Singular propositions (also called ‘‘Russellianpropositions’’) are propositions that are about aparticular individual in virtue of having that individual as a directconstituent. This characterization assumes a structured view ofpropositions — seepropositions: structured.Alleged examples of singular propositions are the propositions [MontBlanc is more than 4,000 meters high], [Socrates was wise], and [She(pointing at Susan) lives in New York]. A singular proposition is tobe contrasted with ageneral proposition, which is not aboutany particular individual, and aparticularized proposition,which is about a particular individual but does not contain thatindividual as a constituent. Examples of the first are thepropositions [Most Americans favor tax cuts] and [Some music isgreat]; examples of the second are the propositions [The inventor ofbifocals was bald] and [The tallest spy is a man]. A singularproposition isdirectly about an individual whereas aparticularized proposition isindirectly about an individualin virtue of that object satisfying a condition that is a constituentof the proposition — in our cases, the conditions‘x uniquely invented bifocals’ and‘x is a tallest spy’.

The acceptance or rejection of singular propositions lies at thecenter of many issues in semantics, the philosophy of language andmind, and metaphysics. In this essay, we shall look at some of thearguments for singular propositions, discuss problems their existencegive rise to, and show how singular propositions are related tocertain questions in metaphysics.

• 1. Fregeanism and Russellianism
• 2. Reasons for Singular Propositions: The modal argument
• 3. Reasons for Singular Propositions: The argument from indexicals and demonstratives
• 4. Reasons for Singular Propositions: The reduplication argument
• 5. Modal Problems for Singular Propositions
• 6. Temporal Problems for Singular Propositions
• 6.1. Temporal Problems for Singular Propositions: Quantitative Change
• 6.2. Temporal Problems for Singular Propositions: Qualitative Change
• 7. Conclusion
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Fregeanism and Russellianism

We will assume without argument a propositionalist semantics,according to which sentences (in context) are assigned propositions ascontents which are the primary bearers of truth values, bearers ofmodal properties like contingency and necessity, and objects of thepropositional attitudes like believing, hoping, and saying. We candistinguish two broad classes of theories aboutpropositions. Proponents of the first, Fregean view accept Frege'sdistinction between sense and reference and proponents of the second,Russellian view do not. If Fregeanism is true, all thought aboutconcrete individuals is indirect, mediated by senses that areindependent of those individuals. (Some maintain that Frege recognizedde re senses — senses whose existence and identity isdependent upon their reference — as the contents of proper names,in which case he would not have subscribed to a Fregean theory, ascharacterized above. The supplementary document

Evans on Frege

contains further discussion.) The easiest way to get a grip on this isto think of senses as purely qualitative satisfaction conditions. Sucha condition determines an object in virtue of the qualities itinstantiates. According to Russellianism, on the other hand, we canthink about an individual directly; we can have a thought about anindividual by having that individual as an immediate constituent ofthe thought. On the standard interpretation of Frege, individuals arenot constituents of propositions. Propositions are composedof senses, not individuals, and senses are individuated independently of any individual. If Fregeanism is true,there are no singular propositions. If Russellianism is true, thensingular propositions play a crucial role in semantics and any complete theory of thought.

Before discussing the reasons for and against singular propositions,we begin with a brief discussion of the views of the historical Fregeand Russell. The hope is that the discussion will provide a clearerunderstanding of the views outlined above.

Gottlob Frege famously distinguished between anexpression's reference and its sense. (The classic source is Frege1892/1948. The distinction was first introduced a year earlier in(1891). It is commonly thought, and Frege asserts as much, that thesense-reference distinction was not present in (1879/1967). But thisearly work does contain a seeming anticipation of the distinction, aswell as the same argument from the opening paragraphs of (1892/1948)against the metalinguistic solution promoted in (1879/1967), which isextremely puzzling. We don't try to resolve the interpretative issueshere.) We focus on proper names, although Frege maintained that thesense-reference distinction applied to all expressions, includingsentences, where the reference of a sentence is a truth value and itssense a thought. The reference of the name ‘Mark Twain’ isthe man Mark Twain himself, while its sense is a mode of presentationor way of thinking of that object.

Frege argued for the distinctness of sense from reference asfollows. Suppose, for reductio, that the sole semantic value of thename ‘Mark Twain’ were its reference. Then, as the name‘Samuel Clemens’ is coreferential, the two names would beidentical in their semantic values. Given a plausibleassumption of compositionality, the sentences ‘Mark Twain was afamous American author’ and ‘Samuel Clemens was a famousAmerican author’ would then express the same proposition. But thatis counterintuitive. It seems that fully competent speakers canbelieve what the one expresses without believing what the otherexpresses. (Imagine our agent had an American literature class,having readHuck Finn andTom Sawyer, in whichbiographical facts were withheld. She will accept the first sentence and reject the second.) If this is so, then the two sentencesexpress different propositions. And if they express differentpropositions, there must be some semantically relevant differencebetween the names ‘Mark Twain’ and ‘SamuelClemens’. As their references do not differ, sense is distinctfrom reference.

An expression's sense is intended to capture itscognitivevalue. The above argument is intended to show that coreferential proper names can present the same object in differentways and it can be a cognitive achievement to come to learn that theobject presented in those different ways is one and thesame. Reference alone, Frege persuasively argued, cannot capturecognitive value. Capturing the cognitive significance of an expressionis a primary role senses played in Frege's system. But they alsoplayed several other roles as well: They are the primary bearers oftruth values, the indirect references of sentences and hence theobjects denoted by that clauses like ‘that Frege denied theexistence of singular propositions’, and the objects ofpropositional attitudes, most importantly. These roles give rise tothe following theses concerning the individuation of senses.

Truth
If two sentences have different truth values, then they have different senses.

Accept
For any pair of sentences,s₁ ands₂, if a competentspeaker can rationally, reflectively, and sincerely accepts₁ while rejectings₂, thens₁ ands₂ have differentsenses.

Attitude
For any pair of sentences,s₁ ands₂, and propositional attitude verbVs, ifthe truth of^⌈a Vs thats₁^⌉ is consistent with the falsity of^⌈a Vs thats₂^⌉, thens₁ands₂ have different senses.

Frege's case for the sense-reference distinction is also a case thatsingular propositions are not the semantic contents of naturallanguage sentences and are not the objects of the propositionalattitudes. Singular propositions are too coarse-grained to account forwhat a competent speaker understands in virtue of grasping the meaningof a sentence. But the content of a sentence is, intuitively, what anagent grasps when she understands a sentence and what she believeswhen she accepts it. Frege concluded that singular propositions areill-suited for the purposes of semantics and psychology, as they leadto violations ofAccept andAttitude. (For further discussion, see the entryFrege.)

Bertrand Russell's views of language and thought areimportantly different from Frege's. (Russell held many distinctviews. We focus here on the Russell roughly from 1905 through 1912.)First, Russell held an acquaintance-based theory, according to whichsome thought about individuals is direct, in the sense of involvingsingular propositions involving those very individuals. Second,whereas Frege introduced senses to help solve the puzzles discussedabove, Russell employed logical analysis and his theory of definitedescriptions. We take each point in turn.

Russell maintained that an agent must be acquainted with everyconstituent of a thought that she is in a position to entertain. Callthisthe Acquaintance Principle. (The principle makes anappearance in (1905), but the view behind the principle isworked out in (1910) and (1912).) Russell thought that we areacquainted only with our occurrent sense data and universals (and hesometimes included the self, when he wasn't feeling skeptical ofawareness of the self as an entity). So, Russell maintained that theonly singular propositions we can grasp are ones with those items asconstituents.

We can trace the fundamental source of Russell's restrictivism aboutacquaintance to the claim that one is acquainted only with that forwhich misidentification is rationally impossible. If it is possiblefor one to be presented witho twice over andrationally not realize it as the same object, then one is notacquainted witho; one's thoughts abouto are, in that case, indirect. This line of reasoningrelies on the Fregean claim that identity confusions are to beexplained in terms of differences in thought constituents. Our Englishstudent's confusion regarding Mark Twain is thus to be explained interms of different thoughts and hence different thought constituentscorresponding to the different ways of thinking about the man MarkTwain associated with the expressions ‘Mark Twain’ and‘Samuel Clemens’. This — that cases ofmisidentification always involve differences in thought contents— marks an important point of agreement between Frege andRussell.

Neo-Russellians are more permissive about the objects of acquaintance,including extra-mental particulars in this class. David Kaplan'spioneering work (1977/1989) is typically the starting point, althoughRussell himself started out with such a position, maintaining, forexample, that Mont Blanc itself is a constituent of the thought thatMont Blanc has snowfields. Neo-Russellians must deny the Fregean claimthat whenever misidentification is rationally possible, there is adifference in thought constituents. They might still agree withFregean intuitions about the truth and falsity of propositionalattitude ascribing sentences — agreeing, for example, that‘Peter believes that Mark Twain was a famous Americanauthor’ is true while ‘Peter believes that Samuel Clemenswas a famous American author’ is false — claiming thatthis does not require a difference at the level of thoughtconstituents, following, for example, Mark Crimmins and John Perry(1989) or Mark Richard (1990). Such neo-Russellians claim that thetruth or falsity of a belief attitude ascribing sentence involves morethan just the agent of the report having among her beliefs theproposition expressed by the sentence embedded in the reportingsentence. Alternatively, the neo-Russellian might deny the Fregeanintuitions about the truth and falsity of propositional attitudeascribing sentences, following, for example, Nathan Salmon (1986) inaccounting for those intuitions in nonsemantic terms. (For furtherdiscussion, seepropositionalattitude reports.) Either way, however, given thatmisidentification of extra-mental particulars is obviously possible,the permissive theory of acquaintance requires denying the claim thatall cases of misidentification involve differences in thoughtconstituents.

We have seen how Russell's adherence to the Acquaintance Principletogether with his adoption of a Fregean attitude towardsmisidentification led him to deny that we can think directly aboutextra-mental particulars. Russell admitted that there is anextra-mental reality filled with extra-mental particulars that we canand do think about. Like Frege, all such thought, Russell insisted, isindirect. But Russell did not follow Frege in introducing senses asthe mediators between individuals and our thought about them. Rather,Russell appealed to logical analysis through his theory ofdescriptions. For Russell, all thought about extra-mental particularsis descriptive. In (1910), the canonical form such thoughttook is the following:The thing that caused THIS[demonstratively referring to one's occurrent sense datum]issuch-and-such, which is singular with respect to the sense datumdemonstrated. We can work up to this by seeing how Russell contrastedthree thoughts about Bismarck to the effect that he unified Germany(1910, 114–17). First, assuming acquaintance with the self, there isBismarck's own thought about himself. This thought is singular withrespect to Bismarck, having as its content the singular proposition[Bismarck unified Germany]. “But if a person who knew Bismarckmade a judgment about him, the case is different. What this person wasacquainted with were certain sense data which he connected (rightly,we will suppose) with Bismarck's body” (114). No human butBismarck, then, can grasp this singular proposition. Someone that hasperceived Bismarck, say, Wilhelm II, has a thought with the followingform, where BOB is the sense datum the agent has in virtue of hisperception of Bismarck.

<[thex:x has a body that is the cause of BOB]x unified Germany>

This proposition is particularized with respect to Bismarck, butdirect and thus singular only with respect to the occurrent sensedatum being demonstratively referred to. Finally, contrast thisjudgment with someone who has never perceived Bismarck but has onlyheard about him indirectly. Such agents cannot relate Bismarckdirectly to their sense data because, unlike Wilhelm, none of theirsense data are caused by Bismarck's body. Hence, they must eitherthink of him purely qualitatively — as, say, the firstChancellor of the German Empire, treatingthe German Empireas if it were a purely qualitative condition — or moreindirectly, as the person written about in the books causing thesesense data, thought standing in front of the books that are the sourceof the agents' thoughts about Bismarck.

For Russell, sense data are the direct objects of thought in terms ofwhich we think about extra-mental reality under descriptions relating,typically causally, those bits of reality to the directly referred tosense data. (It is worth noting that the basic idea does not requireRussell's theory of perception. For example, John Searle, in (1983),has a similar view according to which we think immediately aboutexperiences, which are not analyzed in terms of the mind's beingpresented with sense data. We then think of extra-mental objects asthe causes of such and such occurrent experiences.) For Russell, whilethere are thoughts about particulars that are wholly qualitative andwholly general, the paradigm form our thought about external realitytakes is ultimately grounded in acquaintance, albeit acquaintance withsense data as opposed to extra-mental reality itself. This is in starkcontrast to the canonical form such thought takes in Frege's system,in which there is no direct reference to any individuals, includingsense data, and all thought is entirely indirect. (For furtherdiscussion, see the entriesBertrand Russell,knowledge by acquaintance vs. description, anddescriptions.)

Russell rejected Frege's distinction between sense and referenceand attempted to solve the problems motivating that distinctionthrough logical analysis and scope distinctions. The resulting view isone on which the proposition expressed by a sentence like ‘Theinventor of bifocals was bald’ has neither a Fregean sense northe referent of the subject-position term as a constituent. Instead,Russell had propositional functions — functions from objects topropositions — in place of senses. Yet at the bottom level sucha view seems to require singular propositions, which are the basic oratomic propositions upon which the complex propositions arebuilt. Frege's atomic propositions are composed of senses whileRussell's require individuals.

2. Reasons for Singular Propositions: The modal argument

The first argument in favor of singular propositions we shallexamine is based on Saul Kripke's modal argument in(1970/1980). Kripke presented the argument as an argument that propernames like ‘Nixon’ are not synonymous with ordinarydefinite descriptions like ‘the first US president fromCalifornia’, rather than an argument for singular propositions,the existence of which he never endorsed in print. David Kaplan, in(1977/1989, 512–13), however, used the argument to conclude thatdemonstratives are directly referential expressions and hence expresssingular propositions. The argument can be presented as follows.

Suppose that David is standing at a table with Charles to his immediateleft and Paul to his immediate right. Paul lives in New Jersey and Charles livesin Illinois. David points to the person on his right and utterssentence (1) below at timet.

(1) He lives in New Jersey.

David has said something about Paul. Call the proposition David hasexpressedp.p is distinct from thepropositions expressed by the following sentences.

(2) The person on David's immediate right (att) lives inNew Jersey.
(3) The person David demonstrated (att) lives in New Jersey.

Both of the latter propositions are about Paul indirectly, in virtueof the properties he contingently has (namely, being to David's rightatt and being demonstrated att by David,respectively). Now consider a counterfactual circumstance in whichPaul and Charles have switched places but in which everything elseabout them remained the same, consistent with this switch, and, inparticular, in which Paul still lived in New Jersey and Charles inIllinois.p is true at this circumstance, as Paullives in New Jersey, while the propositions expressed by (2) and (3)are false at this circumstance, as Charles is both to David's rightand demonstrated by David and he doesn't live in New Jersey. So,p is distinct from the propositions expressed by (2)and (3).

It is important to be clear that we are concerned with the truthvalues of the propositions expressed by (1)-(3) at a describedcounterfactual situation, not what propositions those sentences wouldhave expressed in those circumstances. (1) would have expressed adifferent proposition, a proposition about Charles and so false, wereDavid to have uttered it in the described situation. But our claim isthat the proposition expressed by David's actual utterance of (1) istrue at the described counterfactual circumstance, while thepropositions (actually) expressed by (2) and (3) are false at thatcircumstance.

Sincep differs in truth value in the describedcounterfactual circumstance from the propositions expressed by (2) and(3), it follows thatp is distinct from thepropositions expressed by (2) and (3). This is because, aspropositions are the objects that are true or false in counterfactualcircumstances, ifp =p*, thenp andp*have the same truth value in all counterfactual circumstances. Theseconsiderations suggest that the proposition expressed by David'sutterance of (1) is about Paul directly and hence thatp is a singular proposition. Anyproposition that is about Paul indirectly, in virtue of qualities thathe contingently instantiates, will be subject to a similar argument.

There are two main responses to the modal argument in theliterature. The first involves a denial of the principle that, ifp =p*, thenp andp* have the same truth value in all counterfactualcircumstances. Michael Dummett (1991) and Jason Stanley (1997a/b;2002) have developed this response by denying that propositions arethe bearers of modal properties. Dummett distinguishes senses fromwhat he callsingredient senses. Senses give the contents ofexpressions, are the bearers of truth and falsity, and are the objectsof the attitudes. Ingredient senses, on the other hand, are thebearers of modal properties like being necessarily or contingentlytrue or false and being true or false at a world. Because propositionsare not the bearers of modal properties, Dummett and Stanley canaccept that (1) is true with respect to our counterfactual situationwhile (2) and (3) are false even though the proposition expressed by(1) is the same as the proposition expressed by either (2) or (3). (Itmay be possible to get the same results without denying thatpropositions are the bearers of modal properties by offering anonstandard semantics of modal adverbs like ‘necessarily’and ‘contingently’ according to which they ascribeproperties — the property of being true in every/some world, say— to propositions but are sensitive to more than just theproposition they operate on. One model for this is the way‘so-called’ functions in a sentence like ‘Supermanis so-called for his super powers’. To our knowledge such atheory has yet to be worked out in detail, but we have no doubt thatit could be.)

The second response involves moving from contingent properties likethose involved in (2) and (3) to necessary properties, and inparticular to what, following Plantinga in (1974), we will call anindividual essence, which is a property that, necessarily, ifx exists, then it has that property and, necessarily, onlyx has. The propertybeing on David's right is not anindividual essence of Paul, as Paul might have existed without havinghad it and Charles might have had it instead. But it is easy to turnsuch contingent properties into necessary ones byrigidifiying them. Paul necessarily has the property ofactually being on David's right. For any worldw, Paul has that rigidified property inw just in case in the actual world Paul has the(contingent) property of being on David's right. And, if Paul is theonly person to have that property in the actual world, then therigidified property is not only a necessary property of Paul but alsoan individual essence of Paul. Such a property “tracks”Paul across every possible world. Consider then the propositionsexpressed by (4) and (5).

(4) The personactually on David's immediate right (att) lives in New Jersey.
(5) The personactually David demonstrated (att) lives in New Jersey.

As far as the modal argument goes, these propositions can beidentified withp, as, for every worldw, they have exactly the same truth value atw asp intuitively has atw.

We do not claim that either response is ultimatelysatisfying. Indeed, we are satisfied by neither. But their presencedoes show that the modal argument fails to bring out the realdifficulties with descriptivism and the fundamental need for singularpropositions.

3. Reasons for Singular Propositions: The argument from indexicals and demonstratives

David Kaplan, in (1977/1989), and John Perry, in (1977), (1979), (1980a/b), and (2001), argued that an adequate theory of indexicality requiressingular propositions. An indexical is an expression whose content isnot fixed by its linguistic meaning alone but requiresextra-linguistic contextual supplementation. Take, for example, thesentence ‘I am happy’, considered in isolation from anyparticular utterance or specifications of who is uttering it at whattime. The question of whether or not it is true is hardlysensible. That question makes sense only when we either consider anutterance of the sentence or provide the specification of at least anagent as speaker. (We remain neutral on the issue whether utterancesof sentences are the primary bearers of semantic values or sentencesin context.) Both Kaplan and Perry argue that a Fregean account ofindexical expressions like ‘I’, ‘today’, and‘here’ and demonstrative expressions like‘he’, ‘this’, and ‘there’ isinadequate. We focus here on Perry's view.

Perry argued against the Fregean claim that there is a single entity— sense — that answers to the three principles of senseindividuation presented in section 1. He argued that thisidentification leads to several problems when applied toindexicals. Perry's position is that one entity answers toAccept and a distinct entity answerstoTruth andAttitude. Moregenerally, Perry argued that an adequate account of indexicals anddemonstratives in thought and language requires that we have oneentity serving as cognitive values and a distinct entity serving asthe contents of thoughts and sentences and bearers of truth value. Themistake of the Fregean is to think that there is a single item thatcan do all of the work.

Consider the following sentence.

(6) George quit his job today.

(6) doesn't express a complete proposition on its own because‘today’ does not have a complete sense on its own. Supposethat George held exactly one job, which he quit on 1 Aug 2000. (6) isthen true as uttered on 1 Aug 2000 and false as uttered on any otherday. Perry considers three Fregean accounts of the sense expressed bya use of ‘today’ in (6) and argues that they allfail. The first identifies the sense of ‘today’ withits role or character; the second identifies it with an equivalenceclass of ordinary Fregean senses; and the third involves looking tothe beliefs of the speaker for its sense.

We begin with the first, according to which the sense of a use of‘today’ is its role. This account, in effect, denies that‘today’ is an indexical. This is because the role of anexpression is the rule that takes one from a particular utterance ofthe expression to its content on that use, which is the same acrossall uses. An expression's role is related to its linguisticmeaning. The role of ‘today’ is a rule that takes one froma given use to the day of that use and the role of ‘I’ is arule that takes one from a given use to the speaker of that use. So,if the sense of ‘today’ were its role, the same thoughtwould be expressed by every utterances of (6), regardless of the dayof occurrence. But, as we have seen, different utterances of (6) havedifferent truth values. But then, byTruth, thoseutterances express different thoughts. Furthermore, the accountviolatesAccept, as it is possible to rationally takedifferential attitudes towards different utterances of (6). The senseof a use of ‘today’,then, is not its role.

According to the second Fregean account, the sense of a use of anindexical like ‘today’ is the class of referentiallyequivalent ordinary Fregean senses. The equivalence class of thoughtsfor an utterance of (6) on 1 Aug 2000 is the class of thoughtscomposed of the (incomplete) sense of ‘George quit hisjob’ and any completing sense that determines 1 Aug2000. Referential equivalence classes function much like singularpropositions, in that they do not place any restrictions on the way inwhich the agent conceives of the referent of the thought. This makesthem poor candidates for accounting for the cognitive value of asentence, as they lead to violations ofAccept. Consider the following case, derived from acase of Perry's. Suppose that you are sitting in a large harbor cityand see the bow of a ship, with the name ‘Enterprise’clearly in view, sticking out behind a building. You also see thestern of a ship, with no name, sticking out behind another buildingtwo blocks away. The water view is obstructed by buildings for theintervening blocks. You might then accept your companion'sutterance of the sentence ‘This is the Enterprise’,pointing at the bow of the ship, but reject her utterance of thesentence ‘This is the Enterprise’, pointing at the sternof the ship. Associated with both utterances is the same equivalenceclass of Fregean senses, as both uses of ‘this’ refer tothe same ship. But, because you competently accept the one and not theother, byAccept, different senses are expressed. Weget the same results for (6) by considering someone who is confusedabout what day it is. She might then accept an utterance of (6) on 1August 2000 while rejecting an utterance of ‘George quit his jobon 1 August 2000’, without a change of mind and despite the factthat the same equivalence class is associated with both. If the senseof a use of ‘today’ is intended to capture that use'scognitive significance, as it clearly should on a Fregean account, weshould reject this second account.

The failings of the first two accounts as plausible Fregean accountsof (6) are fairly evident. The third Fregean account turns to theattitudes of the speaker to determine the sense of a given use of anindexical. Perry presented the key idea as follows.

To understand a demonstrative, is to be able to supply a sense for iton each occasion, which determines as reference the value thedemonstrative has on that occasion…. [W]e can say that for eachperson the sense of the demonstrative ‘today’ for thatperson on a given day is just the sense of one of the descriptionsD (or some combination of all the descriptions) such that onthat day he believes [‘Today isD’].(1977, 11–12)

Perry required that the descriptionsD should benonindexical. Perry then presented three arguments against thissuggestion. (Kaplan developed similar arguments against what he callsthe Fregean theory of demonstratives in (1977/1989).)

The first objection isthe irrelevancy of beliefobjection. Believing that you live in that time and possessingaccurate descriptive information of the medieval age does not makeyour uses of ‘today’ about 1 August 1204, even though thatis the date that best fits your conception of the date of yourutterance. Uses of ‘today’ are about whatever day theyoccur on, whatever descriptions one associate with one's uses of theexpression and however one conceives of the day of one'sutterance. But if the sense of a use of a ‘today’ weredetermined by the beliefs of the speaker, and if sense determinesreference, then it would seem that your utterance is about 1204. So,the beliefs of the speaker are irrelevant to the day an utterance of‘today’ is about.

This objection works best with “automatic” or“pure” indexicals like ‘today’ and‘I’ rather than “non-automatic” indexicals or“true” demonstratives like ‘she’ and‘this’, which require an associated demonstration to referin context. This is because the reference of a use of a truedemonstrative is at least arguably determined in part by the speaker'sbeliefs and audience-directed intentions, whereas the reference of apure indexical is settled by objective, attitude-independent factorsof the occasion of utterance, like who is speaking when andwhere. (There is a debate about whether or not speaker beliefs andintentions are relevant even to true demonstratives. See Bach 1992,Bertolet 1993, and Reimer 1991a/b and 1992.)

We noted above that Perry assumed that the descriptive beliefs thatdetermine the sense of a use of ‘today’ themselves are notindexical. Lifting this ban removes some of the sting from theirrelevancy of belief objection. For consider the agent's belief thatshe would express by saying, ‘‘Today is the day of thisvery utterance.’’ While the purely qualitative descriptiveconditions a speaker believes the day of her speech satisfies may besatisfied by a different day, it is much less clear that the abovedescriptive condition is satisfied by the wrong day. (It is alsoharder to imagine a nonproblematic case where the agent is confusedabout whether or not the day referred to by her use of‘today’ satisfies this description.) But there are atleast two problems with the Fregean appealing to suchdescriptions. The first is that it is unclear that ordinary agentsactually have such beliefs when they competently utter a sentence like(6). It is also questionable whether all speakers who competently use‘today’ have the concepts ofan utterance. Ifthey do not, then they are in a position to believe what is expressedby an utterance of ‘Today is fine’ without believing whatis expressed by an utterance of ‘The day of this utterance isfine’, in which case, byAccept, the twosentence express different propositions. Second, even if they did, thesame question of the sense of the use of ‘this’ wouldarise once again, with all of the problems Perry raises for the senseof (6). There is no room, in Frege's system, for irreducibly indexicalthoughts, as Frege is clear that thoughts are true or falseabsolutely, which an irreducibly indexical thought could notbe (just as the sentence ‘I am happy’ is not itself trueor false absolutely). Insofar as the Fregean claims that truth is anabsolute property of thoughts, she must explicate the indexicality oflanguage and judgments using only nonindexical propositions orthoughts. (A proponent of a broadly Fregean view might claim that thetruth or falsity of a thought (and not just a sentence) is relative toa sequence of parameters like a person, place, time, etc.. She couldthen claim that the thought expressed by an utterance of (6) is itselfirreducibly indexical and is only true or false relative to anassignment of parameters and in particular to a day.)

Perry's second objection isthe nonnecessity of beliefobjection. This objection turns on the fact that a speaker canrefer to the time at which she is speaking with her use of‘today’ even though she lacks any adequate purelyqualitative conception of what day it is. Consider the case of Rip VanWinkle. “When he awakes on October 20, 1823, and says withconviction ‘Today is October 20, 1803,’ the fact that heis sure he is right does not make him right, as it would if thethought expressed were determined by the sense he associated with‘today’” (1977, 12). (The case of Rip Van Winkle isvery rich. For further discussion, see Evans 1981/1985, Kaplan1977/1989 (538), and Perry 1997.) Van Winkle need not have a correctconception of the day of his utterance to be talking and thinkingabout that day with his use of ‘today’. It suffices tosimply be located on that day and say, ‘‘Today isfine,’’ knowing the general rule of how uses of‘today’ function. A similar point can be made about‘I’, using a case of a person suffering complete amnesia,who intuitively still speaks of herself when she says, ‘‘Iam alive’’, despite lacking true beliefs of identifyingbiographical information, and ‘here’, using a case of aperson who is completely confused about where she is. As was the casewith Perry's first objection, however, the nonnecessity of beliefobjection is less persuasive with true demonstratives, where some kindof correct conception of the intended reference is arguably needed todemonstrate it.

In his response to Perry, Gareth Evans (1981/1985) claimed thatretaining indexical beliefs across changes in circumstance requireskeeping track of the objects those beliefs are about. So, for example,to believe the same thing today that I believed yesterday when Iuttered (yesterday) the sentence ‘Today is fine’ requiresmore than simply competently uttering today the sentence‘Yesterday was fine’. I must in addition, Evans claimed,have kept track of the day and so properly registered the change inday. This makes belief necessary for retention of indexical beliefs,even beliefs expressed by sentences with pure indexicals. As VanWinkle does not successfully track the twenty some years between hisfalling asleep and waking up, he does not retain the temporallyindexical beliefs he had the night he fell asleep. Evans is lessclear, however, that a proper conception of the day is necessary forformation (as opposed toretention) of a temporallyindexical belief, which is what Perry's second objection denies. DoesVan Winkle not think a thought about 1823 when he awakes and thinks tohimself, ‘Today is fine’?) Furthermore, the trackingcondition has consequences that seem contrary to key tenets ofFregeanism. Losing track of time isn't something that is alwaysinternally accessible. Rip Van Winkle and his less well-known brotherKip, both of whom went to sleep after a fine day in October 1803. Kipwoke up 10 hours later and, recalling the previous day, thought tohimself, ‘Yesterday was fine’; Rip slept an additional 20years and woke with memories of what he took to be the previous dayand thought to himself, ‘Yesterday was fine’, beingunaware of the additional passage of time. Because “everythingis all the same” as far as Kip and Rip are concerned uponwaking, there is some pressure to say that their beliefs have the samecontent, assuming belief contents are intended to capture how theagent conceives the world, which is the motivation behind a principlelikeAccept. (There is equally strong pressure to saythat they believe different things, as Kip's belief is true and Rip'sfalse. But that is not generated fromAccept butTruth and Perry's point is that, for important cases,those principles pull in opposite directions.)

Perry's third objection isthe nonsufficiency ofbelief. Consider the case of Hume and Heimson. Heimson believesthat he is Hume. But Heimson isn't just crazy, but also well informedabout every aspect of Hume's life. Still, Hume says something truewhen he utters the sentence ‘I wrote theTreatise’ and Heimson says something false. If so,then, byTruth, they say different things, despitethe similarity in their qualitative descriptive beliefs. Even thoughHeimson's descriptive beliefs about who he is best fit Hume, still hisself-thoughts are about Heimson and not Hume. The Fregean cannot,Perry claims, account for this.

Perry assumed that Fregean thoughts are generally accessible, as theyare entirely composed of logical operations and purely qualitativeconditions. But then the thought Hume grasps when he thinks to himself‘‘I wrote theTreatise’’ is a thoughtavailable for Heimson to grasp as well. (This assumption of generalaccessibility is at odds with what Frege says in his late work(1918/1956), where he claims that “everyone is presented tohimself in a particular and primitive way, in which he is presented tono-one else” (298). In his discussion of Dr. Lauben, Fregedenies that all thoughts are generally accessible and that the thoughtDr. Lauben grasps when he thinks to himself, ‘‘I amcold,’’ for example, is a thought that can be expressed byany sentence with a proper name. It is important to realize that thislimited accessibility thesis Frege held in later work is distinct fromthe view alluded to above according to which a thought is irreduciblyindexical. The former view is consistent with Dr. Lauben's thoughtbeing absolutely true or false, whereas the latter view is not. Fregedid not always hold this limited accessibility view, however. In anearlier, unpublished work intended as a logic textbook he writes:

In this case [the sentence ‘Iam cold’] the mere words do not contain the entire sense; wehave in addition to take into account who utters it. There are manycases like this in which the spoken words have to be supplemented bythe speaker's gesture and expression, and the accompanyingcircumstances. The word ‘I’ simply designates a differentperson in the mouths of different people. It is not necessary that theperson who feels cold should give utterance to the thought that hefeels cold. Another person can do this by using a name to designatethe one who feels cold. (1914, 134–5)

Frege here seems to be claiming that the thought you have when yousay to yourself, ‘‘I am cold,’’ is a thoughtsomeone else can express by pointing at you and saying,‘‘S/he is cold,’’ which is exactly what hedenied in (1918/1956). Furthermore, although Frege only posits privatesenses only for ‘I’, the worries that drove him to thisview can be raised with other indexicals like ‘here’,‘today’, and ‘now’. It becomes less and lessplausible to posit context-bound senses for each place, day, andmoment. In any event, the move to such perspective-bound thoughts hasnot been generally accepted, even by followers of Frege.)

Any generally accessible, absolutely true or false thought, Perryargued, will violateAccept. For suppose that therewere a purely qualitative descriptive conditionFHume associated with his use of ‘I’ that gives its sense;say, the condition expressed by the expression ‘the philosopherwho argued against the rationality of induction’. It would seemthat, insofar as Hume forgot (or never knew) that he himself isuniquelyF but retained his ability to think ofhimself with the expression ‘I’, it is possible for him tocompetently, reflectively, and sincerely accept the sentence ‘Iwrote theTreatise’ while not accepting ‘TheF wrote theTreatise’. No such purelyqualitative, generally accessible proposition, Perry concluded, isequivalent in cognitive significance to Hume's thought that he himselfwrote theTreatise. But Fregeanism entails that there is sucha thought. So Fregeanism is false.

So far we have focused on Perry's case against Fregean accounts ofindexicals in thought and language. Let's move briefly to Perry'spositive, anti-Fregean view of indexicality. Perry's views have gonethrough important and often drastic changes from his early views in(1977) and (1979) to his later views in his (2001), which we shall not try tosort out here, focusing primarily on the earlier view. A view broadlysimilar to Perry's early view is developed in Kaplan 1977/1989,where Kaplan distinguishes content and character, claiming that thelatter captures the cognitive significance of an expression and theformer is the bearer of truth value and the object of thepropositional attitudes, often being a singular proposition. Perryinitially (1977) distinguished “thoughts” and“senses,” but later (1979) and (1980a/b) made the samedistinction in terms of belief contents and belief states. (Perry alsoinitially identified the “thought” associated with anexpression with its role, which is proven false by cases like theEnterprise case discussed above. If an expression's role is identifiedwith its linguistic meaning, then the two occurrences of‘this’ surely have the same role. The two utterances of‘this’ have distinct associated demonstrations, butdemonstrations are not part of linguistic meaning.) The core idea isthat an adequate account of indexicality in thought and languageinvolves two distinct items, one that is roughly characterized byTruth andAttitude —propositions — and the other that is roughly characterized byAccept and is intended to capture the“cognitive significance” of an expression and throughwhich propositions are grasped. The former is, in the case ofindexical beliefs, a singular proposition. This distinction, Perryclaimed, is the key to solving the problems with self-locating beliefsthat we have discussed above; it is the Fregean's identification ofthe items that answer toAccept,Truth, andAttitude that leads tothe problems surveyed above.

Let's apply the view to the case of Heimson. What, on Perry's view,distinguishes Hume from Heimson? Both Hume and Heimson are in the samefirst-person belief state when they say to themselves,‘‘I wrote theTreatise.’’Furthermore, the belief content Hume has when he is in that beliefstate — namely, the singular proposition [Hume wrote theTreatise] — is a belief content readily available forHeimson to entertain as well. However, only Hume can grasp that beliefcontent by being in a first-person belief state. When Heimson is in afirst-person belief state, he grasps the distinct singular proposition[Heimson wrote theTreatise] and when Heimson grasps thesingular proposition [Hume wrote theTreatise], it is only invirtue of being in a third-person belief state. Perry is thus able toaccount for the similarities between Heimson and Hume (they are in thesame belief state) and what is distinctive of Hume (only he grasps thesingular proposition [Hume wrote theTreatise] when in afirst-person belief state).

Belief states are important because they are involved inexplaining, predicting, and rationalizing behavior. Perry provided ahost of memorable cases that make this point. Here's one. Consider twopeople who both utter to themselves the sentence ‘I am beingattacked by a bear’. All other things being equal, both peoplewill act in similar ways. There is a common explanation of theirbehaviors only in terms of their shared belief states, as theyapprehend distinct propositions, each believing a proposition abouthimself. Furthermore, it is crucial to how our agents act that theygrasp the relevant singular proposition in a first-person way and not,say, as one would if one saw one's own reflection in a mirror with thereflection of a bear sneaking up without realizing that the personbeing seen is oneself. So, explanation, prediction, andrationalization are all sensitive to belief states. To quote Perry onthis point:

[I]n virtue of being in a belief state in a certain environment, webelieve a certain object. Because the same object can be believed indifferent ways, from different environments or “points ofview,” classifying people by objects believed is not alwaysparticularly useful…. Consider the sentence ‘There is ahungry lion coming towards me’. Now consider the contextsrelative to which this sentence is true. They all consist of personsand times such that the person is being approached by a hungry lion atthat time. It is a good idea for all of these people to run like crazy[presumably, at that time or at least shortly thereafter]. In a sensethey do not need to know what they believe. Even if they haveforgotten who they are and lost track of time, they know enough torun. (In another sense, they do know what they believe even then.)Most of these people will not believe the same thing. But each of themwill believe in something that provides them with good reason torun. (1980a, 323)

But belief states are not contents; they are not true or false andthey are not what we express when we utter a sentence. We must thusalso recognize belief contents as distinct elements. (For furtherdiscussion of the issues raised in this section, see the entriesindexicals andpropositional attitude reports.)

4. Reasons for Singular Propositions: The reduplication argument

Peter Strawson's reduplication argument, developed in (1959,20–22), can be construed as an argument for singularpropositions. Strawson used the argument to support the related thesisthatdemonstrative identification is fundamental to ourability to identify and hence refer to, in speech and thought,individuals. Demonstrative identification ofo isenabled by one sensibly discriminatingo from otherindividuals. So one can demonstratively identify only individuals thatone has perceived. But one can think about other individuals aswell. These further individuals, then, must be descriptivelyidentified. Individuals that one identifies demonstratively aredirectly identified and not identified in virtue of their satisfiesqualities by which the agent conceives the object, as individualsdescriptively identified are. (This distinction is reminiscent ofRussell's distinction between thought by acquaintance and thought bydescription. We compare Russell and Strawson in more detail below.)Strawson's notion of demonstrative identification is thus closelyrelated to the notions of direct reference and singularpropositions.

A reduplication universe is one in which the same set of qualities aredistributed in the same pattern across two regions. There are bothtemporal and spatial versions of reduplication. We shall focus on thespatial version, as Strawson does. Suppose that Sally lives in areduplication universe. Sally is standing in front of Bill, thinkingthat he has a stain on his shirt. In another region of the universethere is a qualitatively identical set of circumstances. So, there isSally*, who is just like Sally, standing in front of Bill*, who isjust like Bill, thinking that he has a stain on his shirt. For anypurely qualitative condition Bill satisfies, Bill* satisfies ittoo. Nonetheless it seems highly intuitive that Sally is thinkingabout Bill and not Bill* (and Sally* is thinking about Bill* and notBill); after all, it is Bill and not Bill* that she is standing infront of and who is the obvious source of her judgment.

Suppose that all forms of identification were descriptive, so thatidentifying an object required qualitatively discerning it from allothers. Then, as Sally cannot discern Bill from Bill* in whollyqualitative terms, her thought is not determinately about Bill ratherthan Bill*. But intuitively her thoughts are about Bill, in virtue ofthe fact that she is in perceptual contact with Bill rather thanBill*. This is even more clear when we consider Sally's thought aboutherself. When Sally says to herself, ‘‘I amhungry’’, she is thinking of herself and not Sally*. Butif her thought about herself were in terms of purely qualitativeconditions, then she would be unable to think determinately of herselfinstead of Sally*. So, she must be capable of an alternative form ofthought and identification that is distinct from and does notpresuppose descriptive identification. Call this form ofidentificationdemonstrative identification. We have arguedthat it is distinct from and does not depend upon descriptiveidentification.

The argument we have presented above presupposes that Sally and Sally*and Bill and Bill* are numerically distinct but qualitativelyindiscernible pairs of objects. Although many find this to be agenuine possibility, thanks in large part to Max Black (1952)and Robert Adams (1979), there is a long tradition thatsubscribes to the Identity of Indiscernibles (PII), according towhich, for any objectsx andy, if, for everyqualityF,x isF if and only ifyisF (i.e., ifx andy are qualitativelyindiscernible), thenx=y. But the argument can bedeveloped in such a way that it does not presuppose the falsity ofPII. Let there be a quality that Bill and Bill* lacks. Then thedistinctness of Bill from Bill* is consistent with PII. But now letSally (and thus Sally*) be unaware of Bill's (and Bill*'s)instantiating that quality. As long as Bill and Bill* arequalitatively indiscernibleas far as Sally is concerned andyet intuitively Sally is thinking of Bill and not Bill*, the aboveargument for the irreducibility of demonstrative identification todescriptive identification goes through, even if it is not possiblefor there to be distinct objects with all the same qualities.

So far we have argued that demonstrative identification is notreducible to descriptive identification. But Strawson makes thestronger claim that, in the reduplication universe, descriptiveidentification depends on demonstrative identification. To get thisstronger claim consider an object that Sally has never perceived butcan intuitively think about — say, Bill's mother. Strawsonclaims that considering this case proves false the claim “thatwhere the particular to be identified cannot be directly located[i.e., cannot be demonstratively identified because it cannot beperceptually discriminated], its identification must rest ultimatelyon description in purely general [i.e., qualitative] terms”(1959, 21). Bill's mother (call herMorgan) isqualitatively indiscernible from Bill*'s mother. So Sally is unable todistinguish in purely qualitative terms Morgan from every other objectin the universe. But intuitively she can nonetheless think ofher. This is because Sally can demonstratively identify Bill and thushave thoughts determinately about Bill as opposed to his qualitativetwin Bill* and then think of Morgan under the descriptive conditionBill's mother. As Bill is directly given, this is a conditionthat Morgan and not her qualitative twin Morgan* satisfies. ThusSally's ability to descriptively identify objects in the universe isultimately grounded in her ability to demonstrative identify somestock of objects, identifying other objects in virtue of the uniquerelations they bear to members of that stock. Strawson argues that thegeneral way of relating objects one has not perceived to thosedemonstratively identified is by way of spatio-temporalrelations. (See (1959, 22) in particular, but much of the discussionthat follows in chapter 1 is aimed at establishing the Kantian claimthat spatio-temporal relations are the privileged set of relations forenabling identification of particulars.)

Let's grant that to have a thought determinately about an individualin a reduplication universe requires possessing an irreducible,fundamental form of demonstrative identification. What bearing doesthat have on thought about individuals in nonreduplication universesand in particular thought about individuals in our universe, which wetake, rightly we can suppose, to be a nonreduplicationuniverse. Although Strawson does not argue in this way, the followingseems compelling. Grant that our universe is in fact not areduplication universe. But it could have been. Had there been, insome distant part of the universe, a qualitative duplicate of me andmy surroundings, my thought would not have taken a different form thanit actually has. But the considerations above show that, had we beenliving in a reduplication universe, then demonstrative identificationwould have been irreducible and fundamental. But then it is actuallyirreducible and fundamental.

We end this section by briefly comparing Strawson's view withRussell's and the contemporary neo-Russellian's views. We have seenthat, for Russell, like Strawson, demonstrative identification plays acrucial role, in the form of acquaintance. But unlike Strawson,Russell denies that we demonstratively identify extra-mentalindividuals. Russell can deliver the intuitively correct results thatSally's thoughts are determinately about Bill and not Bill*, eventhough she is not, on Russell's view, able to demonstratively identifyBill. This is because Sally can demonstratively identify her sensedata that are caused by Bill and not Bill*. On Russell's view, Sallydescriptively identifies even Bill, but the descriptive condition sheemploys contains direct reference to her occurrent sense data. She isthus able to form a descriptive (although not purely qualitative)condition that Bill satisfies and Bill* does not. For this reason,Russell is better able to handle the reduplication argument than theFregean.

Both Strawson and Russell claimed that thought about particulars isultimately grounded on direct reference. But they disagree about whatwe can directly refer to, with Strawson claiming that it includesperceived objects in the external world and Russell that it onlyincludes mental particulars. It is important to note, however, that asfar as the reduplication argument is concerned, this difference is oflittle consequence. As long as there is a stock of individuals thatare thought of directly and not in terms of purely qualitativeconditions that can serve as the anchors in terms of which thequalitatively indiscernible objects can then be discerned, theintuition that Sally is thinking determinately of Bill and not Bill*is respected.

Strawson maintained that an agent can demonstratively identifyonly objects that she has perceived. Neo-Russellians typically go astep further, claiming that an agent can think directly about objectsshe has not perceived in virtue of standing in the appropriatecommunicative chains ending in the object. So, even though you havenever perceived Plato, we will safely suppose, you can neverthelessthink directly about Plato in virtue of your standing in acommunicative chain that ultimately traces back to perceptions (on thepart of other agents in the communicative chain) of Plato. (For arepresentative of this view, see Bach's (1994, chapter 2).) Someneo-Russellians go even further and maintain that there needn't be anyperceptual contact at all with an object to think about itdirectly. (See, for example, Kaplan 1975b, where he defends the thesisthat the dthat-operator can transform any designating expression intoa directly referential term, competence with which enables an agent tothink about the designation of the original term directly. Hence, LeVerrier was able to think about Neptune directly despite the lack ofperceptual contact with the planet (we will suppose) in virtue of hiscompetence with the expression ‘dthat[the cause of theperturbations in Uranus's orbit]’. See also Robin Jeshion's(2002) for a similar view, in that she too thinks perceptual contactwith an object is not necessary for thinking of that object directly,although she does not appeal to Kaplan's dthat-operator. (For more onthese topics, see the papers collected in Jeshion 2010.)

We thus have a spectrum of views that agree that there is directreference to individual in thought and language but disagree about itsscope, from Russell's restrictive view of direct reference, accordingto which an agent can only think directly about her occurrent sensedata, to the liberal view of direct reference held by Kaplan andJeshion, according to which objects that have never been perceived canbe thought about directly. All of these views respect the intuitionthat Sally's thoughts are determinately about Bill and notBill*. Thus, while the reduplication argument makes a powerful casethat there issome direct reference and hence that singularproposition are necessary for an adequate account of reference toindividuals in thought and language, it does not settle the furtherissue of how much of our thought is direct and involves the graspingof singular propositions and what is thought by description. That is,while the reduplication argument might settle that there are singularpropositions, we must appeal to different considerations, like thoseinvolved in the argument from indexicals and demonstratives, toresolve the further issue of what individuals can be constituents ofsingular propositions and under what conditions.

5. Modal Problems for Singular Propositions

In sections 2–4, we discussed three sets of argument for the thesisthat there are singular propositions. The first, the modal argument,was broadly linguistic in nature and the other two, the arguments fromindexicals and reduplication, were pyschological. But singularpropositions also give rise to a number of important metaphysicalproblems, in addition to those involving propositional attitudes andapparent substitution failures already discussed. We end this essay bydiscussing two related problems: Modal problems and temporalproblems.

Consider the following proposition.

(7)George Bush does not exist.

(The number designates the proposition actually expressed by‘George Bush does not exist’, not the sentence itself.)While (7) is false, it might have been true. But suppose (7) is asingular proposition, involving George Bush as a constituent. Thenthere are problems, given the following two principles.

(P1) Necessarily, for all propositionsp, hadp been true, thenp would haveexisted.
(P2) Necessarily, if (7) were true, then George would not have existed.

Both principles are highly plausible. (P1) is plausible becausebeing true is a property and there must be something that hasa property in order for that property to be instantiated. So, had itbeen that a given proposition were true, then there must have beensomething — namely, that proposition — that would have hadthe property of being true. (P2) states the intuitive truth conditionsof (7), being an instance of the modalized propositional equivalent ofthe Tarski truth-schemas is true iffs. But theseprinciples seem to entail that, if (7) is a singular proposition, thenit is not possibly true. For suppose it were. Then there is a worldw in which (7) is true. By (P1), (7) exists inw. But then all of its constituents exists inw as well, as a complex does not exist in a worldunless all of its constituents exist in that world. But then GeorgeBush exists inw. So, by (P2), (7) is not true inw, which contradicts our original assumption that itis true inw. So, either (7) is not a singularproposition or it is not possibly true.

The basic structure of this argument derives from Alvin Plantinga'sargument from his (1983) against what he calledexistentialism, the thesis that all individual essences aredependent upon the individuals that instantiate them. Plantingaconcluded that a singular proposition abouto canexist even thougho does not exist. (See inparticular (1983, 8–9), where he argued that the notion ofconstituency is too confused to allow us to conclude that theconstituent of a singular proposition must exist in a world for thatproposition to exist in that world.) Plantinga also argued that thepropertybeing identical too can existwithouto, even though that property is constructedby λ-abstraction from the proposition [ois identical too]. Plantinga would have been muchbetter served, we believe, by denying that propositions like (7) aresingular propositions, on the grounds that, if they were, they wouldnot be possibly true. Instead, propositions like (7) containindividual essences as constituents. (Plantinga should not conceive ofan individual essence as constructs form an individual identityproperty, as that property is dependent on the individual thatinstantiates it. Instead, an individual essence is either a primitiveproperty stipulated to be necessarily related to the individual whoseessence it is or would have been that can nonetheless existunexemplified or the rigidification of some condition that theindividual uniquely satisfies, following Plantinga's response to themodal argument above in section 2.) LetH be such anindividual essence of Bush. Then (7) is true just in caseH is uninstantiated, the proposition [Bush ispresident] is true just in caseH and the propertybeing president are coinstantiated, etc.. The pay-offis that (7)'s being true in a possible world does not violate (P1) and(P2), as there are possible worlds in which Bush's individual essenceexists but is unexemplified.

There are several responses to Plantinga's argument, differing intheir metaphysical underpinnings. The first involves the possibilist'sthesis that there are individuals that are not actual. (See Lewis's(1986).) In that case, what exists in a world does not exhaust whatexists simpliciter. Bush is around to serve as a constituent of aproposition, even with respect to worlds in which he does not exist,because he exists simpliciter by existing in other worlds. Thepossibilist can thus claim that the truth of (P1) does not entailthat, ifp is true inw, thenp exists inw; rather, it onlyentails thatp and all its constituentsexists.

Matters are more difficult if one is an actualist, subscribing to thethesis that absolutely everything is actual. Then, if one accepts theexistence of singular propositions, one has two options. First, onemight deny that propositions like (7) are possibly true, acceptingthat necessarily everything necessarily exists, as Bernard Linsky andEdward Zalta, in their (1994) and Timothy Williamson, in his(2001), do. This position is only as plausible as theexplanation on offer of the intuitive contingency of ordinary objectslike Bush. If being and existence are necessary properties, then somecontingent property must be offered in place that can be used toexplain the intuition that (7) might have been true. Linsky and Zaltaclaim thatbeing concrete is a contingent property. Theyclaim that Bush might have been nonconcrete and that, when we considera world in which he is nonconcrete, we are inclined to say that hedoes not exist there. Although the virtues of this view are many, notthe least of which is the simple and straightforward modal logic itvalidates, we are very reluctant to accept that concreteness is acontingent property.

Finally, if one insists that propositions like (7) are singularpropositions that are possibly true, then one must claim that (7) istrue at worlds in which it does not exist, thus denying (P1). (Examples include Adams 1981, Deutsch 1994, Fine 1977 and1985, Fitch 1996, and Menzel 1991 and 1993.) A propositionp is truein a worldw justin case, werew actual, thenp wouldhave been true. Call thisinner truth. (P1) is true for innertruth and there are no singular negative existential propositions like(7) that are true in any possible worlds. But there is another notionof truth with respect to a possible world that is associated withgenuine necessity and contingency. Adams describes this notions asfollows.

A world-story [a maximal, consistent set of actually existingpropositions] that includes no singular proposition about meconstitutes and describes a possible world in which I would notexist. It represents my possible non-existence, not by including theproposition that I do not exist but simply by omitting me. That Iwould not exist if all the propositions it includes, and no otheractual propositions, were true is not a fact internal to the worldthat it describes, but an observation that we make from our vantagepoint in the actual world, about the relation of that world story toan individual of the actual world. (1981, 22)

The world-story corresponding to a possibility where George Bush doesnot exist does not, then, contain (7) as a member. Instead, (7) istrue with respect to the possibility that world-story describes invirtue of the world-story omitting mention of Bush altogether. Fromthe perspective of the actual world, and with its resources, we cansay that (7) is true at that possibility, even though, from theperspective of the possibility itself, there is complete silence aboutGeorge Bush. Call thisouter truth.

The intuitive possible truth of (7) is an example of one side of ourintuitions of the contingency of existence, being an example of thepossible nonexistence of a thing that actually exists. An example ofthe other side of those intuitions concerns the possible existence ofsomething that does not actually exist. As a matter of fact, NataliePortman and George Bush did not have any children together and so,given plausible essentialists intuitions, nothing that actually existscould have been their child. But they could have had a child. Hadcertain contingent happenings occurred, then there would have been aperson parented by Portman and Bush. So, (8) below is intuitivelytrue.

(8) Nothing that actually exists could have been parented by Portman and Bush, but it is possible that there is someone parented by Portman and Bush.

The possibilist maintains that what actually exists is a proper subsetof what exists. So, while nothing in the domain of the actual worldcould have been Portman and Bush's child, there are things in the mostinclusive domain of quantification, which includes merely possibleindividuals, that are parented by Portman and Bush in some possibleworlds. On Plantinga's view, there is an uninstantiated individualessence that could have been instantiated and, had it beeninstantiated, it would have been instantiated by something that wasparented by Portman and Bush. On Linsky and Zalta's view, there is anonconcrete individual that could have been concrete and, had it beenconcrete, it would have been parented by Portman and Bush. All threeviews, then, seem to easily account for the truth of something closeto (8). (The last view must offer a slight revision of (8): While anonconcrete individual actually exists and could have been parented byPortman and Bush, nothing that is actually concrete could have beenparented by Portman and Bush.) Proponents of the last view consideredabove, however, do not countenance merely possible individuals,uninstantiated individual essences, nor contingently nonconcreteindividuals. Instead they must give a different account of the secondside of our intuitions that what exists is contingent.

Following Adams 1981, proponents of our final view can claim that theactually existing quantified proposition [There is someone parented byPortman and Bush] is a member of a world-story corresponding to thepossibility in which Portman and Bush have a child together, but noatomic proposition of the form [o is parented byPortman and Bush] is a member of that set, as there is no suchproposition that could have been true. (If there were such an atomicproposition, then there would be something that could have beenparented by Portman and Bush, which there is not.) So, there arequantified propositions that are true at a possible worldw even though there are no witnesses of thosepropositions — i.e., no corresponding singular propositions— true atw. This requires abandoning a generalanalysis of the truth of quantified propositions to the truth ofatomic propositions. The best that a proponent of this account can sayis that, had one of the possibilities in question been actual, thenthere would have been such a singular proposition and so there wouldhave been a witness to the possibly true quantified proposition. But,as things actually are, the quantified proposition could have beentrue even though there is no singular proposition that could have beentrue.

None of the solutions considered in this section are without theirproblems. The possibilist recognizes a distinction between existingand actually existing that requires a bloated ontology. Plantinga'ssolution requires mysterious entities — individual essences thatcould exist unexemplified and thus that are individuated independentlyof the individuals that instantiate them. Linsky and Zalta's solutionruns contrary to the robust intuition that what individuals therehappen to be is a contingent matter and requires that ordinaryexistents could exist as nonconcrete objects. And the final solutionrequires a distinction between how matters stand in a possible worldor from the perspective of that possible world and how matters standat that world, which many find mysterious and claim to require anunpalatable form of realism about possible worlds. The account alsorequires complicating one's quantified modal logic, as it entails thatthere are theorems of classical quantificational logic (for example,∃x(a=x)) that are contingent, requiring either arevision of classical quantificational logic, and a movement to a freelogic, in which case those problematic classical theorems are nolonger theorems, or a restriction on the standard Rule ofNecessitation of standard modal logic, in which case there arecontingent logical truths. (For a more detailed discussion of theissues raised in this section, see the entry on thepossibilism-actualism debate.)

6. Temporal Problems for Singular Propositions

Singular propositions are a combination of the abstract andconcrete, which leads to problems. The modal problem arises because,on the one hand, there are reasons to think that all propositions, asabstract objects, exist necessarily, but, on the other hand, it ishighly intuitive that ordinary individuals might not have existed andothers could have existed, in which case the singular propositionscontaining them as constituents exist contingently. The solutions tothis problem discussed above involve denying that there are singularpropositions, denying that ordinary objects are contingent existents,or denying that propositions are necessary existents. The temporalproblems we shall consider in this section arise because ordinaryindividuals change over time, including coming into and going out ofexistence. Propositions, on the other hand, are usually taken to beeternal objects — things that do not change over time and existat all times.

Consider the following proposition.

(9)Socrates existed but does not exist.

(9) seems like a true singular proposition, as Socrates died longago. How then is (9) true, as its constituent Socrates does not existand so it does not exist? This is clearly the temporal analog of themodal problem discussed in the previous section. Moreover, if (9) is asingular proposition, then what is the constituent of (9) like? Howold is it? Is it sitting or standing? It seems absurd to say that theage of a constituent of a proposition is thus and so and that it issitting and not standing, yet if Socrates himself is a constituent of(9), then he must be a determinate age and must be in a determinateposition; no person exists without being a determinate age and beingin a position. Our second set of questions also have modal analogs andit may help clarify the issues to present them before exploringanswers to the temporal problems.

Bush in fact has two arms, but he might have had only one. But then ifBush himself is a constituent of the proposition that Bush has twoarms, he must either have exactly two arms or exactly one arm, itwould seem, as no person exists without having a determinate number ofarms. But neither answer seems satisfying. This issue is related toproblems of temporary and accidental intrinsics. (See his (1986,chapter 4).)

In the next two sub-sections we consider each set of issues inturn.

6.1. Temporal Problems for Singular Propositions: Quantitative Change

In section 5 we considered the modal version of the first set ofissues and saw how one's account is connected tolarger issues in the metaphysics of modality. Similarly, one'saccount of the temporal problems is connected to larger issues in themetaphysics of time. Recall the possibilist solution from section5. The temporal analog of possibilism is eternalism, according towhich what exists at a time is but a proper subset of what existssimpliciter. (Works that defend eternalism include Heller 1990,Lewis 1986, Mellor 1981 and 1998, Quine 1963, Sider 1997 and 2001,Smart 1955, and Williams 1951.) The eternalist maintains that,although Socrates does not presently exist, he does exist simpliciterand so is available to be the constituent of (9), even at times atwhich he does not exist. (9) is true, then, because Socrates is in thedomain of a past time but not in the domain of the present time.

Presentism is the temporal analog of actualism. Presentists maintainthat absolutely everything is present; entities, like Socrates, thatdo not presently exist, simply do not exist. (Works that defendpresentism include Crisp 2002, 2005, and 2007a/b, Hinchliff 1988 and1996, Markosian 2003, Prior 1959, 1962, 1965, 1970, and 1977, andZimmerman 1996 and 1998a/b.) Presentists have a hard row to hoe inaccounting for the apparent truth of (9). In the previous section weoutlined three actualist accounts of (7) and (8). Each has a temporalanalog that can be applied to (9).

First, the presentist might appeal to Plantingian individual essences,claiming that (9) is not a singular proposition containing Socrateshimself as a constituent, as there is no such entity, but rather aproposition with Socrates's individual essence as a constituent. (9)is then true because that individual essence was instantiated in thepast but is no longer instantiated.

Second, the presentist might claim that Socrates does exist, albeit asa nonconcrete object, adopting the temporal analog of the view held byLinsky and Zalta. Then, although (9) is false, if the predicate‘x exists’ is regimented as∃y(y=x), a related proposition concerning Socrates'sconcreteness is true. Socrates was concrete and now, while he stillexists, is nonconcrete. (This view carries a commitment to the claimthat a concrete objectbecomes nonconcrete and that anonconcrete objectbecomes concrete, which is even moreproblematic than the claim that concreteness is a contingentproperty.)

Third, the presentist might follow Adams and distinguish aproposition's being truein a time from its being trueat a time. Consider first a negative existential about acurrently existing object. It is true that George Bush did not existin 1820 because the singular proposition [George Bush exists] is falseat 1820. The proposition is not true in 1820, because it did not existwhen 1820 was present, as its constituent Bush did not existthen. (9), however, is a negative existential about a past object thatno longer exists. It is, then, more analogous to (8) from above,illustrating the second half of our intuitions that existence iscontingent, than to (7). (8) has a quantificational form on itssurface, while (9) appears to be singular. This difference makes isquestionable whether appeal to the truth in/truth at distinction canbe used by the presentist to develop an account of (9)'s truth andthus whether there is a viable presentist analog to Adams's actualistview.

To see why, focus on the first conjunct of (9): ‘Socratesexisted’. This appears to have the formP∃x(s=x), whereP is the past-tenseoperator ‘it was the case that’. But that carries acommitment to the wholly past object Socrates, contrary topresentism. The presentist must, then, reinterpret (9) so that it doesnot involve a proposition singular with respect to Socrates, even oneembedded in the scope of tense operators. This is problematic, as itentails that the sentences ‘George Bush was sitting’ and‘Socrates was sitting’ express propositions with radicallydifferent forms, despite their evident surface grammaticalsimilarity.

Finally, there is a fourth presentist solution worth discussing, whichalso has a modal analog not discussed in the previous section. Onemight insist that, although Socrates does not exist, Socrates isnonetheless a constituent of reality, in the range of the mostunrestricted of quantifiers and available as a constituent of singularpropositions. This is because there are entities that do notexist. This form of Meinongian presentism, according to whicheverything thatexists at all presently exists, althoughthere are things that do not presently exist and so do not exist atall, has been defended by Mark Hinchliff (Hinchliff 1988; 1996). Manyfind the distinction between being and existing obscure and theMeinongian metaphysics incredible, but the view promises a solution tothe problems similar to possibilist and contingent concretenesssolutions but with an alternative metaphysics. (For further discussionof eternalism and presentism, see the entriesspacetime: being and becoming in modernphysics andtime. For discussion ofMeinongianism, seeexistence andnonexistent objects.)

6.2. Temporal Problems for Singular Propositions: Qualitative Change

We raised two questions concerning (9). We discussed the first insection 6.1 and we now turn to the second. In order to better focusattention on the second issues, we switch to an apparent singularproposition about a presently existing object, setting aside theissues connected with the problems of section 6.1.

(10)Bush is sitting.

Bush changes his position, sitting att and standing att'. Then (10) is true att and false att'. (Not all would agree that the proposition, as opposed totensed sentence, varies its truth value across time. We discuss thisbelow.) Suppose that (10) is a singular proposition with Bush as aconstituent. What is that constituent like? No answer seems tosatisfy. By the law of excluded middle, either it satisfies thecondition ‘x is sitting’ or it doesn't. If itdoes, then why is (10) false, as it is att'; if it doesn't,then it why is (10) true, as it is att? It also seemsstrange to think of that (10) itself as changing in its constituentsacross time, as one and the same proposition is beingevaluated at the different times.

One's answers to these questions depends on one's views on the natureof persistence through time and change. Broadly speaking, there aretwo realist views of change: Perdurantism (or four-dimensionalism orthe doctrine of temporal parts), which reduces persisting objects tomore fundamental, momentary objects, and endurantism (orthree-dimensionalism), which takes persisting objects as primitive,maintaining that a persisting object is “wholly present”at each time it exists (see Crisp and Smith 2005 for an interestingattempt to articulate this notion). Proponents of the perdurantisminclude Armstrong 1980, Heller 1990, Jubien 1993, Lewis 1971, 1976, 1986, and 1988, Quine 1960 and 1963, Robinson 1982, Russell1927, Smart 1955 and 1972, Taylor 1955, and Williams 1951, amongothers. Versions of endurantism are defended in Chisholm 1976,Forbes 1987, Geach 1966 and 1967, Haslanger 1985, 1989a/b, and 2003,Hinchliff 1988 and 1996, Johnston 1983 and 1987, Lowe 1987, 1988, and1998, Mellor 1981 and 1998, Thomson 1983, van Inwagen 1990 and 2000,Wiggins 1968, 1980, and 2001, and Zimmerman 1996 and 1998a/b, amongothers. (There are important differences between the versions ofendurantism defended in these works, related to whether or not“tense is taken seriously”, presentism is accepted orrejected, whether or not seemingly monadic properties likebeing age 64 are treated as relations betweenindividuals and times, and whether or not the instantiation relationbetween individuals and properties is claimed to obtain only relativeto a time. See the entriesidentity overtime andtemporal parts forfurther discussion.)

Perdurantists maintain that a persisting object is a sum of momentarytemporal parts. An object persists through an interval of time byhaving numerically distinct temporal parts existing at each moment inthat interval. An object undergoes a change in its qualities acrosstime by having numerically distinct temporal parts with contraryqualities. A close cousin of perdurantism is the stage view, defendedin Hawley 2001 and Sider 1996, 1997, 2000, and 2001, according towhich the subject of temporal predication is a momentary temporalpart. Whereas perdurantists claim that a name like ‘Bush’designates a sum of temporal parts, stage theorists maintain that itdesignates a momentary object. A past tense predication like‘x was sitting’ is true of that momentary stages, assuming this a case of the simple past tense, just incase there is an earlier temporal part that bears the counterpartrelation tos that satisfies the condition ‘xis sitting’ (and similarly for future tense predications). Ifsingular propositions are the contents of those sentences, then it isnatural to claim that different propositions, with different temporalparts as constituents, are expressed by utterances of the sentence‘Bush is sitting’ at different times. There are, then, twodistinct propositions corresponding to (10).

(S-10₁) Bush-at-t is sitting.

(S-10₂) Bush-at-t' is sitting.

(S-10₁) is false simpliciter, being false both att andt', while (S-10₂) is truesimpliciter. In general, then, the constituent of a singularproposition is a temporary object.

Proponents of perdurantism and the stage view have natural answers toour questions about the subject constituent of singular propositions like(10). Perdurantists can claim that the subject constituent of (10) is a sum oftemporal parts. (10) is true att because the part of thatsum that directly exists att has the property of sitting;(10) is false att' because the part of that sum thatdirectly exists att' has the property of not sitting. Stagetheorists can claim that there are a host of distinct propositionscorresponding to (10), each with a distinct momentary stage as subjectconstituent in whatever state the object is in at the time of itsexistence. Momentary objects have their properties absolutely. So,Bush-at-t is simply sitting, although itwill be notsitting in virtue of there being a numerically distinct momentaryobject that is not sitting that is the first's latercounterpart. Bush-at-t' is simply not sitting, although itwas sitting in virtue of its earlier counterpart'sproperties.

These accounts of the constituents of singular propositions concerningan object's changing properties presuppose theories of qualitativechange incompatible with the intuition that a persisting objectdirectly bears each of its changing qualities at each time it exists,not inheriting those qualities from the properties of numericallydistinct objects. Endurantists take this intuition as acenterpiece. One and the numerically same object, endurantistsmaintain, exists at different times and directly bearers the qualitiesthe persisting object possesses at any time. The endurantist must,then, develop alternative answers to our questions about (10).

On one version of endurantism, relationalism, seemingly monadicproperties like sitting and not sitting are really time indexedproperties like sitting-at-t and not sitting-at-t',which are properties that an object simply has, instantiating them (ornot, as the case may be) absolutely. Unlike the original unindexedproperties of sitting and not sitting, these two indexed propertiesare not contraries and so there is no problem saying that one and thesame object simply has both of them. Like the stage theorist, therelationalist claims that there are in fact a multitude of distinctpropositions related to (10), like the following.

(R-10₁) Bush is sitting-at-t.

(R-10₂) Bush is sitting-at-t'.

(R-10₁) and (R-10₂) have absolute truth values,the first being true simpliciter and the second false simpliciter. Anutterance of the sentence ‘Bush is sitting’ ontexpresses (R-10₁) while an utterance of that sentence ont' expresses the distinct proposition(R-10₂). This much is analogous to the stagetheorist's account. But unlike the stage theorist, the relationalist claimsthat there is a single object that directly bears the properties inquestion, the time index qualifying the property and not the subjectof predication. So, there is a single common subject constituent toall of the distinct (R-10) propositions.

The stage theorist and relationalist both reject the claim that apersisting object directly bears each of contrary properties it haswhen it undergoes a change in qualities, the stage theorist rejectingthat the same object directly bears the qualities at the differenttimes and the relationalist denying that the properties are genuinelycontrary. Some claim that rejecting either of the claims is tantamountto rejecting the very notion of a thing's changing its qualitiesthrough time. A proponent of the final version of endurantism, adynamic relativist, insists that one and the same object, Bushhimself, in the case of (10), directly bears the genuinely contraryproperties of sitting and not sitting. The relativist avoidscontradiction by claiming that an object doesn't simply have (or lack)a property simpliciter but has (or lacks) a property relative to atime. Bush has, relative tot, the property of sitting andlacks, relative tot', the property of not sitting. Aproponent of this view rejects the idea that there is a single,fundamental, coherent way things are that transcends how things are ata time. While there are several distinct dynamic accounts worthdistinguishing, what unites them all is the idea that, at the mostfundamental level, a temporally neutral proposition like (10) is trueat one time and false at another. A proponent of this view should beparticularly troubled by our question about the constituent of(10). While (10) is true att and false att', thetime relativization does not affect anything intrinsic to theproposition itself; both Bush and the property remain the same whenthe proposition is evaluated at these different times. But then whatis the subject constituent of (10) and what is its connection to theproperty of sitting?

There are two competing theories to consider. According to the bundletheory, an individual is a bundle of properties. According to thesubstance theory, an individual is an entity distinct from itsproperties in which those properties inhere.

One attractions of the bundle theory is its promise of explainingpredication in terms of membership, where the object identified with abundleB of properties instantiates a propertyF just in caseF is amongB. This, however, works against a relativist invokingthe bundle theory to answer our second problem. Suppose that thesubject constituent of a singular proposition is a bundle ofproperties. What properties are in the bundle? If the object undergoesa change, then is (i) exactly one member of the pair of contraryproperties among that bundle, (ii) both properties, or is the bundle(iii) incomplete, containing neither of the pair? (Recall, therelativist claims that it is the same proposition that is true at onetime and false at another and so nothing intrinsic to the propositionalters; it must, then, be the same bundle of properties that is theobject constituent in both cases.) None of the options seemappealing.

Suppose that, corresponding to (i), the constituent of (10)includes exactly one of the contrary properties of sitting and notsitting: say, not sitting. Then it is hard to see how (10) is true, asit is att, given that the object constituent is a bundle ofproperties including the property of not sitting. Suppose that,corresponding to (ii), both properties are among the bundle. Then itis hard to see how Bush exists, given that he is an inconsistentbundle of properties. Finally, suppose that, corresponding to (iii),the bundle of properties identified with the object constituent of(10) contains neither of its changing contrary properties sitting nornot sitting. Then, given the bundle theorist's offered theory ofpredication, (10) is not true, even att.

Consider now the substance theory. The relativist proponent of thesubstance theory might claim that the object constituent of (10) is abare particular, independent of all its properties in which all thoseproperties inhere. (10) can then be said to vary its truth valueacross time, being true att and false att',without more ado, as the constituent of (10) neither includes norexcludes sitting. (See the entrysubstancefor further discussion.)

Many reject the substance theory because they think it entails thatsomething could exist without any properties whatsoever. Whilesubstance theorists do claim that the basic bearers of properties areindependent of those properties, being the entities in whichproperties are, in the first instance, instantiated, it does notfollow from this that there is something that can exist without anyproperties at all. To see why, distinguish, first, an object'stemporary properties (i.e., the properties it has at some times of itsexistence and not at others) from its permanent properties. As far asthe problem of temporal qualitative variation goes, the constituent ofa singular proposition witho as a constituent neednot exclude its permanent properties and so need not be a completelybare particular, as the object instantiates those permanent propertieswhenever it exists.

Not all permanent properties are necessary. The property of havingbeen conceived in Provo is a permanent property of Susan butcontingent, as her mother could have been elsewhere when Susan wasconceived. In response to the modal version of our second problem, asubstance theorist should claim that the constituents of singularpropositions are independent of their contingent properties butinvolve their necessary properties. WhereF is anecessary property ofo andG acontingent, temporary property ofo, the singularproposition [o isF] is true at eveyindex while the proposition [o isG]is true at some times and worlds and false atothers.o is thus independent of its contingent butnot necessary properties. The substance theorist can insist, then thatthe object constituent of (10) is not a property-less bare particular,but instead an entity clad in its necessary properties.

Finally, many substance theorists, following Aristotle, have found itnatural to distinguish necessary from essential properties, claimingthat there are some necessary properties that are accidental. Forexample, everything necessarily has the property of beingself-identical, but that property is a poor candidate as an essentialproperty. A thing's essence provides its definition, answering theWhat is it? question. Being told that the thing isself-identical does not provide much by way of an answer to thatquestion, as it does not offer grounds for distinguishing the thing inquestion from other things. Contrast this with the general essence ofbeing human. Being told of some particular that it is a human doesprovide insight into what the thing is. And the property beingidentical too is a good candidate for a singularessence. While the latter property does not so much ground theidentity and diversity ofo as simply presuppose it,it is a property cognitive grasp of which constitutes an understandingof whato is.

A temporary, contingent singular proposition like (10) is true atsome indices and false at others, while a necessary singularproposition, like the proposition [Bush is such that 2+2=4], has thesame truth value at every index. Essentialist singular propositions,like the proposition [Bush is human], also have the same truth valueat every index, but, unlike mere necessary propositions, areintrinsically true, in the sense that an adequate account of thesubject position constituent, and so a full understanding of what thatentity is involves conceiving of it as having that property, provides one with the grounds to recognize it as true without furtherlogical operation or inference. An individual and its essentialproperties may still be conceptually distinct entities for thesubstance theorist, the substance theorist can still claim that anindividual is nonetheless tightly connected to some of itsproperties. The substance theorist can thus does not need to conceiveof the object constituents of singular propositions as bareparticulars.

7. Conclusion

There are compelling reasons to countenance singular propositionsas the contents of some sentences of natural language and ourattitudes. But singular propositions give rise to metaphysicaldifficulties, as propositions have traditionally been taken to benecessary, permanent existents, but ordinary objects arenot. Solutions to these difficulties require stances on general issuesin the metaphysics of modality and time. In this essay we havesurveyed some of the reasons for accepting singular propositions,examined the metaphysical difficulties they create, and distinguishedseveral strategies for solving those difficulties.

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Acknowledgments

Sadly, Gregory Fitch passed away January 27, 2007. Prior to hisdeath, he made arrangements for Michael Nelson to take over the entryas co-author. Although the two authors discussed much of thismaterial and shared a common perspective on the content of thisarticle, Sections 3 and especially 4 are new and were writtenindependently by the new co-author. Fitch's original, solely authoredentry is available in the SEP Archives, at <https://plato.stanford.edu/archives/sum2005/entries/propositions-singular/>. (Seetheversion history.) Thanks to Penelope Mackie for extremely helpful editorial advice.