representational capacities of
propositions in the representational capacities of agents. Soames
claims that the event tokens of agents ascribing redness to *o*
are things that inherently have truth conditions. They are things that
are inherently true iff *o* is red. These tokens are for Soames
tokens of the event type that is the proposition that *o* is red:
the event type of an agent predicating redness of *o*. Soames
claims that the event type that *o* is red has truth conditions
because of its "intrinsic connection" to the event tokens
of agents predicating redness of *o*, which, as indicated, are
themselves things that inherently have truth conditions.



In King, Speaks, & Soames [2014] and Soames [forthcoming], Soames
amends his theory of proposition in several respects. Two of those
changes are the following. First, Soames [2010] had rejected the view
that cognitive act types are propositions on the grounds that act type
are things that we do, but propositions are not. In King, Speaks,
& Soames [2014], Soames makes clear that he no longer finds this
argument persuasive and is inclined to identify propositions with
cognitive act types. Second, Soames gives a new account represent
things as being a certain way. On the new account, propositions
represent things as being a certain way in a derivative sense. Just as
an act can be intelligent in the derivative sense that in performing
it an agent is acting intelligently, the proposition that o is red
represents in the derivative sense that in performing that act an
agent represents o as being red. 



Peter Hanks [2015] defends a view with some similarities to
Soames' view discussed above. As did Soames, Hanks follows King
in endorsing the three novel claims from King [2007] and subsequent
work mentioned above: (i) Hanks rejects theories according to which
propositions have truth conditions and so represent the world as being
a certain way by their very natures and independently of minds and
languages as mysterious; (ii) holds that an adequate theory of
propositions must *explain* how\why propositions have truth
conditions and so represent the world as being a certain way; (iii)
and holds that since the representational capacities of propositions
cannot be something they have inherently and by their natures, their
representational capacities must derive from and be explained by the
representational capacities of thinking agents. 



In simple cases of judging and asserting, Hanks claims we perform
actions of predicating properties of objects. In judging that Donald
Trump is a demagogue without speaking, one thinks of Trump (refers to
him in thought), thinks of the property of being a demagogue
(expresses the property in thought) and predicates the property of
Trump. In asserting that Trump is a demagogue, one refers to him,
expresses the property and predicates it of him, here using linguistic
means. According to Hanks, in predicating a property of an object, one
portrays the object as being a certain way and so does something that
is true or false. Hence, Hanks claims these token acts of predicating
are true or false. Hanks notion of predication is inherently assertive
and committing, unlike Soames' notion of predication. There is
not some non-committal thing you do in predicating and then add
endorsement or commitment. On Hanks view, predicating *is*
committing to the object possessing the property in question. The
proposition that Donald Trump is a demagogue is the act *type* of
predicating *being a demagogue* of Trump. Hanks holds that this
act type would exist even if it had no tokens. In general, whether
they have tokens or not, Hanks holds that the act types that are
propositions exist. 



The proposition that Trump is a demagogue is the act type of referring
to Trump, expressing the property of being a demagogue and predicating
it of Trump, as we have seen. What Hanks calls the *interrogative
proposition* expressible by the question 'Is Trump a
demagogue?' is the act type of referring to Trump, expressing
the property of being a demagogue and combining Trump and the property
in an interrogative way (rather than *predicating* the property
of Trump). Hanks gives a similar account of the *imperative
proposition* expressed by the command 'Trump, be a
demagogue!' As a result, Hanks rejects the claim that there is
some common underlying content running through the (assertive)
proposition, imperative proposition and interrogative proposition
regarding Trump being a demagogue. There are just three different
propositions here with their different "forces"
(assertive, interrogative, imperative) built in. 



Hanks' explanation of why propositions as act types of the sort
described have truth conditions comes in two steps. First, Hanks
argues that token acts of predicating properties of objects have truth
conditions. Hanks recognizes that some may doubt whether act tokens
are the kinds of things that can be true and false. His main argument
that they can be is that we have adverbial modifiers
'truly' and 'falsely' and that these attribute
properties to action tokens. So just as 'quickly' in
'Obama quickly stated that Clinton is eloquent.'
attributes a property to Obamas's action, so Hanks claims that
'truly' in 'Obama truly stated that Clinton is
eloquent.' attributes the property of being true to an action of
Obama. Hanks then tries to argue that the action *type* of
predicating being a demagogue of Cruz inherits the property of having
truth conditions from its instances. Note that here it must be actual
and possible instances that truth conditions are inherited from, since
Hanks wants propositions that have never been and never will be
tokened to have truth conditions. The argument here is complex since
Hanks notes that types inherit certain kinds of properties from tokens
and not others. Hence, Hanks seeks to explain why the having of truth
conditions is the kind of property a type inherits from its (actual
and possible) tokens. 



On Hanks' theory there are many more propositions than one might
have thought. First, there is the proposition that is the act type
consisting of referring to Clinton using 'Clinton' and
predicating eloquence of her. It is true iff Clinton is eloquent. Then
there is a distinct proposition with those same truth conditions that
is the act of referring to Clinton in any way whatsoever and
predicating eloquence of her. Next, there is another proposition with
these same truth conditions consisting of the act of referring to
Clinton using 'Clinton' while thinking of her as
Obama's former secretary of state and predicating eloquence of
her. In addition, there is another proposition with the same truth
conditions consisting of referring to Clinton using
'Clinton' while thinking of her as a former first lady and
predicating eloquence of her. And so on. Again, all these propositions
are true iff Clinton is eloquent. There is even a proposition
consisting of referring to Clinton using 'Clinton' while
drawing a round square and predicating eloquence of her.
 [22]




Above we saw that for Hanks, predication endows propositions with an
inherent element of judgment or assertion. Predicating a property of
an object *commits* the predicator to the object having that
property. For Hanks, she did something false if it doesn't. But
this raises a problem for him. In disjunctive, negated, conditional
propositions and others, embedded propositions do not have assertive
force. They aren't asserted. But if these embedded propositions
inherently have an assertoric or judgmental element, how can this be?
To address this Hanks claims that 'or', 'if'
and 'not' create cancellation contexts. Since e.g.
'or' creates a *cancellation context* on Hanks'
view, in uttering the following sentence I fail to assert that Trump
is a demagogue:



Trump is a demagogue or Clinton is eloquent. 



Each disjunct expresses a proposition that includes as a sub act the
act of predicating a property of the object according to Hanks. But
the predication is cancelled. Hence, the asserting/committing element
in the proposition is cancelled. Hanks must walk a very fine line
here. The inherently assertive committal aspect of predication is what
explains both that propositions are true and false and that unembedded
propositions make
 assertions.[23]
 To explain why some embedded propositions don't make
assertions, Hanks appeals to the notion of the predication being
cancelled in virtue of occurring in a cancellation context. But of
course Hanks will want to say that the embedded proposition still has
truth conditions and is true or false. Somehow in canceling the
predication, though assertive force is cancelled the truth conditions
and truth-value aren't, even though predication is responsible
for both. 



Above it was mentioned that King [2007] and subsequent work endorsed
three novel claims about propositions. Two of these are: (i) theories
according to which propositions have truth conditions and so represent
the world as being a certain way by their very natures and
independently of minds and languages are mysterious and to be
rejected; (ii) an adequate theory of propositions must *explain*
how\why propositions have truth conditions and so represent the world
as being a certain
 way.[24]
 It was also noted that Soames and Hanks follow King in this respect.
In a sense, Speaks does too insofar as he feels the need to explain
the "aboutness" or intentionality of some mental
 states.[25]
 So most recent literature has taken onboard King's two claims
above. Philosophy being what it is, however, there have been recent
theorists who want to return to something like the classical theories
of Frege and Russell, where propositions were thought to be mind and
language independent abstract objects that by their very natures had
truth conditions and so represent the world as being a certain way. On
such a view, both of King's claims are rejected. Propositions
are precisely held to have truth conditions by their natures and
independently of minds and languages; and it is denied that there can
be any explanation of how/why propositions have truth conditions.
Trenton Merricks [2015] defends such a view. According to Merricks,
propositions are abstract, necessary existents that essentially
represent the world as being a certain
 way.[26]
 He also holds that the fact that propositions essentially represent
things as being a certain way is primitive. That is, this fact has no
 explanation.[27]
 Further, Merricks holds that propositions are simple: they have no
 constituents.[28]
 On this last point at least Merricks departs from the classical views
of Frege and Russell on which propositions do have constituents. 



Lorraine Juliano Keller [2014] expresses sympathy for a similar view
that she calls *propositional primitivism*. On this view,
propositions are fine-grained *sui generis entities*. They are
not reducible to nor can they be explained by entities in another
ontological category. Her primitivist thinks that not much of anything
can be said about the inner nature of propositions except that they
are abstract, mind and language independent entities with no
constituents or structure. While King, Soames, Hanks and perhaps
Speaks see in such a view mystery or worse, primitivists like Keller
and Merricks see elegance and simplicity. 


### 3.2 The Structured Intension Approach



Having seen the main features of neo-Russellian approaches, let us
turn to structured meaning accounts. The roots of these accounts can
be traced to Rudolf Carnap [1947], and his notion of intensional
isomorphism. David Lewis [1972] and Max Cresswell [1985] have worked
out similar, detailed versions of the structured meanings approach,
though there are important differences in their views.
Cresswell's [1985] version of the view will be discussed
 here.[29]
 Because our concern is with conceptions of structured propositions,
there are many features of Cresswell [1985] that will not be discussed
(e.g. Cresswell's account of the semantics of verbs of
propositional attitude).



Both Lewis [1972] and Cresswell [1985] are motivated by some of the
same considerations that motivated neo-Russellians like Salmon and
Soames. Lewis and Cresswell both wish to find a more fine grained
"semantic value" for sentences than functions from worlds
(or, as in Lewis [1972], indices) to truth values or, equivalently,
sets of worlds. For example, Cresswell [1985] claims that verbs of
propositional attitude are (sometimes) sensitive to more than the
intensions (functions from worlds/indices to truth values) of the
sentences they embed. Thus Cresswell claims that




...one might easily have two sentences *a* and
*b* that are true in exactly the same worlds and yet are
such that



*x* *ph*s that *a*



is true, but



*x* *ph*s that *b*



is false. (Cresswell [1985] p. 73; *ph* of course is a verb of
propositional attitude).




Thus Cresswell wishes to associate with a sentence (or more
accurately, a 'that' clause) some semantic value that is
more fine grained than a set of worlds, so that attitude verbs may
(sometimes) distinguish between sentences that are true in exactly the
same worlds. Strictly, Cresswell holds that sometimes attitude verbs
are sensitive only to the sets of worlds in which the sentences they
embed are true (i.e. their intensions); but sometimes attitude verbs
are sensitive to more than this. In these latter cases, Cresswell
wishes to associate a semantic value more fine grained than a set of
worlds with the embedded sentence (or 'that' clause).
Cresswell accomplishes this by holding that 'that' in
English attaches to a sentence to form a name, and that
'that' in this role is highly ambiguous. In one of its
meanings, 'that' attaches to a sentence and forms a name
of the intension of the sentence (i.e. the set of worlds in which it
is
 true).[30]
 In such cases, the attitude verb is sensitive only to the intension
named by the 'that' clause following it. However,
'that' has another meaning on which it combines with a
sentence to form the name of a much more fine-grained entity (in the
sense that sentences true in all the same worlds may be associated
with different fine-grained entities). In such cases, verbs of
attitude are sensitive to differences in these fine-grained entities.
Since our concern is with structured propositions, or with semantic
values of sentences more fine grained than sets of worlds, the focus
will henceforth be on Cresswell's account of these fine-grained
entities named by some 'that'
 clauses.[31]
 Henceforth, then, when the fine grained entity associated with a
sentence or 'that' clause on Cresswell's view is
discussed, what is being discussed is what a 'that' clause
containing the sentence names, given that the meaning of
'that' in the 'that' clause is the one that
when combined with the sentence yields a name of the most fine grained
entity named by any 'that' clause in which the sentence
occurs. This is important to bear in mind, since for Cresswell,
strictly speaking, a sentence not in a 'that' clause does
not express this fine grained entity.



Consider the sentence


* (7) Max
runs.



For Cresswell, the meaning of a predicate like 'runs' is
essentially its intension: a function from individuals to sets of
worlds (it maps an individual to the worlds at which she
 runs).[32]
 Let *I**r* be this intension. The meaning of a
name like 'Max' (in some cases at least) is simply its
referent: *o*. Thus, the fine grained entity associated with (7)
is the ordered pair:


* (7a) < *o*,
*I**r* >



The negation of (7) will be associated with the following:


* (7b) < NOT,
< *o*,
*I**r* > >



where NOT is the function from sets of worlds to sets of worlds that
maps a set of worlds to its complement. Finally, the sentence:


* (8) Someone
runs.



is associated with


* (8a) < S,
*I**r* >



where S is the function from functions from individuals to sets
of worlds to sets of worlds such that S(*f*)={*w*: for
some *o*, *w* is in *f*(*o*)}. 



It should be clear that as on the neo-Russellian approach, sentences
that are true in all the same worlds may be associated with different
fine grained entities of the sort posited by Cresswell. For example,
even if 'All brothers are siblings' and 'All
bachelors are male' are true in exactly the same worlds, the
fine grained entity associated with the latter will contain the
meaning (function from individuals to sets of worlds) of
'male' and the fine grained entity associated with the
former will not. It should also be clear that the semantic values of
expressions are recoverable from the propositions expressed by
sentences containing them. For example, the semantic value of
'runs' as it occurs in (7) is a constituent of the
fine-grained entity expressed by (7) (i.e. (7a)). Similar remarks
apply to (7b) and (8a).



A final remark about Cresswell's view is in order. The
fine-grained entities we have been discussing are what verbs of
propositional attitude are sensitive to when they are sensitive to
more than the intension/set of worlds associated with a sentence they
embed. However, they do not seem to be the primary bearers of truth
for Cresswell. For Cresswell, each sentence is associated with a set
of worlds/intension, which Cresswell calls a proposition; and the
truth or falsity of a sentence at a world is determined by what
proposition it expresses. So these seem to be the primary bearers of
truth and falsity for
 Cresswell.[33]
 Thus, it appears that for Cresswell, in contrast to the
neo-Russellians, the primary bearers of truth and falsity and the fine
grained entities associated with the sentences (or 'that'
clauses) that verbs of attitude embed and to which they are
(sometimes) sensitive are different.


### 3.3 The Algebraic Approach



Finally, we turn to algebraic approaches. Though Bealer in some sense
adopts an algebraic approach to propositions (see the above
discussion), he apparently holds that propositions have no (set
theoretic or mereological) parts, and so doesn't count as a
structured proposition theorist in the sense in which the term is used
here. Thus, we will consider here adherents to the algebraic approach
who do hold that the propositions yielded by their algebras are
complex and have "parts". Aside from Bealer [1979, 1982
and 1993], work in this tradition includes Edward Zalta [1983 and
1988], and Christopher Menzel [1993]. The focus here will be on the
formulations in Edward Zalta [1988]. Though Zalta has an extensive,
axiomatized theory of propositions, and ordinary and abstract
individuals, properties, and relations, we confine our attention here
to his view about propositions. Still, since Zalta views propositions
as zero-place relations, we will say something about his views on
properties and relations.



Advocates of the algebraic approach such as Zalta, like the
neo-Russellians and the advocates of structured meaning approaches,
think that a good theory of propositions must allow for distinct,
necessarily equivalent propositions. Thus, he writes:



> 
> "Necessarily equivalent propositions may be distinct. If the
> theory of propositions is not fine-grained enough to distinguish
> necessarily equivalent propositions, the ability to accurately
> represent belief is lost" (Zalta 1988, p. 57)
> 



To appreciate how Zalta achieves the goal of having a fine-grained
theory of propositions, we begin by discussing how he views relations
generally, since, as just mentioned, Zalta takes propositions to be
zero-place relations (and properties to be one-place relations). Zalta
holds that relations are "primitive entities", by which he
means that they are not to be explained or "defined" in
terms of other entities/notions. But at least some relations are
complex. For example, if we take a two-place relation (between
objects) *R**x**y* and "plug" one of its
argument places with the object *b*, we get the one-place
relation (property) *R**x**b* ("bearing *R*
to
 *b*").[34]
 This one-place relation is complex, having *b* and *R* as
parts. Similarly, if we take a three-place relation
*S**x**y**z* and "universalize" the
third argument position, we get a two place relation that we might
represent thus: (*z*)*S**x**y**z*
("*x* and *y* (in that order) stand in *S* to
everything"). Here again, the two-place relation is complex,
having S and (something corresponding to)
"universalization" as parts. Zalta's idea is that
properties, relations and individuals can be "harnessed
together" to form new, complex relations. In his axiomatized
theory of relations, Zalta introduces a comprehension schema for
relations (see Zalta [1988] p. 46) that insures that all manner of
complex relations will be available. To insure that all instances of
the comprehension schema are true in all interpretations of his
axiomatized theory, Zalta has these interpretations include the
following group of "logical functions":
PLUG*i*, NEG, COND, UNIV*i*,
REFL*i*, *j* CONV*i*, *j*,
VAC*i*, NEC, WAS and WILL. Roughly (and suppressing
reference to worlds and times) PLUG*i* is a function
that maps an *n*-place relation *R* and an object *b*
to the *n*-1 place relation *R*' such that
< *o*1, ...,
*o**i*-1, *o**i*+1,
..., *o**n* > stand in
*R*' iff < *o*1, ...,
*o**i*-1, *b*,
*o**i*+1, ...,
*o**n* > stand in *R*. NEG is a
function that maps an *n*-place relation *R* to an
*n*-place relation *R*' such that *n* things
stand in *R*' iff they don't stand in
 *R*.[35]
 Thus the repeated application of these functions yields appropriate
relations to make true the instances of Zalta's comprehension
schema for relations. For example, consider the following two
instances of his comprehension schema (where '*F*' is
a variable ranging over one-place relations; '*b*' is
a name of an individual; and the other predicate letters are constants
and so name particular
 relations):[36]



([?]*F*)(*F**x* iff *R**x**b*) 



([?]*F*)(*F**x* iff ~*P**x*) 



If we apply PLUG2 to the individual denoted by
'*b*' and the (two-place) relation denoted by
'*R*', we get a one-place relation that makes the
first instance of the schema true; and if we apply NEG to the
denotation of '*P*', we get a one-place relation that
makes the second instance true.



As we have mentioned, propositions are zero-place relations for Zalta.
Thus, PLUG*i* and the rest of the "logical
functions" mentioned above can be applied to various entities to
yield propositions. Thus the proposition expressed by a sentence like




Ed runs.



is the result of applying the PLUG1 function to the
property of running and Ed. This proposition consists of Ed saturating
the one argument place of the running property. Similarly, a sentence
like



Ed does not run.



expresses the proposition that is the result of applying
PLUG1 to running and Ed as before, and then applying NEG to
the output of PLUG1. Finally, a sentence like



Everything runs.



expresses the result of applying UNIV1 to the property of
running. This idea that there is some group of "logical
functions" whose repeated application to some other entities
yield complex propositions (and relations) is characteristic of what
are being called algebraic approaches.



It should be clear that necessarily equivalent sentences may express
distinct propositions on Zalta's view. For example, the
sentences 'All brother are male siblings' and 'All
bachelors are unmarried' express propositions that are true in
all possible worlds. But the first expresses a proposition that
results from applying COND to the properties of being a brother and
being a male sibling, and applying REFL1,2 and then
UNIV1 to the output of COND. The second does not, but
instead results from applying these functions in the same order to the
properties of being a bachelor and being unmarried. Further, it should
be clear that the semantic values of expressions are recoverable from
the propositions expressed by sentences in which they occur. E.g. both
Ed and the property of running, which are the semantic values of
'Ed' and 'runs', are constituents of the
proposition that Ed runs, which is expressed by 'Ed runs',
since this proposition consists of Ed saturating the one argument
place in the property of running.



Having sketched Zalta's view of propositions it is worth
mentioning a couple points about it. First, at least in some cases,
what binds together the constituents of a proposition is in some sense
"built into" one of the constituents of the proposition
for Zalta, (as we shall see below, the same is true for Frege and
Russell). Consider again the sentence:



Ed runs.



Recall that this sentence expresses the proposition that results from
applying PLUG1 to Ed and the property of running. The
output is Ed saturating ("plugged into") the one argument
place of the property of running. There are two things to notice about
this proposal. First, it is one of the constituents of the
proposition, the running property, that binds the constituents of the
proposition together. The proposition is held together in virtue of Ed
"plugging" the one argument place in the running property.
Second, the proposition just is Ed "plugging"/possessing
that property!



Such a view immediately raises a worry about false propositions
(discussed below in connection with Russell's POM account of
propositions). For one might argue as follows. Suppose Ed
doesn't run. Then Ed doesn't plug/saturate the one
argument place in the property of running (i.e. doesn't possess
this property). But Ed possessing the running property just is the
proposition that Ed runs. Thus there is no proposition that Ed runs.
Similar reasoning shows that any other false proposition fails to
exist. So there are no false propositions.



Obviously, Zalta does not want to be saddled with this result, and he
isn't. He holds that the even if Ed doesn't run, there is
a proposition consisting of Ed saturating the argument place in the
running property. That proposition simply isn't true. To put the
point somewhat paradoxically, even if Ed doesn't run, he
possesses the property of running, so that we have our (false)
proposition.



To some, Zalta will appear to have confused a proposition with what
makes it true. Ed possessing the running property isn't the
proposition that Ed runs, one might think. It is what makes that
proposition true! Of course Zalta must deny this. Having identified
the proposition with the thing that other theorists take to be what
makes the proposition true, Zalta holds that nothing outside of the
proposition makes it true:



> 
> The metaphysical truth or falsity of these logical complexes
> [propositions] is basic. If a proposition is true, there is nothing
> else that "makes it true". Its being true is just the way
> things are (arranged). (Zalta [1988] p.56)
> 



So the idea is that whether Ed runs or not, he saturates the one
argument place in the running property, so that we have the
proposition that Ed runs. If Ed does run, so that the proposition is
true, it is just a basic, brute fact that the proposition is true.



Finally, though we shall not go into it here, it is worth mentioning
that when Zalta gets to the semantics of verbs of propositional
attitudes, it is not only the propositions considered thus far that
are objects of the attitudes and make belief ascriptions true or
false. Zalta ends up claiming that sentences embedded with respect to
attitude verbs are ambiguous, sometimes expressing the sorts of
propositions we are discussing, and sometimes expressing other
propositions that instead of containing the individuals, properties
and relations thus far discussed, contain senses of these individuals,
properties and relations. These senses are "abstract"
individuals and relations, instead of the ordinary individuals and
relations discussed thus far. Hence Zalta ends up with a theory of
belief ascriptions that invokes both fine-grained propositions and
neo-Fregean senses. The interested reader should consult Zalta [1988].



## 4. Historical Antecedents to Current Views: Frege



As with many ideas discussed in contemporary philosophy of language,
the idea that propositions are structured is present in Gottlob
Frege's writings. Frege had a view both about the constituents
of structured propositions and about what held these constituents
together in the proposition. Frege held that simple linguistic
expressions are associated with entities he called senses. Though
there is some controversy about precisely how to understand the notion
of sense, Frege explicitly distinguishes the sense of a linguistic
expression from both the subjective ideas speakers associate with the
expression and the thing in the world the expression "stands
for". Further, the sense of an expression determines what thing
in the world the expression stands for. Thus the sense of a proper
name such as 'Ronald Reagan' must be distinguished from
any subjective ideas speakers associate with the name (e.g. feelings
of anger, fondness, etc.) and from Reagan himself. And the sense of
the name "picks out" Reagan as the thing in the world the
name stands for. It may help to think of the sense as some descriptive
condition satisfied uniquely by Reagan (and not to think any more
about what is meant by a descriptive condition). Complex linguistic
expressions are also associated with senses. And Frege held that the
sense of a complex expression is a function of the senses of its
simple parts and how they are put together. Frege called propositions
thoughts (Gedanken), and held that the thought/proposition expressed
by a sentence is itself a sense. And, like the senses of other complex
linguistic expressions, the proposition/thought expressed by a
sentence is a function of the senses of the words in the sentence and
how they are put together. Now Frege at least sometimes appears to
hold the stronger view that the sense of a sentence
(proposition/thought) has as constituents the senses of the words in
the sentence. And as the following quotation shows, his account of how
these sense-constituents are held together in the proposition/thought
depends on different kinds of linguistic expressions having different
kinds of senses:



> 
> For not all parts of a thought can be complete; at least one must be
> 'unsaturated', or predicative; otherwise they would not
> hold together. For example, the sense of the phrase 'the number
> 2' does not hold together with that of the expression 'the
> concept prime number ' without a link. We apply such a link in
> the sentence 'the number 2 falls under the concept prime
> number'; it is contained in the words 'falls under',
> which need to be completed in two ways--by a subject and an
> accusative; and only because their sense is thus
> 'unsaturated' are they capable of serving as a link.
> (Frege [1892] p. 54)
> 



Remarks like this suggest that Frege's view was that
propositions are complex entities whose parts are other senses. The
proposition is held together in virtue of the fact that at least one
of the senses is unsaturated (Frege sometimes also says predicative,
or in need of supplementation). Other senses "saturate" or
complete the unsaturated senses and in so doing are bound to them to
form the proposition/thought. Thus, on this way of interpreting Frege,
the mechanism for binding together the constituents of a structured
proposition is built right into some of the constituents, (recall that
this was true of the view of Zalta [1988] as well).


## 5. Historical Antecedents to Current Views: Russell



Bertrand Russell, to whom many current structured propositions
theorists attribute the idea of structured propositions, held various
views about the nature of propositions over the course of his career.
However, the account of propositions held by Russell that is thought
by many to be the progenitor of current accounts of structured
propositions is the one Russell defended in Russell [1903]. We shall
confine our attention to that account here. Russell differed with
Frege both on what the constituents of structured propositions are and
on what binds them together in the proposition. Russell uses the word
'term' for constituents of propositions. Thus he
writes:



> 
> Whatever may be an object of thought, or may occur in any true or
> false proposition ...I call a term....A man, a moment, a
> number, a class, a relation, a chimaera, or anything else that can be
> mentioned, is sure to be a term; and to deny that such and such a
> thing is a term must always be false. (Russell [1903] p. 43)
> 



Thus we already see that Russell differs from Frege on what kinds of
things can be constituents of propositions. For Frege, all
constituents of propositions are senses. For Russell, a man or a
mountain can be a constituent of a proposition. In a now famous
correspondence with Frege, Russell replied to Frege's assertion
that the sense of the name 'Mont Blanc', and not Mont
Blanc itself "with all its snowfields", occurs in the
proposition/thought that Mont Blanc is 4,000 meters high, by saying:




> 
> I believe that in spite of all its snowfields Mont Blanc itself is a
> component part of what is actually asserted in the proposition
> 'Mont Blanc is more than 4,000 metres high'. (Frege [PMC]
> p. 169)
> 



Russell goes on to distinguish two kinds of terms or propositional
constituents:



> 
> Among terms, it is possible to distinguish two kinds, which I shall
> call respectively things and concepts. The former are the terms
> indicated by proper names, the latter those indicated by all other
> words. (Russell [1903] p. 44)
> 



So for Russell, all propositional constituents are things or concepts.
On Russell's view, a sentence such as:



Socrates is human



expresses a proposition with three constituents, corresponding to the
three words in the sentence. Socrates himself is one of the
constituents, the other two constituents being the concepts
contributed by 'is' and 'human'.



Having seen that Russell held different kinds of things to be
constituents of propositions than did Frege, we shall turn to his
views on what binds together the constituents of structured
propositions. Russell appears to hold that the propositional
contributions of verbs (which contributions Russell often calls verbs)
hold together the constituents of propositions. Thus he writes:



> 
> Consider, for example, the proposition '*A* differs from
> *B*'. The constituents of this proposition, if we analyze
> it, appear to be only *A*, difference, *B*. Yet these
> constituents, thus placed side by side, do not reconstitute the
> proposition. The difference which occurs in the proposition actually
> relates *A* and *B*, whereas the difference after analysis
> is a notion which has no connection with *A* and *B*.
> (Russell [1903] p. 49)
> 



And later Russell writes:



> 
> Owing to the way in which the verb [propositional contribution of a
> verb] actually relates the terms of a proposition, every proposition
> has a unity which renders it distinct from the sum of its
> constituents. (Russell [1903] p. 52)
> 



Russell's idea that a proposition is something beyond the sum of
its constituents certainly seems correct. The collection, or
mereological sum, of *A*, difference and *B* is not the
proposition that *A* differs from *B*. Different
propositions may have the same Russellian constituents, as with the
propositions expressed by the following sentence pair:



Jason loves Patti.



Patti loves Jason.



However, Russell's idea that the propositional contribution of
the verb binds the constituents together (in different ways in the
case of our pair of sentences) is hard to understand. In the next to
last quotation from Russell above, he suggests that the proposition
expressed by '*A* differs from *B*', whose
constituents are *A*, difference and *B*, is held together
by difference actually obtaining between *A* and *B*. If we
call difference a relation, the proposition would consist of *A*
standing in the relation of difference to *B*. Russell makes a
number of remarks that suggest that this is his view. But it would
seem that this cannot be correct. Intuitively, *A* standing in
the relation of difference to *B* is what makes the proposition
that *A* differs from *B* true. It is not the proposition
itself. For if it were, it would seem that if *A* doesn't
stand in the difference relation to *B*, then there is no (false)
proposition to the effect that *A* differs from *B*. And
quite generally, for the same reason it would appear that there are no
false propositions. Perhaps Russell meant that propositional
contributions of verbs hold propositional constituents together in
some other manner. But it certainly is not clear what that manner
would be. Or perhaps he held a view similar to Zalta's discussed
above.