Propositions

First published Mon Dec 19, 2005; substantive revision Fri Sep 29, 2023

The term ‘proposition’ has a broad use in contemporaryphilosophy. It is used to refer to some or all of the following: theprimary bearers of truth-value, the objects of belief and other“propositional attitudes” (i.e., what is believed,doubted, etc.^[1]), the referents ofthat-clauses, and the meanings ofsentences.

One might wonder whether a single class of entities can play all theseroles. If David Lewis (1986, p. 54) is right in saying that “theconception we associate with the word ‘proposition’ may besomething of a jumble of conflictingdesiderata,” thenit will be impossible to capture our conception in a consistentdefinition.

The best way to proceed, when dealing with quasi-technical words like‘proposition’, may be to stipulate a definition andproceed with caution, making sure not to close off any substantiveissues by definitional fiat.

Propositions, we shall say, are the sharable objects of the attitudesand the primary bearers of truth and falsity. This stipulation rulesout certain candidates for propositions, including thought- andutterance-tokens, which presumably are not sharable, and concreteevents or facts, which presumably cannot be false. These consequencesfit well with contemporary usage. Our definition leaves open many ofthe questions dividing propositionalists: which additional roles arepropositions fit to play? would propositions have to bemind-independent or abstract? what individuation conditions would theyhave? how would they relate to facts? We examine these issues below,as well as the fundamental issue of whether there are propositions atall.

1. Brief History

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

It is difficult to find in the writings of Plato or Aristotle a clearendorsement of propositions in our sense. Plato’s mostchallenging discussions of falsehood, inTheaetetus(187c–200d) andSophist (260c–264d), focus on thepuzzle (well-known to Plato’s contemporaries) of how falsebelief could have an object at all. Thinking that Theaetetus flieswould seem to require thinking the non-existent flying Theaetetus.Were Plato a propositionalist, we might expect to find Socrates or theEleactic Stranger proposing that false belief certainly has an object,i.e., that there is something believed in a case of falsebelief—in fact, the same sort of thing as is believed in a caseof true belief—and that this object is the primary bearer oftruth-value. But it seems no such proposal is seriously considered. Inboth dialogues, it is suggested that thought is a kind of inwarddialogue carried on in the mind itself (Theaetetus189e–190a andSophist263e), and that judgment resultswhen the two inward voices affirm the same thing. Plato is standardlyunderstood as explaining false belief (doxa) in terms of theassertion of a false statement (logos). But it is far fromclear that he takes the objects of belief to be statements rather thansimply the ordinary concrete objects (e.g., Theaetetus) and forms(e.g.,flying) which the statement is about, and still lessclear that he takes statements to besharable between minds.Statements, for Plato, might simply be tokens of inner speech, asNuchelmans (1973, p. 21) suggests.

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

Arguably, the first employment in the western philosophical traditionof the notion of proposition, in roughly our sense, is found in thewritings of the Stoics. In the third century B.C., Zeno and hisfollowers, including Chrysippus especially, distinguished the materialaspects of words from that which is said, orlekta. Amonglekta, they distinguished the complete from incomplete (ordeficient), the latter corresponding roughly to the meanings ofpredicates, the former to the meanings of sentences. Among completelekta they includedaxiomata, or the meanings ofdeclarative sentences. For the Stoics, onlyaxiomata, and notthe words used to articulate them, were properly said to be true orfalse.Axiomata were therefore the proper subject matter ofStoic logic.

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

For instance, I see Cato walking; the sense of sight reveals this tome and the mind believes it. What I see is a material object and it isto 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 nowstate, but a certain affirmation about him… (Epistulae morales,117, 13)

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

Abelard distinguishes betweendicta or what is said and actsof assertion (or thinking), the former being the fundamental bearersof truth-value. While Abelard himself seems to have had little to sayabout the nature or identity conditions ofdicta, hissuccessors took up the subject with vigor (Nuchelmans 1973, pp.162–3). Aredicta particular acts of thinking, concreteevents or facts, or entities having the same sort of being asuniversals? Each of these views is considered and evaluated in thetreatiseArs Meliduna, of unknown authorship.

A similar debate raged among the English scholastics in the fourteenthcentury. Against Ockham’s nominalistic account, under which theobject of assent is a complex token mental sentence, Adam Wodeham, forexample, maintained that the object of assent is not any sort ofmental entity, nor even athing at all, properly speaking,nor of course anothing but rather abeing the case(see Wood 2003, and Nuchelmans 1996, IV for further discussion ofWodeham and his contemporaries).

One complicating factor for the contemporary reader in examiningMedieval (and later) work on the topic is that the term“propositio” was standardly used, following Boethius, torefer to sentences, mental as well as written or spoken (oratioverum falsumve significans, i.e., speech signifying what is trueor false). Propositions in our sense were what was signified by thesepropositiones if they signified at all.^[2]

When we turn to the early modern period, it is not easy to find, atleast in the writings of major philosophers, an unabashed assertion ofthe reality of propositions. Unsurprisingly, one looks in vain in thewritings of the British empiricists. As for Descartes, particular actsof judgments serve as the primary bearers of truth-value (althoughthere is considerable debate about the status of his eternal truths).Leibniz’scogitato possibilis have some of thecharacteristics of propositions. Thesepossible thoughts seemto play the role of thought-contents and the fundamental bearers oftruth-value. However, it is a matter of debate whether they areaccorded real ontological status.

Propositionalists were by no means rare in the 19th century, GottlobFrege being the best known example. The Czech philosopher andmathematician Bernard Bolzano also deserves special mention. In hisWissenschaftslehre, orTheory of Science, publishedin 1837, he argued for the existence of what he called‘Sätze an sich,’ or sentences in themselves,which he clearly distinguished from linguistic items or mentalphenomena. They are the fundamental bearers of truth and falsity, andthe objects of the attitudes. It is the goal of every science,including mathematics, to state the fundamental true sentences inthemselves pertaining that subject matter. (This marks a cleardeparture from the psychologizing approaches of many ofBolzano’s contemporaries.) Like Frege after him, Bolzanoconceived of propositions as complexes composed of wholly abstractmind-independent constituents (Vorstellungen an sich).Bolzano’s work has had a profound influence on Husserlianphenomenology and the development of modern logic.

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

In 1892, Frege published his classic paper “On Sense andReference”. This paper contains his first formulation of thedistinction between sense (Sinn) and reference(Bedeutung). Roughly speaking, the sense of an expression isthe mode of presentation of its referent, or the cognitive value ofits referent. Expressions were said toexpress their senses.Sentences, too, had both referents and senses, according to Frege. Thereferent 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 senseof a proposition: a sharable content. Thus, in Fregean jargon,meaningful sentences express thoughts.

Frege conceived of thoughts as structured complexes of senses. Thethought expressed by ‘The evening star is bright’ consistsof the sense of ‘the evening star’ and the sense of‘is bright’. (It should be noted that this claim aboutstructure does not strictly follow from the fact that sense iscompositional, i.e., that the sense of a whole expression is fixed bythe senses of its constituent parts and their syntactic mode ofarrangement.) In his late masterpiece, “The Thought”(1922), Frege is explicit about the nature of thoughts. They are notpart of the outer realm, which consists of those entities perceivableby the senses. This Frege thinks is obvious. Nor are they part of theinner realm, which consists of ideas. Unlike ideas, thoughts do notrequire 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 berecognized, he tells us—a realm of abstract eternal entitieswhich we cangrasp by virtue of our power of thinking.However, Frege is explicit that thoughts do act:

Thoughts are not wholly unactual but their actuality is quitedifferent from the actuality of things. And their action is broughtabout by a performance of a thinker; without this they would beinactive, at least as far as we can see. And yet the thinker does notcreate them but must take them as they are. They can be true withoutbeing grasped by a thinker; and they are not wholly unactual eventhen, at least if theycould be grasped and so brought intoaction (Beaney 1997, p. 345).

This is perhaps thelocus classicus for platonism in themodern sense of that term, that is, for the doctrine that there existmind-independent abstract entities.

In their early writings, Russell and Moore endorse propositionalism.In his 1903 bookThe Principles of Mathematics, Russellaffirms the existence of propositions, taking them to be complexes ofordinary concrete objects (the referents of words) rather than ofFregean senses (p. 47). Propositions so conceived are now standardlycalledRussellian, and propositions conceived as complexes ofsenses or abstract entities are calledFregean. In his 1899paper, “The Nature of Judgment,” Moore affirms theexistence of propositions, taking them to be broadly Fregean in nature(in particular as being complexes of mind-independent Platonicuniversals which he calls concepts).

Russell and Moore later grow suspicious of propositions (althoughRussell seems to have accepted them later as a kind of derived orimmanent entity). Interestingly, Moore’s thinking on the matterseems to have changed dramatically during the winter of 1910–11,as his published lecturesSome Main Problems of Philosophyreveal. Before Christmas, Moore claims:

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

After Christmas, Moore is more skeptical. While the theory ofpropositions is admittedly simple and natural (p. 286), there are goodreasons to reject it. He specifies two problems, both having to dowithfacts, a topic he avoided in his earlier lectures. Thefirst is that the theory of propositions suggests the“primitivist” theory of truth, previously held by Mooreand also Russell, according to which truth is a simple unanalyzableproperty of propositions. Primitivism, Moore now claims, requires theclaim that facts consist in the possession by a proposition of thesimple property of truth. This Moore now finds unacceptable. Thesecond problem is simply that the theory seems intuitively false:

…if you consider what happens when a man entertains a falsebelief, it doesn’t seem as if his belief consisted merely in hishaving a relation to some object which certainlyis. It seemsrather as if the thing he was believing, theobject of hisbelief, were justthe fact which certainly isnot—which certainly is not, because the belief isfalse. (p. 287)

Russell echoes similar sentiments in essays afterPrinciples.In 1910 he writes that “we feel that there could be no falsehoodif there were no minds to make mistakes” (Slater 1992, p. 119),and in the 1918 he remarks that a person with “a vivid instinctas to what is real” cannot “suppose that there is a wholeset of false propositions about ” [Russell 1956, p. 223).

These doubts led Russell (1912) to propose a multiple relation theoryof judgment, to replace the standard two-place relational theory(which is discussed at length in section 3.1). To use Russell’sexample, in judging that Desdemona loves Cassio, Othello stands, notin a binary relation to a proposition, but rather in a multiple ormany-placed relation to Desdemona, loving, and Cassio. Othello’sjudgment is true when there is a fact of Desdemona loving Cassio andotherwise false. This theory, and its contemporary incarnations, isdiscussed in a supplementary document.

Moore’s doubts led him to postulate what appear to be merelypossible facts as the objects of the propositional attitudes. When asubject believes that x is F and x is not F, the object of belief isthe non-existent but possible fact that x is F. See section 9 belowfor further discussion of possible facts and their relations topropositions.

2. Roles for Propositions: Modality

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

If possible worlds are understood in this way, however, it isimportant to distinguish two meanings for talk of ‘the actualworld’. This may refer either to the totality of what exists, towhat Lewis calls “I and all my surroundings”, or to themaximal consistent set which includes all the true propositions. Thelatter is part of I and all my surroundings, but only a properpart.

3. Roles for Propositions: Semantics

3.1. The Relational Analysis

By our stipulation, ‘proposition’ is used to pick out theobjects of the attitudes and the bearers of truth and falsity. Onewould therefore expect that if there are propositions, they wouldfigure importantly in the semantics of attitude- andtruth-ascriptions. One would expect, in particular, that in‘\(S\) believes that \(p\)’, and in ‘that \(p\) istrue’, thethat-clauses would refer to propositions.^[3]

One might doubt whetherthat-clauses could reallyrefer, if reference is understood on the model of propernames. For,that-clauses are not proper names, nor are theynoun phrases.^[4] Still, because propositions are the objects of the attitudes and thebearers of truth, mustn’t they somehow be semanticallyassociated with ascriptions of attitudes and of truth? FollowingJeffrey King (2002), we will use the term ‘designate’ as acatch-all covering any sort of semantic association between alinguistic item and an entity. We follow standard terminology in usingthe word ‘express’ to pick out the relation between apredicate and the property which is its sense or semantic content.

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

The Relational Analysis of Attitude Ascriptions:: An attitude ascription ‘\(S\) \(V\)s that \(p\)’ istrue iff ‘\(S\)’ designates a person who stands in theattitude relation expressed by ‘\(V\)’ to the propositiondesignated by ‘that \(p\)’ (and false iff‘\(S\)’ designates a person who doesn’t stand insuch 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 ofwhich we will simply callThe Relational Analysis—isthe 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 twoprimes.
So, John believes Goldbach’s Conjecture.

These inferences are valid if they have the following simple logicalforms:

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 didnot 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 themore standard terminology, thesemantic contents ofsentences, and so are commonly taken to be central to semantics andthe philosophy of language. However, there is room for doubt aboutwhether propositions are the right sort of entity for the job (Lewis1980). Here is why. Note that a sentence would appear to contributethe same content regardless of whether it occurs as a proper part of alarger sentence. So, a sentence such as ‘in the past, Reagan waspresident’ would seem to be true depending on whether thecontent of ‘Reagan is president’ is true at some pasttime. But this would seem to imply that this content must lacktemporal qualification—that it can change in its truth-valueover time. Similarly, it seems there are locative sentential operators‘in Chicago, it is raining’. If so, then by a similarargument, it would seem that the content of ‘it israining’ would have to lack spatial qualification. The problemis this: it seemspropositions, being the objects of belief,cannot in general be spatially and temporally unqualified. Supposethat Smith, in London, looks out his window and forms the belief thatit is raining. Suppose that Ramirez, in Madrid, relying onyesterday’s weather report, awakens and forms the belief that itis raining, before looking out the window to see sunshine. What Smithbelieves is true, while what Ramirez believes is false. So they mustnot believe the same proposition. But if propositions were generallyspatially unqualified, they would believe the same proposition. Ananalogous argument can be given to show that what is believed must notin general be temporally unqualified.

If these worries are well-taken, then the meanings or contents ofsentences 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 abovearguments, that there are no genuine locational or temporal operatorsin English. King claims that ‘somewhere’ and‘sometimes’ are better regarded as quantifiers overlocational and temporal entities (i.e., either locations and timesthemselves 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 asquantifiers over times rather than temporal operators. ‘Johnflunked chemistry’, thus, would have the form ‘there issome 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 thatpredicates like ‘is raining’ and ‘flunks ’include extra argument places for locations and times.

King emphasizes that his argument is thoroughly empirical. It relieson results from empirical linguistics. If King is right, however, theview that the contents of sentences are propositions can bemaintained.

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 commonalitiesbetween beliefs, utterances, or sentences, and infers a common entity.Thus, it has been suggested, less in print perhaps than inconversation, that propositions are needed to play the role of beingwhat synonymous sentences have in common, what a sentence and itstranslation 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 singleentity. Two red things have something in common, in that they are bothred, but it does notfollow that they bear a common relationto a single entity, the universal of redness. Similarly, twosentences, in virtue of being synonymous, can be said to havesomething in common, but that fact alone does not entail they arecommonly related to a proposition. When a relation \(R\) is symmetricand reflexive with respect to a certain domain, it may be useful tospeak of the things in the domain which bear \(R\) to one another as“having something in common”, but nothing of ontologicalsignificance follows. Thus, the conclusion is drawn: we need anargument for thinking that commonalities require common relations to asingle entity.

4.2 Metalinguistic Arguments

One standard sort of argument for propositions is metalinguistic.Thus, many argue that we think ofthat-clauses as designatingexpressions if we are to explain how certain argument patterns (suchas those considered in Section 2) are valid and in fact have soundinstances (Horwich 1990, Higginbotham 1991, Schiffer 1996, Bealer1998). Since some of these sound argument instances contain aspremises sentences attributing truth to the designata ofthat-clauses, those designata must be bearers oftruth-values. Similarly, premises of some of these sound instancesascribe attitudes toward the designatum of athat-clauses,these designata would seem to be objects of attitudes. In brief, inorder to explain these facts about validity and soundness, it seemsthat-clauses must not only designate but must designateentities fitting the propositional role.

Whether propositions are needed for the semantics of natural languageis a matter of continuing dispute. For more on these matters, see theentry ontheories of meaning.

4.3 The Metaphysics 101 Argument

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

When someone has a belief, we can distinguishwhat shebelieves fromher believing it. I have a belief thatHomer wroteThe Iliad, for example. We can distinguishwhat I believe in believing that Homer wroteTheIliad—the content of my belief—frommy believingthat Homer wrote The Iliad. What I believe in believing this issomething you believe, too. What we both believe is the propositionthat Homer wroteThe Iliad. This same proposition may beasserted, doubted, etc. And, in fact, this proposition is true: HomerwroteThe Iliad. So, there are propositions, and they are thecontents of beliefs and other attitudes and they are the bearers oftruth and falsity.

One might attempt to regiment these remarks, somewhat artificially, totake the form of an argument, which we will dub theMetaphysics101 argument:

With respect to any belief, there iswhat is believed andthe believing of it, and these are distinct.
What is believed is something that may be rejected, denied,disbelieved, etc. by multiple subjects, and is something that may betrue or false.
There are beliefs.
So, there are propositions (i.e, sharable objects of the attitudesand bearers of truth-values).

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

The Metaphysics 101 Argument is not metalinguistic. It does not relyon premises about English. This can be verified by noting that theargument looks just as good after it is translated into otherlanguages. Nevertheless, it might be claimed that the argument derivesits apparent force from a seductive mistake about how English (andother languages) function. Perhaps this is another case of whatWittgenstein 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 oughtnot accept propositions. Any such argument will involve controversialclaims about the nature and status of propositions. These issues arediscussed in section 7. However, one increasingly popular reply toarguments for propositions is to argue, (1), that they presuppose theRelational Analysis, and (2), that the Relational Analysis does a poorjob of accounting for certain linguistic data.

5.1 The Substitution Problem

The problem here is quite simple. If, as the Relational Analysisentails, attitude-ascriptions of the form ‘\(S\) \(V\)s that\(p\)’ assert relations to propositions, then we should be ableto replace ‘that \(p\)’ with ‘the proposition that\(p\)’ without affecting truth-value. But in general wecan’t do this. Therefore, the Relational Analysis is false. Hereare 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 problemsarise—the “problematic” attitude verbs—can bedivided into two subclasses: one consisting of verbs which do notgrammatically tolerate substitutions (e.g., intransitive verbs such as‘insist’, ‘complain’, ‘say’, andVPs of the form ‘Aux Adj’, such as ‘ispleased’, ‘was surprised’); the other consisting ofverbs which grammatically tolerate substitutions but for whichtruth-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 theSubstitutionProblem. (See also Vendler 1967, Prior 1971, Parsons 1993, Bach1997, McKinsey 1999, Recanati 2000, King 2002, Moffett 2003, Harman2003.)

5.2 The Objectivization Effect

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

The problem here can be described as follows. If the RelationalAnalysis is true, then propositional attitudes are relations topropositions; but then it seems very odd that we should be unable toretain the content meaning by substituting ‘the proposition that\(p\)’ for ‘that \(p\)’.

5.3 Defensive Responses

Defensive Response #1. The above arguments against theRelational Analysis prove too much. Similar problems arise for theappeal to facts (as distinct from true propositions), properties, andevents in semantics. Here are several examples of substitutionfailures.

\(S\) 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 aproblem around rather than solve it. One might argue that relationalanalyses invoking propositions, facts, properties, and events all makethe same mistake of reading too much ontology into English.

Defensive Response #2. From ‘\(S\) believes that\(p\)’ wecan infer ‘\(S\) believes theproposition that \(p\)’ and ‘\(S\) believes aproposition.’ And the same goes for ‘reject’,‘assert’, ‘deny’, and many other attitudeverbs. If we concede that these sentences assert relations topropositions, then we are conceding that there are propositions.

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

5.4 The Syntax Response

Next, following Jeffrey King (2002), the propositionalist might give apurely syntactic answer to the problems. King (pp. 345–6)claims, first, that there is a very simple syntactic explanation forthe substitution failures that produce ungrammaticalities: such verbsdon’t take NP complements at all, and so don’t takenominal complements, which are NP complements. (A verb can takethat-clause complements without taking NP complements,becausethat-clauses are not NPs.) One might say somethingsimilar, for example, about why we cannot substitute descriptions fornames in apposition (e.g., ‘The philosopher Plato believed inuniversals’ is true but ‘the philosopher the teacher ofAristotle believed in universals’ is not true.) King claims,second, that the other class of failures are explained by shifts inverb meanings (i.e., because of objectivization). These shifts are dueto syntactical matters, in particular the syntactic category of theverb complement. If the complement is an NP, the verb has an objectmeaning. If it is athat-clause, it has the content meaning.King recognizes the need for qualifications: verbs in the problematicclass can have the content reading with certain special NPs, e.g.,quantifiers (‘everything Bill holds, Bob holds’), andanaphoric pronouns (‘I hold that, too’.). In the finalanalysis, King claims only that all the syntactic properties of thecomplement (and not just its general syntactic category) determine theverb’s meaning when taking that complement.^[8]

5.5 Semantic Responses

The relationalist might respond by making claims about the semanticsofthat-clauses, ‘the proposition that \(p\)’, orsome combination of these. We discuss two such proposals here.

First, the relationalist might claimthat-clauses areambiguous, and in particular that they pick out different kinds ofentities depending on which attitude verb they complement. How do wetell what kinds of entities are picked out? We look at substitutionfailures. Thus, it might be argued the truth of ‘\(S\) remembersthat \(p\)’ requires that the subject bear the rememberingrelation 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, someattitude verbs seem not to permit substitutions no matter whichnominal complement is chosen. King (2002) gives the example of‘feel’. What sorts of entities, then, dothat-clauses designate when they complement‘feel’? No answer is possible. Is the Relational Analysistherefore false of such verbs? Perhaps even more damaging, there areverbs which are near synonyms of ‘believes’, at least inattitude ascriptions, and which grammatically take NP complements, butwhich exhibit substitution failures and objectivization.‘Feel’ is one example, as are ‘maintain’,‘hold’, ‘judge’, ‘expect’, and‘suspect’. How could ‘believes’ designate arelation 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 propositionalistwith a general solution to theSubstitution Problem and theObjectivization Effect, it may help in explaining otherlinguistic phenomena, such as the distributional differences betweenvarious 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 thetraditional view thatthat-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 thisview, denotepropositional concepts—functions fromsituations 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) arguedthat ‘the number of insect species’ does not denote anumber, but an individual concept—a function from situations(world-time pairs) to individuals (in this case, a number). The copulain the second premise specifies, rather than equates, the value of theindividual concept relative to this situation.

Nebel presents an analogous puzzle involving a proposition-likedescription:

The evidence that vaccines cause autism is that vaccines containthiomersal
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 theproposition that provides evidence for \(p\) in that situation. The‘is’ of the first premise again specifies the propositionthat is the value of the propositional concept in that situation; itdoes not state an identity between ‘the evidence that\(p\)’ and ‘that \(q\)’. In general, all propositiondescriptions are said to denote propositional concepts. In the case of‘the proposition that \(p\)’, the propositional concept isa constant function that designates the same proposition in everysituation.

Nebel supports this view by noting particular uses of propositiondescriptions. 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 theassassination of Franz Ferdinand being the cause of WWI, and theproposition that Fido barks being the denotation of ‘that Fidobarks’. To explain this, Nebel appeals to the notion of aconcealed question; in certain contexts—for instance,when the complement of ‘explains’ is a nounphrase—the meaning of the noun phrase is given by aninterrogative clause. Thus, (1a) means that the teacher explainedwhat caused World War I. In the same way, the propositiondescription in (2b) conceals a question, although it is a murkier, andoften context-sensitive, matter exactly which question is concealed.Nebel suggests that Sally explainedwhat the proposition that Fidobarks is, means, or involves.

If proposition descriptions sometimes function as concealed questions,then it is plausible that they share a semantics with interrogativeclauses. Interrogative clauses have been taken to denotequestionintensions, functions from situations to propositions that trulyanswer the question in that situation. If this is correct, thenquestion intensions are just propositional concepts. Nebel takes thisto provide evidence for his view: If proposition descriptions denotepropositional concepts (and not propositions), then we should predictthat proposition descriptions can be used as concealed questions incontexts which permit interrogative complements, which is what wefind.

Since ‘that \(p\)’ and ‘the proposition that\(p\)’ denote different entities, Nebel’s proposal seemsable to explain the substitution failures that result from replacingproposition descriptions forthat-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 andreturns a predicate that is true of Sally iff she believes thatproposition. In cases like (3), ‘believes’ takes anon-propositional entity (her mother) as argument and forms apredicate that is true of Sally iff she believes somecontextually-salient proposition that is associated with her mother.Nebel proposes that (2) is like (3); in this case, thecontextually-salient proposition associated with the propositionalconcept is that Fido barks. Thus, (1) and (2) have the same truthconditions, despite thethat-clause and propositiondescription denoting different entities.

One may object that many descriptions which denote proposition-likeentities (statements, rumors, claims, etc.) can take predicates thatdon’t apply to abstract objects like propositional concepts. Forexample, in the sentence ‘the rumor that Jim consumes peyote isvicious,’ the description ‘the rumor that Jim consumespeyote’ is said to denote the function from situations to theproposition rumored at that situation. But it seems to be a categorymistake to say that a propositional concept (or even a proposition) isvicious. Similarly, van Elswyk (2022) appeals to points made byMoltmann (2013) that certain descriptions permit causal predicates, asin ‘the statement that durian is pungent causedastonishment’. On Nebel’s view, ‘the statement that\(p\)’ denotes a propositional concept. But if propositionalconcepts are abstract, then they cannot enter into causal relations.On a more natural reading, the description designates an act ofstating (or perhaps its product, as Moltmann maintains), which can bea cause.

Finally, we may ask whether this view can explain the ObjectivizationEffect. If proposition descriptions denote propositional concepts, andthese are functions from situations to propositions, then why do weget the object readings with proposition descriptions? For ‘thenumber of insect species is increasing’ we do not get an objectreading for the NP, but a “structural” reading that makessense if ‘the number of insects’ denotes an individualconcept. The same applies to ‘the evidence that vaccines causeautism is scant’. However, in ‘John fears the propositionthat a bear is behind the tree’, we do not get a structuralreading. John does not fear the function itself, nor any structuralfeature of it. We get an objectual reading of the sort Kingpredicts.

5.6 Substitution and Objectivization Problems for Everyone?

Although the dominant view in the literature is that theSubstitution Problem and theObjectivization Effectare problems principally for defenders of the Relational Analysis(e.g., Prior 1971, Bach 1997, Recanati 2000, Moltmann 2003; 2004), itis intriguing to ask whether some version of these problems arise foreveryone—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 intaking nominal complements but which differ with respect tosubstitutions. This seems to be a fact that everyone must explain. Itseems likely that the substitutional differences must be explained interms of shifts in verb meaning. Because substitution does not affectthe meaning of ‘assert’, it must affect the meaning of‘claim’, and, intuitively, it does. This does leave thequestion of how theObjectivization Effect itself is to beexplained. But one might hope that a broadly syntacticsolution—perhaps like King’s—would be available toanyone, regardless of one’s stance on propositions.

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

That said, the relationalist may have to take account of otherlinguistic puzzles. She will need to explain why it sounds sopeculiar, e.g., to talk of “my believing what you desire, or mydreading what the thermometer indicated.” And, even with purelycognitive attitude verbs, similar puzzles arise: the mild peculiarityof “I doubt/assert what you contemplate/entertain,” forexample, will require explanation. (For more on these matters, seeVendler 1967 and Harman 2003.)

5.7 Modifying/Replacing the Relational Analysis

Let us suppose, for the sake of argument, the linguistic problemsdiscussed above undermine the Relational Analysis. Can apropositionalist dissociate herself from that analysis, and itslinguistic difficulties, while still endorsing the arguments wediscussed for propositions in section 5.1?

Some modifications of the Relational Analysis do not avoid thelinguistic problems. For instance, it is not enough to claim thatattitude verbs designatethree-place relations betweensubjects, propositions, and modes of presentation.

One possibility is to deny that attitude verbs designate relationswhen complemented bythat-clauses, and to claim that theyrather make a syncategorematic semantic contribution. Under oneapproach,that-clauses in attitude ascriptions designatepropositions which serve to “measure” attitudes conceivedof as mental particulars (Matthews 1994). It is not clear that thisview will be immune to substitution and objectivization problems. SeeMoltmann (2003) for further discussion.

Another possibility is to abandon the Relational Analysis altogether,in favor of a version of Bertrand Russell’s “multiplerelation” theory. Following Russell (1911; 1913; 1918), Newman(2002) and Moltmann (2003; 2004), have recently argued thatthat-clauses in attitude ascriptions do not designatepropositions but rather provide a number of entities as terms of a“multiple” attitude relation. These philosophersnonetheless do accept propositions, and use them to explain sentencesin which ‘proposition’ explicitly occurs, e.g.,(‘Some proposition that John believes is true’,‘John believes the proposition that snow is white’). Thebasic idea is that there are propositions, but they have the status of“derived objects”—derived from our attitudes, whichthemselves are not relations to propositions. It is an interestingquestion whether a Russellian is positioned to endorse the argumentsfor propositions given in section 4. (For more on the Russelliantheory, see the supplementary document:

The Multiple Relation Theory

An alternate proposal which abandons the Relational Analysis takesthat-clauses to be predicates. Van Elswyk (2020) argues thatthis explains whythat-clauses can compose with nouns, as in‘the belief that snow is white’, as well as whythat-clauses can follow the adverb ‘now’, as in‘now that Giannis will be named MVP, Giannis will be offered asupermax contract’. In the first case, thethat-clausespecifies 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’. Thethat-clause serves as a predicate thatis satisfied by \(e_2\). Even rejecting the Relational Analysis, vanElswyk finds a need for propositions as meanings of sentences and thethings 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 aprenective view of attitude reports inspired by Prior (1971).Whereas the Relational Analysis treats the attitude verb \(V\) inascriptions of the form ‘\(S\) \(V\)s that \(p\)’ ascontributing a dyadic relation between \(S\) and the propositiondesignated by ‘that \(p\)’, this view treats V asprenective, meaning that it acts as a predicate at one end and asentential connective at the other. So, the prenective view deniesthat ‘that \(p\)’ is a singular term, instead parsing ourascription as ‘[\(S\)] \(V\)s that [\(p\)]’, where‘\(p\)’ is a sentence that expresses the propositioncontent of S’s attitude. In denying thatthat-clausesare singular terms, Trueman avoids reifying propositions, and insteadidentifies propositional contents as truth-conditions of sentences.Thus, to believe the proposition that \(p\) is to stand in thebelieving relation to the truth-condition of ‘\(p\)’.

One might worry that the prenective parsing of belief reports clasheswith the syntactic data that motivated treatingthat-clausesas 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 thecomplementizer ‘that’ moves with ‘Sharon isfunny’ rather than staying put with ‘believes’.Trueman responds in two parts. First, the mere fact thatthat-clauses are syntactic units does not imply anythingsemantic about them—viz., that they are singular terms.(Hofweber 2016 gives a sustained defense of this point.) Second, hemodifies the proposal from Prior’s original parsing; rather than‘[\(S\)] \(V\)s that [\(p\)]’, attitude ascriptions areparsed as ‘[\(S\)] \(V\)s [\(p\)]’. The complementizer‘that’ is semantically vacuous, but functions to indicatethat ‘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 propositionsare the metalinguistic arguments and the Metaphysics 101 argument. Theformer arguments are plainly theoretical: they appeal to theexplanatory power of semantical theories invoking propositions. Toresist 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 thoroughlyintuitive, and so resisting the argument requires giving a story abouthow and why intuition goes wrong. In this section, we will considerone general strategy for doing this.

The Metaphysics 101 argument can seem Janus-faced: its premises seemutterly shallow, and yet its conclusion seems to resolve a deepontological debate. One is apt to think, “Sure, what I believeis different from my believing it. And so we can distinguish thecontent of a belief from the attitude of belief. These contents arepropositions. Fine, but now it seems there must be a domain ofentities here, whose nature remains to be investigated. How could thatbe?” One might suspect some sort of equivocation or ambiguity isat work, some oscillation between a shallow and a deepinterpretation.

6.1 The Internal/External Distinction

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

Relying on Carnap’s distinction, within certain linguisticframeworks, such as that presupposed by the Metaphysics 101 argument,it is almost trivial that there are propositions. All it takes issomething as superficial as the Metaphysics 101 argument, or thefollowing even less enlightening argument, “The proposition thatsnow 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 thepropositions outside such frameworks. Such questions have no cognitivecontent.

One of the chief difficulties for Carnap is to explain the truth ofinternal statements. If ‘there are propositions’ is true,even within a framework, what does its truth consist in? If truth in aframework is explained in terms of truthgiven the axioms of theframework, we will want to know about the truth-value of theaxioms themselves. If they are true, what makes them true? If they arenot true, why can’t we conclude that there really are nopropositions?

Even if we must reject Carnap’s internal/external distinction,perhaps some form of “Neo-Carnapian” ambiguity hypothesiscan help explain away the appeal of the Metaphysics 101 argument.

A number of questions arise for the Neo-Carnapian. First, how are theinternal and external readings to be distinguished? Second, howpervasive is the ambiguity? are there different readings not only forquantified sentences but for attitude- and truth-ascriptions as well?Third, what is the status of the Metaphysics 101 argument, given thetwo readings? The argument must be unsound when understood externally,but must it be invalid, or is it a valid argument with a falsepremise? If so, which is false? Fourth, how could philosophersregularly 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 byreference to fictions. Internal statements are statements made withinor relative to a fiction, and they are to be assessed as true or falserelative to the fiction.

However, any fictionalist interpretation of the internal/externaldistinction would have to explain why the fiction of propositions,like the fictions of properties and numbers, is not a mere game, butcan be used for describing reality. We will briefly discuss a kind offictionalism designed to do just this:figuralism. (Fordiscussion, see Yablo (2000, 2001), Yablo and Rayo (2001), Yablo andGallois (1998), and for a similar view, Balaguer 1998a and 1998b).

Relying on pioneering work by Kendall Walton (1990), Yablo argues thatpretense can serve serious practical and theoretical purposes. To useWalton’s example, by pretending that Italy is a boot, I caneasily convey to you the location of the Italian town of Crotone. HereI am, in effect, using a pretense to convey information about the realworld. Literally, Italy is not a boot, but my interest is not inspeaking the literal truth, but in conveying a rather complicated factto you as effectively as I can. Similarly, Yablo and Gallois claim,one may pretend there are certain entities in order to better conveycertain facts (1998, 245–8). One might pretend there aredirections in order to facilitate communication of facts about whichlines stand in which geometric relations to which other ones. Perhapsone could do the same with propositions?

However, Yablo (2001) emphasizes that the figuralist need not becommitted to any psychological thesis about making-believe.We may not consciously pretend that there are propositions when we saythat what we believe is true, just as we may not consciously pretendthat there are such things as stomach butterflies when we say we havebutterflies in our stomach. Figuralism requires only that there is asemantical distinction between literal content and figurative content,and that by asserting sentences with certain false or at least highlydoubtful literal contents, we may also express genuine facts, whichwould be well nigh impossible to express literally. (See Balaguer1998a and 1998b on the concept of representational aids)

Figuralism makes it possible to diagnose the failure of theMetaphysics 101 argument as follows. If its steps are interpretedliterally, the argument is unsound but valid. If its steps areinterpreted figuratively, it is sound. Why are we fooled, then? Onepromising suggestion is that it can be very difficult to distinguishfigurative from literal content, particularly when the figuresemployed have little presentational force.

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

6.3 Two Readings for Quantifiers

Some philosophers have suggested that ordinary English quantifiers aresusceptible to multiple readings, or different readings in differentcontexts of use. Thus, Hilary Putnam (1987, 2004) has argued thatthere is no single meaning associated with the vocabulary ofquantification, 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 speaktruly in asserting ‘any objects compose a further object’,whereas an assertion of the negation of this sentence might true indifferent contexts. (Note that Putnam is clear that the phenomenon heis describing isn’t mere quantifier-restriction.)

The acknowledgement of different meanings for the quantifiers is notenough by itself to explain away the intuitiveness of the Metaphysics101 argument. As we mentioned earlier, what is needed is an account ofthe apparent oscillation between a shallow and a deep interpretation.There could, in principle, be a plurality of interpretations of thequantifiers even if none of the readings differed with respect tometaphysical depth.

Recently, Thomas Hofweber (2005, 2016) has claimed to have found therequired pair of readings. A quantifier, he claims, may have either adomain-conditions orinferential role reading. Thedomain-conditions reading is just the familiar reading we know fromfirst order semantics: ‘there are \(F\)s’ is true iffthere exists an entity in the relevant real domain which satisfies‘\(F\)’. This reading is therefore ontologicallycommitting and sodeep (and thus external). The inferentialreading, by contrast, brings with it no ontological commitment, and sois shallow (and thus internal).

Hofweber explains that the inferential role reading serves animportant function. It enables us the easy expression of partialinformation. For example, I might not recall a name or uniquedescription of Fred’s favorite detective, but if I want expressthe partial information I have, I can do this by saying “Fredadmires some detective.”. Now, on the domain-conditions reading,what I express is false, and so I have misinformed my audience. Whatwe need, to achieve the desired end, is a reading for ‘there isan \(F\)’ which validates existential generalization, regardlessof whether the names occurring in the premise refer to an entity. Thisis what the inferential role reading provides. Thus, we say“Fred admires some detective—yes, it’s SherlockHolmes!”

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

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

For an account like Hofweber’s to succeed, it must be possiblefor attitude- and truth-ascriptions to be true even ifthat-clauses do not designate. For if they designate, thenthe 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 torather dramatic answers to questions about the nature and status ofpropositions. Below is one standard line of argument, versions ofwhich can be found in Bealer (1998) and Schiffer (2003). (See alsoCartwright (1962) and Soames (1999).)

The proposition that there are rocks, which we denote \(\ltb\)thereare rocks\(\gtb\), does not entail the existence of any beings thathave or are capable of having mental states. It entails this neitherin a strictly or broadly logical sense. That is, it ispossible in the broadest sense for \(\ltb\)there arerocks\(\gtb\) 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 ismind-independent. This is an easy argument for the mind-independenceof at least some propositions.

A parallel “easy argument” can be given for theabstractness of at least some propositions. \(\ltb 2+2=4\gtb\) doesnot entail the existence of concrete entities. So it is possible forit 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 ofabstract entities, then it follows that \(\ltb 2+2=4\gtb\) is in factabstract. One might want to extend such arguments to contingentpropositions. Consider \(\ltb\)there are trees\(\gtb\). Thisproposition is false in a world without concrete entities. But if itis false in such a world, it must exist in that world, and so ispossibly, and so actually abstract.

Similar arguments can be constructed for properties. If properties arewhat weassert of objects and what istrue/false ofobjects, then there are simple arguments for the conclusion that atmany properties are mind-independent and abstract.

It is dangerous to generalize these sorts of “EasyArguments” toall propositions (particularly singularpropositions). But even if they cannot be fully generalized, theythreaten to show that propositions would be mind-independent abstractentities. Now, given that propositionsde jure are sharableobjects of attitudes, it is antecedently unlikely that they shouldturn out to be, say, token utterances. But one might have thought thatpropositions 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 acceptpropositions, we must accept Platonism.Conceptualism aboutpropositions seems ruled out.

Many philosophers deny that there are propositions precisely becausethey accept the validity of these Easy Arguments (and the truth ofcertain attitude ascriptions). There are familiar problems besettingthe believer in abstract entities. The two “Benacerrafproblems,” in particular have received much attention in theliterature: the epistemological problem and identification problem.The epistemological problem for abstract propositions, roughly, isthis: how can we know about abstract propositions, given that wecannot causally interact with them? The identification problemrequires a bit more explanation. If propositions are abstract, thenthere will be many distinct candidates for propositions which seem toplay the proposition role equally well. If certain entities, the\(F\)s, are candidates for being propositions, why won’t theentities consisting of an \(F\) paired with the number 1 count asadequate candidates as well, so long as we reconstrue predicates forpropositions in such a way as to make the number 1 irrelevant? Butpropositions cannot be both \(F\)s and these new entities, becausethese new entities are not \(F\)s. Is it simply indeterminate whatpropositions are? See the entry onplatonism in metaphysics. (See also J. Moore 1999.)

The Easy Arguments can appear suspicious. How can the seeminglyobvious acknowledgement that there are propositions—i.e., thatbeliefs have sharable objects which bear truth-values—commit usto there being mind-independent abstract entities? We will discuss twosorts of reply found in the literature. Both are objections to theinference from there being propositions to the claim thatpropositions have the surprising features. We are putting asideobjections to the claim that there are propositions.

7.2 Reply #1: Truthin a World vs. Truthat 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 \(\ltbp\gtb\) to be true while not-\(q\).

This assumption is needed to reason from premises about propositionsfailing to entail other propositions about there being mental statesor being concrete entities to the possible truth of those propositionsin 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 theformer is true and not-\(q\)?

Some philosophers (Pollock 1985, King 2007) have argued thatprinciples like (A) have two readings, one clearly acceptable butuseless to the Easy Arguments and the other useful to those argumentsbut false. The two readings correspond to two ways of understandingtalk of truth with respect to possible worlds. One way for somethingto be true with respect to a world requires the truth-bearer to existin the world and be true there. Another way is for the truth-bearer to“correctly describe” the world, where this does notrequire existing in the world. Pollock gives the example of a picturedepicting the non-existence of all pictures. The picture couldcorrectly depict a situation even though the situation it depicts isone in which the picture itself does not exist. Similarly, theMedieval philosopher Jean Buridan discusses the example of anutterance of ‘there are no negative utterances’. Thisutterance correctly describes a certain possible situation even thoughthat situation is one in which the utterance would not exist.Following Adams (1981), we may call the former way of being true withrespect to a worldtruth in a world and the lattertruthat a world. The conceptualist may claim that propositions can betrue at worlds without being true in them, by analogy with theexamples from Pollock and Buridan. A proposition like \(\ltb\)thereare no propositions\(\gtb\) is true at certain possible worlds buttrue in none. Since we do not want to say that such propositions arenecessary, we must understand necessity as truthat everypossible world. Correspondingly, to preserve the connections betweenentailment and necessity, we must understand entailment in terms ofthe entailed proposition being true at every world at which theentailing proposition is true. Given all this, we can distinguish tworeadings 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 \(\ltbp\gtb\) is truein \(W\) 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 \(\ltbp\gtb\) is trueat \(W\) 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 2is true but useless to the Easy Arguments. Thus, the conclusions ofthose arguments are blocked.

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

If worlds are concrete particulars (“I and all mysurroundings”), as they are for David Lewis (1986), then wecould say that a proposition is trueat a world if theproposition is about the entities that are parts of that world and istrue, and truein a world if true at a world and also part ofthat world. There may well be difficulties of explaining how aproposition could be part of more than one concrete world (and why itwould only be part of some concrete worlds but not all), but thisframework seems to make conceptual room for the possibilitypropositions 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 understandwhat is true at a world in terms of what is true in it, together withcertain facts about the actual world. However, the conceptualistcannot abide this approach. For, on this approach, the members of anyworld are true in that world. But since the members of any and everyworld are propositions, it would follow that, contrary toconceptualism, that it is necessary that there are propositions. Amore conceptualist-friendly approach is to reverse the order ofexplanation, 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? Anatural proposal is to understand it as membership in a worldstory.

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

The conceptualist might hope to take the relevant notion ofconsistency as primitive and reject the gloss in terms of jointpossible truth. Still, we should ask about the broader implications ofdenying the joint possible truth of consistent world stories.Consider, for instance the notion of actuality. Only one of the manypossible worlds is actual, although each is actual relative to itself.The actual one, on the world story view, is the one all of whosemembers are true. But if this is what actuality for worlds amounts to,then assuming possible worlds are possibly actual, it would followthat 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 fallingback on Lewis’s concrete realism about possible worlds, byunderstanding worlds in terms of properties or states of affairs,rather than propositions. Following Stalnaker (1976), one might thinkof worlds as properties which are ways things could have been.Following Plantinga (1974) and others, one might think of worlds asmaximal consistent states of affairs, where these are thought of asdistinct from propositions.

However, this retrenchment may end up only shifting the Platonistworries elsewhere. To distinguish theways that are possibleworlds (or possible world-states) from those which are not, it isdifficult to avoid appealing to a gloss in terms of being possiblyinstantiated: the possible worlds are not only maximal but they couldbe instantiated. Taking this line would require conceding that inevery world there are properties. Something similar holds for theconception of possible worlds as maximal consistent states ofaffairs.

One might think, however, that Platonism about properties is lessproblematic than Platonism about propositions. The former do notrepresent the world, whereas the latter, as truth-bearers, do (Jubien2001, King 2007). However, properties can apply or fail to apply toobjects, and can be said to be true or false of objects, and so it isnot clear that worries about representation clearly gain more tractionfor propositions than for properties. Similar considerations apply tostates of affairs.

Despite these worries, the conceptualist might be encouraged by theexample of singular propositions. Hasn’t the truth in vs. truthat distinction been useful in dealing with the modality of singularpropositions? For example, consider any singular proposition aboutSocrates, e.g., the proposition that Socrates was a philosopher. Suchpropositions, plausibly, depend for their existence on the object theyare directly about. One might therefore think that no singularproposition about Socrates could exist unless Socrates existed.Consider, then, the proposition that Socrates does not exist. It isclearly contingent that Socrates exists; things could have beenotherwise. But then the proposition that Socrates does not exist wouldappear to be possible without being possibly true. Unlike the examplesfrom Pollock and Buridan, however, we cannot understand suchpossibility without possible truth in terms of expressing a possiblytrue proposition while not being possibly true itself. Propositions donot express propositions, of course, and so we cannot understand theirpossibility without possible truth in this way (Plantinga 1981). Whatis it, then, for such a singular proposition to be possible but notpossibly true? Answering this question was one of the key motivationsin the development of the distinction between truth in and truth at aworld. But while Adams and others attempted to do this by thinking oftruth at a world as determined by what is true in that world togetherwith a certain set of facts about the actual world, the conceptualisthopes to kick aside the ladder of truth in a world altogether. Whetherthis hope is reasonable or not is an important issue in contemporarywork 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 deflatetheir significance by deflating propositions. The Easy Argumentssucceed, but their success marks no great philosophical discovery andraises no hard questions of the sort that have traditionally botheredmetaphysicians 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 isnothing more to them than what our concept of a propositionguarantees. One may call them “abstract entities,” if onelikes, but this label should not encourage the thought that our mindscan reach beyond the physical world to make contact with denizens of aPlatonic universe. We know about propositions, not by interacting withthem, as we do with rocks and cats, but by being participants incertain sorts of linguistic or conceptual practice. It’s becausewe speak or think in certain ways that we are able to know aboutpropositions.

Schiffer argues, in effect, that given our proposition-talk andthought, propositions are, in D. M. Armstrong’s phrase, a kindof “ontological free lunch.” That is, the key“axioms” of our proposition-talk and thought areguaranteed to be true. These include the instances of the equivalenceschema (E) for propositions:The proposition that \(p\) is trueiff \(p\). Given the truth of such axioms, it follows thatpropositions exist and have the features attributed to them by ouraxioms. Moreover, because these axioms are constitutive of the conceptof a proposition, it follows that, by possessing that concept, we canknow the truth of these axioms.

One might concede to Schiffer that the axioms are constitutive of ourconcept 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. Themind-independence of propositions, after all, is implicit in thoseaxioms.

Schiffer’s argument for pleonastic propositions is of a piecewith his argument for pleonastic entities generally, includingfictional entities, events, and properties. A pleonastic entity, forhim, is an entity that falls under a pleonastic concept. The latter isthe key notion and is defined as follows.

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

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

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

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

Schiffer’s final formulation of the conservativeness testis:

For any theory \(T\) and sentence \(S\) expressible in \(T\), if thetheory obtained by adding to \(T_{/{\sim}F} \ltb\)the theory resultingfrom restricting quantifiers in \(T\) to \({\sim}F\)s\(\gtb\) theconcept of an \(F\), together with its something-from-nothing\(F\)-entailment claims, logically entails \(S_{{\sim}F}\ltb\)thesentence 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, andthat all that matters is that the new entities not interfere with theempirical world. If so, then the test would mention only empiricaltheories not all theories. But, as Matti Eklund (2007) points out, twokinds of entity that are individually non-interfering with respect tothe empirical world might interfere with one another. Schiffer isaware of this problem (see his discussion of anti-fictional entities,pp. 55–6), and this is why he turns to the more complicatedaccount.

Schiffer’s picture is this. If a concept satisfies theconservativeness test, then its instantiation would be unproblematicbecause it would interfere with nothing else. Its instantiation comesfor free. If a concept doesn’t meet this test, it doesn’tcome for free.

Although Schiffer’s view of propositions can be described asdeflationary in one sense (because it attempts to deflate questionsabout the existence and nature of propositions), the meta-ontologyunderlying Schiffer’s approach is, if anything, inflationary:all “non-interfering” kinds of entity areinstantiated.

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

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

Even if \(F\)s would be non-interfering in Schiffer’s sense, thepostulation of \(F\)s logically conflicts with some consistenttheories, e.g., ‘There are no \(F\)s’. Schiffer placesseverer constraints on the denial of entities than on the acceptanceof them. Suppose \(F\)s would be non-interfering. Then adding themwould not add information about non-\(F\)s. But suppose also thatdenying \(F\)s would not add information about non-\(F\)s. Whyisn’t this a reason to deny \(F\)s? So, in this sense, thetheory denying \(F\)s passes a corresponding conservativenesstest.

(2): How can the deflationist explain how these propositions havetruth-conditions?

If the proposition that snow is white is a simple, necessary andeternal object, why does its having a property (truth) have anythingto do with concrete snow’s having a property (whiteness)? Doinstances of the T-schema simply state brute necessary connectionsbetween abstract objects and concrete ones? Or do these necessaryconnections 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 accepttheir conclusions but to give an account of the nature of propositionswhich will make these conclusions palatable. One promising line ofthinking, in this regard, is to think of propositions as types, thetokens of which are mental or linguistic acts or events, and inparticular the acts that would be thought toexpress theproposition. Such views have been developed in recent years by Dummett(1996), Hanks (2011, 2015), and Soames (2010, 2014a, 2015). We focushere on the recent proposals put forth by Hanks and Soames.

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

Two problems arise for the Platonist’s position. First, how docognizers come to be acquainted with such propositions? Second, whatexplains how propositions represent things as being a certain way?Platonists appear to have no answer to the epistemic question, andpresumably accept representation as a primitive feature ofpropositions. Type theorists, however, explain the relation between acognizer and a proposition simply as an instance of the generalrelation between type and token. Consider, as Dummett (1996, p. 259)does, one’s humming of a tune. The tune is a species or type ofmusical performance capable of having multiple performances atdiffering times or locations, while the humming of it is a token actbelonging to that type. One might then see the relation of aproposition to a mental or linguistic act as one between the type ofact performed and the performance of the act.

What type of acts should one identify with propositions? For bothHanks and Soames, propositions are types ofpredicative acts.The notion of predication here is simply, for atomic propositions, oneof an agent’s representing an object \(o\) as having property\(F\). (Hanks (2015, p. 64) characterizes predication ascategorization, or the sorting of things into groupsaccording to a rule. We will take this to be a form ofrepresentation.) Since representation is primarily something done bycognitive agents, according to Hanks and Soames, one might wonderwhether the proposition itself is representational, and so possessestruth-conditions, on the type view. Both theorists respond to thisconcern by claiming that propositions are representational in asecondary, derivative sense. There are many examples of types thatinherit features of their tokens (a sonata (type) can be discordant invirtue of performances of it being discordant; a movie can befrightening in virtue of its tokens being so, etc. See the entry ontypes and tokens.) Just as anact can be described as intelligent in order tocommunicate that theagent acted intelligently in performingthe act, type theorists will claim that a proposition represents \(o\)as \(F\) in a similarly derivative sense wherein any agent whoperforms the act of predicating \(F\) of \(o\) will thereby represent\(o\) as \(F\). One question that arises for such a view is whetherpropositions are genuinely representational entities withtruth-conditions, or whether the claim that a proposition representsthings as being a certain way is simply a convenient manner ofspeaking indirectly about the actual and possible representationalacts of thinkers.

As we have seen, the type view reverses the traditional order ofexplanation concerning the nature of predication, representation, andtruth-conditions. On the traditional, Fregean picture, propositionsexist as objective, mind-independent entities “waiting” tobe entertained, judged or asserted, so to speak. On this view, for asubject S to predicate \(F\) of \(o\) is for S to entertain theproposition that \(o\) is \(F\); for S to represent \(o\) as \(F\) inthought or language is to have a thought or utterance with theprimarily representational propositionthat o is F as itscontent, etc. On the type view, a proposition’s representationaland predicative properties are derived from the fundamentallyrepresentational and predicative acts of agents.

A concern for the type view is whether there will be “missingpropositions”—truths or falsehoods which have never beenentertained. One drawn to the type view may allow for the existence ofuninstantiated types to account for the existence of thesepropositions. However, given that propositions are claimed to derivetheir representational features from their tokens, such uninstantiatedtypes would lack representational features, and so lacktruth-conditions. Hanks suggests dealing with such propositionscounterfactually. Even if no one had ever predicated eloquence ofClinton, the proposition that Clinton is eloquent is true iff Clintonis eloquent because if someonewere to predicate eloquence ofClinton, the token would be true iff Clinton is eloquent. Predicativetypes, then, inherit their representation features from both theiractual and possible tokens. This response, however, leaves us with thequestion of truths for which there are not even any merely possibletokens—for example, mathematical truths that are too complicatedfor any finite mind to grasp. What, if anything, provides thetruth-conditions of these propositions?

Hanks (2015, p. 27) allows that propositions are mind-independent andobjective entities which do not depend for their existence on havingany tokens, just as one might think about a difficult type of divethat has never been performed. Thus, while Hanks’ view appearsto be a rejection of a traditional Platonism about propositions, itseems nevertheless to accept a Platonism about types by untetheringtheir existence from their tokens. (Compare to Dodd’s (2007)defense of Platonism about types.) Soames (2014a,b) also allows foruntokened types, but only those whose constituents have been referredto or predicated in other propositions. For Soames, a proposition\(p\) may exist in \(w\) even if no token of \(p\) has been performedin \(w\). For Soames, if in \(w\) a predicative event has occurred inwhich 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 ofact 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, itwould seem that there can be truths in a world about objects that havenever been thought of or referred to in that world. In response tothis, 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 toother, albeit controversial, cases in which an object can have aproperty despite not existing. For instance, Socrates can have theproperties ofbeing referred to orbeing admireddespite no longer existing. Thus, Soames’ accommodation of ourintuitions concerning propositions that have never been thoughtappears to involve a rejection of Actualism.

The type view has been argued to provide solutions to severaltraditional problems for propositional thought, includingFrege’s puzzle, first-person belief, Kripke’s puzzle aboutbelief, and the problem of empty names. In responding to theseproblems, Soames invokes “Millian modes of presentation,”or ways of cognizing an object in thought which do not affect therepresentational content of the act, to preserve a non-Fregean,Millian view of semantic content for names and natural kind termswhile individuating propositions finely enough to solve traditionalproblems in the philosophy of language. Hanks, by contrast, invokesdistinct types of referential and expressive acts as the constituentsof propositions. On this view, each use of a name falls under severaldifferent 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 theperceived need to explain how propositions represent things as being acertain way on the grounds that a view which accepts primitivelyrepresentational propositions is objectionably mysterious. Somequestion, however, whether the representational properties ofpropositions can (or need to) be explained at all (McGlone 2012,Caplan, et al. 2013, Merricks 2015). Merricks, for example, arguesthat we should accept that there are fundamentally representationalentities, but that we have no reason to favor mental states (such asbeliefs) over propositions as being the fundamental bearers ofrepresentational properties. For if, e.g., beliefs are fundamentallyrepresentational, then it is either a primitive fact about them thatthey represent what they do, or it is a feature capable ofexplanation. If it is a primitive fact about them, then the viewappears just as mysterious as one which accepts that propositions areprimitively representational. If it is a fact capable of explanation,as the type theorists contend, then it is presumably explained interms of an agent’s ability to predicate properties of objects.But unless there is some explanation of how an agent can engage inpredication, predication must itself be a primitive representationalability, and the theory has not made any genuine progress on what wasto be explained.

A final question worth considering at this stage is whetherpropositions are representational entities at all. Richard (2013) andSpeaks (2014), for instance, each develop views of propositions whichdeny that they are. Consider the view defended by Richard. Sentences,beliefs, and the like represent things as being a certainway—snow as being white, for example. Put another way, thesentence ‘Snow is white’ represents snow’s beingwhite, where this is simply a way for things to be—a state ofaffairs or property that is either instantiated or not (but does notrepresent things as being any way, just as properties are not ingeneral representational). On this approach, the proposition expressedby the sentence is identified with the way that things are representedas being, not as something which has representational propertieseither primitively or in need of explanation by more fundamental actsof predication. If an approach along these lines is correct, the typeview appears to lose one of its central motivations.

8. The Individuation of Propositions

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

It is a controversial matter whether Quine was right to demand suchrigorous criteria of identity as a condition for acceptance of a classof entities. However, even if Quine asks too much, any good theory ofpropositions ought to have something to say about when propositionsare identical and when they are distinct. Developing theories whichgive such accounts in a way that fits well with intuitive dataconcerning propositional attitude ascriptions would enhance ourreasons to accept propositions.

The question of identity conditions for propositions is importantlyrelated to the question of whether propositions are structuredentities. Propositions are structured if they haveconstituents, in some broad sense, and the order of theconstituents matters. Order matters only if there could be twostructured propositions sharing all the same constituents, but whichare distinct due to differences in the way under which thoseconstituents are “united” in the proposition. E.g., if theproposition that \(a\) loves \(b\) is the ordered triple\(\ltb\)loving, \(a, b\gtb\), it is distinct from theproposition that \(b\) loves \(a\), which would be the ordered triple\(\ltb\)loving, \(b, a\gtb\).

If propositions are structured entities, then sameness of constituentsand sameness of order will entail identity. There are, of course,dangers, in regarding propositions as structured. Prima facie, onewould rather not claim that the proposition that \(x\) is triangularis identical to the proposition that \(x\) is trilateral, since asubject might believe one but not the other. It will be important,then, not to individuate propositions too coarsely. However, one mightworry, in the opposing direction, about overly fine individuations ofpropositions. Is the proposition that John loves Mary different fromthe proposition that Mary is loved by John? For more on structuredpropositions, see the entry onstructured propositions.^[10]

Any theory that construes propositions as structured entities wouldseem to face the problem of theunity of the proposition. Itis not entirely straightforward to say what this problem or set ofproblems is. But at the very least, there are at least two problemshere. There is the problem of explaining why one sort of structuredwhole, a proposition, can be true or false, while the set of itsconstituents is not. A list isn’t true or false, and aproposition with the same constituents is; why is this? Second, thereis a general problem of explaining how two distinct things could haveall the same constituents. For a thorough discussion of the history ofphilosophical 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 areunstructured. 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 inStalnaker 1976), then \(P=Q\) iff \(P\) and \(Q\) have the same worldsas members iff \(P\) and \(Q\) are true in the same worlds. As iswell-known, this theory leads to a very coarse individuation ofpropositions, too coarse, arguably, to handle propositional attitudes.(See Soames (1987) for a discussion of this theory as well as thetheory of propositions as sets of concrete situations or facts.

If propositions are unstructured and distinct from sets, there areseveral 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 toproperty identity in the manner of Myhill (1963) and Zalta (1983).Thus, Zalta (1983, 72) offers the following definition of propositionidentity: \(\ltb p\gtb =\ltb q\gtb\) if and only if the property ofbeing such that \(p\) is identical to the property of being such that\(q\). A third proposal, not incompatible with the second, is toexplain proposition identity in terms of the “freegeneration” of propositions from a stock of certainnon-propositional entities, e.g., individuals, properties andrelations, by algebraic operations (Bealer 1982, Menzel 1986, Zalta1983 and 1989).^[11] Although propositions on this approach are unstructured, eachproposition may be represented by its “constructionsequence.” To avoid identifying \(\ltb\)Hesperus isbeautiful\(\gtb\) with \(\ltb\)Phosphorus is beautiful\(\gtb\), therelevant inputs cannot simply be Hesperus (Phosphorus) and theproperty of being beautiful. A well-known strategy to cope with thisproblem, due to Frege, is to appeal to different modes of presentationassociated with the different names, each contributing somethingdifferent to the proposition expressed. However, these modes need notbe understood as complex properties uniquely exemplified by referentof the name. For instance, Bealer (1998) invokes what he calls“non-Platonic” modes of presentation. Whether thesenon-Platonic modes of presentation are understood as words, as causalchains of word use, or in some other way, the important point is thatthe mode associated with ‘Hesperus’ will be different thanthat associated with ‘Phosphorus’. Zalta (1989) introducespropositions with abstract constituents to do the work of these modes.On Zalta’s view, such singular propositions are built out ofabstract individuals that encode the cognitive content of names. Sincethese abstract individuals encode this cognitive content, there is noneed for the referent of the name to instantiate it, and a fortiori noneed for the content to be a property uniquely instantiated by thisreferent. For more on encoding vs. instantiating, see section 6 of theentry onexistence. Thus, these theorists hope to use the metaphysical tools of thesealgebraic accounts to accommodate some of the key Fregean intuitionsabout differences in propositions expressed while avoidingdifficulties with the Fregean doctrine of sense.

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

9. Propositions, Facts, and States of Affairs

Frege famously wrote, “‘Facts, facts, facts’ criesthe scientist if he wants to bring home the necessity of a firmfoundation for science. What is a fact? A fact is a thought that istrue.” (1918, p. 25)

Is a fact just a true proposition? There are metaphysical andlinguistic arguments to the contrary. Here is a standard metaphysicalargument. The fact that snow is white couldn’t exist if snowwasn’t white, but the true proposition would (only it would befalse). Therefore, the fact isn’t the true proposition (SeeMoore 1953, p. 308). Facts might be, still, insome sense,derivative from true propositions, even if the identity claim fails.Following Moore (1953, pp. 261–2) and Slote (1974, p. 99), KitFine (1982, pp. 52–3) suggests that facts may be conceived asconcretizations of true propositions. Thus, the fact that \(p\) is thetruth of \(\ltb p\gtb\). However, so construing facts makes them poorcandidates for truthmakers: the truth of \(p\), presumably, is notwhat makes \(\ltb p\gtb\) true.

One well-known linguistic argument against identifying facts with truepropositions is closely related to the Ambiguity Response to TheSubstitution 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”, orHarman’s (2003) “The true proposition that fires are hotmakes it the case that fires are hot.” If facts were truepropositions, so it is argued, one would expect the substitutions topreserve truth.

Nonetheless, there are other uses of ‘fact’ that supportthe identification:

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

Used in this way, ‘fact’ seems to apply to entities thatresemble propositions, in that they have two modes of being: existenceand 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) Thereare 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 withoutobtaining). “Bipolar” facts correspond, roughly, to whatsome philosophers call possible states of affairs.

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

King (1995, 2007, 2014) argues that all propositions are facts,although not the ones that we might expect. The proposition that Maryloves John is not the fact that Mary loves John but rather (to a firstapproximation) the following fact: Mary, loving, and John being thesemantic values of linguistic items standing in a certain syntacticrelation (represented by a phrase marker tree) which encodesinstantiation. King argues that his account has many virtues. It helpssolve the problem of the unity of the proposition (see the previoussection), insofar as the structure of a proposition derives from thesyntactic structure of a corresponding sentence. It requiresrelatively minimal ontological commitments: if one accepts that thereare languages with expressions designating objects and properties andin which certain syntactic relations encode instantiation, then onewill accept King-propositions. The account also provides for finelyindividuated propositions: differences in syntactic structure ofsentences will carry over to differences in the propositionsexpressed. Given that the existence of King-propositions seems todepend on their being language-users who use language in certain ways,King is a conceptualist about propositions. (See section 7.2above).

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 ofproperties. Following standard terminology, let us say that when apredicate has a property as its semantic content, the predicateexpresses that property. (For simplicity, we will assume thatsentences can have propositions as semantic contents.) Under anabundant conception of properties, whether a predicate expresses aproperty depends only on its broadly syntactic facts about it. Thesimplest abundant conception holds that every well-formed predicateexpresses a property. According to sparse conceptions, not everysyntactically well-formed predicate expresses a property.

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

10.1 Expressivism and Moral Propositions

One motivation for accepting a sparse conception of propositions isexpressivism in metaethics. “Old-fashioned” expressivists(e.g., Ayer and Stevenson) claimed that moral sentences arenon-cognitive. We cannot believe that lying in politics is wrong, norcan we have any broadly cognitive attitudes (e.g., disbelief) of theform ‘\(A\)-ing that \(p\)’ where ‘\(p\)’contains moral terms. If we cannot have such attitudes, thenpresumably there are no moral propositions. (If there were suchpropositions, why wouldn’t there be possible cognitive attitudeshaving them as contents?). And if there are no moral propositions,then moral sentences do not express propositions, and so lacktruth-value.

We certainly talk and think as if we have moral beliefs, as if webelieve moral propositions. For the old-fashioned expressivist, then,many of our apparently sincere ordinary claims will have to berejected. Endorsing such a sparse conception of propositions thusleads to the surprising consequence all moral sentences lacktruth-value.

Some contemporary expressivists (Blackburn 1998, Horwich 1993, Stoljar1993) are less averse to moral propositions, moral properties andmoral 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 moralpropositions, but they are mere shadows of moral declarativesentences. (Even if they are shadows of our sentences in some sense,they are not shadows in another sense, at least if the Easy Argumentsfor mind-independence and abstractness are successful: what ismind-independent and abstract is, in a clear sense, not merely ashadow of sentences.)

At least three important questions can be asked about the combinationof expressivism and deflationism about moral propositions. First, ifthe expressivist accepts moral propositions, what is the differencebetween expressivism and realism? Second, by accepting deflationarymoral propositions, can the expressivist avoid the familiar problemsfor moral realism (and cognitivism) which helped motivate expressivismin the first place? Third, can the realist avoid these familiarproblems equally well by accepting deflationary moralpropositions?

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

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

Blackburn’s supervenience argument is a second argument againstrealism. Blackburn formulated the argument in terms of moralproperties, as follows. If there are moral properties, then theysupervene on non-moral properties as a matter of conceptual necessity.That is, in every conceptually possible world, if two things share allnon-moral properties, they share all moral properties. But if thereare moral properties, the pattern of supervenience is not itselfconceptually 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: ifmoral properties can come apart from non-moral propertiesacross worlds, why can’t they come apart from themwithin worlds? That is: what explains the “ban on mixedworlds”? A similar problem can be formulated for truth as afeature of moral propositions. What explains the ban on conceptuallypossible worlds in which one moral proposition \(\ltb x\) is \(M\gtb\)is true, while another moral proposition \(\ltb y\) is \(M\gtb\) isfalse, but in which all relevant non-moral propositions \(\ltb x\) is\(P\gtb\) and \(\ltb y\) is \(P\gtb\) are alike in truth-value? Whatis not immediately clear is, first, how deflationary moralpropositions will prove useful to the expressivist in answering thisquestion, and second, how, supposing they do prove useful, why theywon’t prove equally useful to the realist.

What the expressivist seeks is a conception of propositions (and oftruths, facts, and beliefs) substantive enough to explain and validateour ordinary realist-seeming discourse but deflationary enough toavoid the traditional problems for realism. Whether it is possible tonavigate the two is the subject of intense scrutiny in contemporarymetaethics.

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Thanks to Berit Brogaard, Marian David, Shane Duarte, Anthony Everett,Thomas Hofweber, Robert Johnson, Jeff King, Jon Kvanvig, Peter Markie,Friederike Moltmann, Jay Newhard, Stephen Schiffer, Robin Smith, ChrisMenzel, and the subject editors for helpful comments.

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