The descriptive content of names as predicate modifiers
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Abstract
In this paper I argue that descriptive content associated with a proper name can serve as a truthconditionally relevant adjunct and be an additional contribution of the name to the truthconditions. Definite descriptions the soandso associated by speakers with a proper name can be used as qualifying prepositional phrases as soandso, so sentences containing a proper name NN is doing something could be understood as NN is doing something as NN (which means as soandso). Used as an adjunct, the descriptive content of a proper name expresses the additional circumstances of an action (a manner, reason, goal, time or purpose) and constitute a part of a predicate. I argue that qualifying prepositional phrases should be analyzed as predicate modifiers and propose a formal representation of modified predicates. The additional truthconditional relevance of the descriptive content of a proper name helps to explain the phenomenon of the substitution failure of coreferential names in simple sentences.
Keywords
Names Substitutivity Modified predicates Qualification Adverbs Adjuncts1 Introduction
 (1)

The President of Belarus is blacklisted
 (2)

The chairman of the Belarusian Olympic Committee is not blacklisted
 (1)

\(\begin{aligned} & {\mathfrak{M}}^{g w t} { \vDash }\left( {\lambda y.B\left( y \right)} \right)\left( {\iota x.P\left( x \right)} \right)iff \\ & {\mathfrak{M}}^{{g(_{y}^{d} ) wt}} { \vDash }B\left( y \right),where\,d = I_{{\left\langle {w, t} \right\rangle }}^{g} \left( {\iota x.P\left( x \right)} \right). \\ \end{aligned}\)
 (2)

\(\begin{aligned} & {\mathfrak{M}}^{gwt} { \vDash }\left( {\lambda y.\sim\,B\left( y \right)} \right)\left( {\iota x.C\left( x \right)} \right)\,iff \\ & {\mathfrak{M}}^{{g(_{y}^{d} )wt}} { \vDash }\sim\,B\left( y \right),\,where\,d = I_{{\left\langle {w, t} \right\rangle }}^{g} \left( {\iota x.C\left( x \right)} \right)\,iff \\ & {\mathfrak{M}}^{{g(_{y}^{d} )wt}} { \nvDash }B\left( y \right),\,where\,d = I_{{\left\langle {w, t} \right\rangle }}^{g} \left( {\iota x.C\left( x \right)} \right). \\ \end{aligned}\)
 (3)

Cassius Clay was never beaten whereas Muhammad Ali lost five times.
The paper is structured in the following manner. In the next two sections I explain the notion of asphrases modification and list its semantic properties. In Sect. 4 I propose a formal representation of asphrases modification and, in Sect. 5, I briefly outline a way in which the puzzle of substitution failure of proper names in simple sentences could be solved with the help of this formalism. Section 6 contains concluding remarks and finally in Sect. 7 I present the formal machinery for predicate modifiers and prove some statements.
2 Qualifying prepositional asphrases
Let us look again at (1), (2) and (3) sentences. It is very natural to paraphrase all of them using asphrases: Lukashenko had a ban on visiting the EU as the President of Belarus but had no ban on visiting the EU as the chairman of BOC. Similarly the greatest boxer was never beaten when he fought as Cassius Clay and he lost five times when he fought as Muhammad Ali.^{2} All the paraphrases contain the as preposition which, as with all prepositions, syntactically should be completed by a NPphrase (Carnie 2006: 69). Such a NPphrase could be very complex and contain explicitly expressed predicates or it could be represented by the anaphoric pronoun such (as such). The presence of the such pronoun in a paraphrase is evidence of adjectival anaphora with a propertydenoting expression taken as antecedent.^{3},^{4} For example, if we paraphrase (1) as ‘The President of Belarus is blacklisted as such’ we naturally understand that the anaphoric pronoun such stands in this sentence for ‘the President of Belarus’. Similarly in cases of sentences containing an asphrase and a proper name (as in Forbes’ example ‘Lex fears Clark, not as such but as Superman’) the proper name is understood as standing for a property, and that is why it can be replaced by the pronoun such which takes an adjective as an antecedent.
 (1′)

The President of Belarus is blacklisted as the President of Belarus
 (2′)

The chairman of the BOC is not blacklisted as the chairman of the BOC
The codenoting descriptions ‘the BOC chairman’ and ‘the President of Belarus’ have different descriptive content which modifies the main predicate differently, and that is why the change of one description to another could affect the sentence truthconditions. In effect, this possible change in truthcondition blocks the substitution of descriptions. I think that we have the same phenomenon in the case of the substitution failure of coreferential proper names. But before I go further and present the semantics for modified predicates and outline how the descriptive content of proper names could be a predicate modifier, I need to mention the objections against predicate modification by asphrases raised by Szabó (2003).
Szabó raised two objections against treating asphrases as predicate modifiers (2003: 392). His syntactic objection has a general form and is raised against treating asphrases as modifiers of any sort. If asphrases are modifiers it should be possible to iterate them but it is not the case (‘*John earns $50,000 as a judge as a janitor’). His semantic objection concerns an intuitive semantic connection between initial and modified predicates. Intuitively from ‘John was invited as a mathematician to the congress’ it is possible to conclude that ‘John was invited to the congress’ but for those who advocate predicate modification, an initial and modified predicates are different, so the connection between them is lost. Keeping in mind these objections, in the next two sections I will briefly present my proposal for treating asphrases as predicate modifiers.
3 Semantic properties of prepositional asphrases
 (4)

Sebastian strolled through the streets of Bologna at 2 a.m.
 (4′)

\(\exists_{e} \left( {Strolled\left( {S,e} \right) \wedge Through \,the \,streets\, of \,Bologna\left( e \right) \wedge At \,2\, a.m.\left( e \right)} \right)\)
Clark (1970) proposed an alternative treatment of adverbs and prepositional phrases.^{9} The core of his proposal is the idea that predicates could be built recursively out of nplace predicate constants by adding modifiers which have i places in total. So let us take ‘stroll’, for example. It is 1place predicate. If you add the adverb ‘slowly’ to ‘stroll’ (getting ‘slowly stroll’) you would not increase the number of argument places. So ‘slowly’ is a 0place modifier (as are many other adverbs). The extension of ‘slowly stroll’ is a subset of the extension of ‘stroll’ (Clark 1970: 325) and that is why you can infer from ‘Sebastian slowly strolled’ that ‘Sebastian strolled’ but not the other way around. This type of adverbial entailment failure is known as NonEntailment (Davidson 1967; Katz 2008). Now take ‘at’ and ‘through’. Each of them are 1place modifiers and if you add them to ‘stroll’ (getting ‘strollthroughat’) you will increase the number of argumentplaces and will get a new 3place predicate out of a 1place initial one. You can infer from ‘Sebastian strolled through the streets of Bologna at 2 a.m.’ (Davidson 1967: 167) that ‘Sebastian strolled’ because the new 3place predicate is connected with the initial 1place predicate ‘stroll’ by a requirement that an object occupying the first place of the triple (Sebastian) should belong to the extension of ‘stroll’ (this type of entailment is called Drop). I will leave aside a syntactical definition of adjuncts [see (Carnie 2006: 162; 2008: 151)] together with all syntactic features specific for adjuncts such as iteration, reordering [called Permutation, see (Davidson 1967; Katz 2008)] and the ability of adjuncts to stand next to each other (Carnie 2006: 168). By ‘an adjunct predication’ I will understand predication fulfilling NonEntailment and Drop semantic requirements [see (Davidson 1967; Katz 2008)].
Except for the mentioned adverbial entailment properties, sentences with asphrases have one more type of entailment. I will use one of Szabó’s examples (2003: 406) to explain it. Consider: ‘John is rational as a chessplayer’. Applying Drop we are able to infer from this that John is rational. But intuitively we can’t infer that John is rational simpliciter—he is rational in quite a specific way, that is, as a chessplayer (compare a similar case with another prepositional phrase (Szabó 2003: 400): ‘I am happy about the news’. Intuitively, you can’t infer that I am happy simpliciter). From the conclusion you get after applying Drop, ‘X is φ’, you cannot infer that ‘X is φ simpliciter’.^{10} The Drop entailment seems to be unproblematic whereas conditions for the simpliciter entailment are not so easy to discern (cf. Szabó 2003: 403–404). It seems that it is possible to infer from \(A \,as\, B\, is\, C\) that \(A \,is\, C\) simpliciter when for any D (such that \(A \,as\, D\, is\, C\) is true) both \(A \,as\,D \,is\, C\) and \(A \,as \sim\,D\, is\, C\) are true (so there is no need to qualify, ‘She likes him as a philosopher and not as a philosopher—she simply likes him’) but this condition could be too strong, so I leave this entailment unsolved.
4 Modified predicates semantics
I propose to treat prepositional asphrases (‘invited as a mathematician’) as 0place predicate modifiers. Unlike other prepositional phrases, asphrases do not increase the number of argumentplaces (‘invited’), and, unlike adverbs, they do not modify a predicate with all its argument places as a whole. Instead, they modify it on one argumentplace only. Imagine a situation in which an object d is an agent of two simultaneous actions, A and B, but only one of these actions is such that d is doing it as φ. Szabó attempted to give an appropriate truthconditions for such a situation by means of a requirement that only one action from A and B was a part of d’s state φ. I will preserve the spirit of such an intuition but instead of assuming a mereology of states and events I will use the inclusion relation between predicates’ extensions (we will see that these two ideas, whilst the same in spirit, will give different results, see footnote 14). Note that if you know that d is doing A and B and is φ, you can’t infer that A or B is done by d as φ (by NonEntailment). This entailment failure shows that the extension of a modified predicate \(doing \,A \,as\, \varphi\) although depending on the extensions of A and φ (by Drop), is not fully determined by them. As we see, the NonEntailment property is the key property in solving the failure of the substitution puzzle. Now let me present the core of modified predicates analysis.
4.1 Syntax
The core idea is simple: intuitively, predicate modifiers make predicates from predicates (see Clark 1970: 320; Pörn 1982: 294; Thomason and Stalnaker 1973: 201; van Fraassen 1973: 104, 107). Formally predicates are built from predicate constants in a recursive way and, due to this, we will use the term ‘predicate’ to refer to all kinds of predicates—atomic predicates (predicate constants), predicate abstracts, modified predicates and modified predicate abstracts.
Let us start from modifiers. By modifier we will understand all predicates abstracted from an atomic formula or a conjunction of atomic formulas with one free variable, e.g., \({\lambda x.Q(x), \, \lambda x.(P(x)\, \wedge\, Q(x)) }\). I assume for simplicity that modifiers are subclass of predicates abstracts and have no free occurrence of variables. Now I will define how atomic predicates are modified:
Definition 1
If \(Q\) is a nplace predicate constant and (\({\lambda x.\varphi }\)) is a modifier then \(Q_{\lambda x.\varphi }^{i}\) is nplace predicate modified by (\({\lambda x.\varphi }\)) on ith argument place of \(Q\) (where 1 ≤ i ≤ n).
Notation ‘\({\lambda x.\varphi }\)’ means that a predicate \(Q\) is modified by a predicate \({\lambda x.\varphi }\) on ith argument place: \(Q\left( {y_{1} , \ldots ,\underbrace {{y_{i} }}_{\lambda x.\varphi }, \ldots , y_{n} } \right)\). We can treat \({\varphi }\) as complex adjective—it can’t change the number of arguments of a predicate (as we remember, it is 0place modifier). Let me give an example: \(greet\) is a twoplace predicate, \({\varphi(x) }\) is a formula with one free variable in which \({\varphi }\) means ‘a host of a party’. \(greet_{\lambda x.\varphi }^{1}\), \(greet_{\lambda x.\varphi }^{2}\) are predicates built via modification from the predicate constant \(greet\); we read them ‘as a host of a party \(x\) greets \(y\)’ (modification on the 1st argument place) and as ‘\(x\) greets \(y\) as a host of a party’ (modification on the 2nd argument place). We will use a simplifying convention and in case a modifier is a predicate abstracted from an atomic formula, \(P(x)\), we will simply write ‘\(Q_{P}^{i}\)’ instead of ‘\(Q_{\lambda x.P\left( x \right)}^{i}\)’ and in case \(Q\) is 1place predicate we will write ‘\(Q_{P}\)’ instead of ‘\(Q_{P}^{1}\)’.
By modifying the same predicate see on different argument places we could avoid the structural ambiguity and emphasize the meaning which could not be emphasized by a conjunction of predicates. The sentence ‘Sherlock saw the man and was using binoculars’ is true in a situation in which Sherlock saw the man ‘with the unaided eye’ and was using binoculars (for example, scratching his knee with them). Intuitively the truthconditions of the sentence describing the situation on the left picture differ from the truthconditions of the sentence with a conjunction of two predicates.
I allow predicate modification only on one (ith) argument place and do not say how to modify a predicate on other argumentplaces or on the same argument place again (I do not allow for iteration).^{12} Nevertheless, the iteration of asphrases is preserved in a limited form, because I allow that predicates abstracted from a conjunction of atomic formulas could be modifiers. Modifiers could be iterated by conjoining with and connective. In that way the Szabó example ‘*John earns $50,000 as a judge as a janitor’ is ungrammatical (in the same way as ‘*John eats his steak with a fork with a knife’ because you cannot saturate the same argument position twice) but paraphrased with a conjunction (‘John earns $50,000 as a judge and as a janitor’) becomes grammatical (this is my response to Szabó’s syntactic objection).
Now let me say a few words about the modification of predicate abstracts. Although a predicate could be abstracted from any formula, I will limit predicate abstracts which could be modified to predicates abstracted from atomic formulas and the negations of atomic formulas, \(\lambda x.Q\left( {z_{1} , \ldots ,z_{n} } \right)\) and \(\lambda x.\sim\,Q\left( {z_{1} , \ldots ,z_{n} } \right)\). A modifier \({\lambda y.\psi }\) modifies a predicate abstract on ith argument place of \(Q\) (written ‘\((\lambda x.\varphi )_{\lambda y.\psi }^{i}\)’ in general notation).^{13} Formulas with all kinds of predicates are built in a standard way.
4.2 Semantics
The definition of the interpretation of a modified predicate has the following general form:
Definition 2
If \(Q\) is a nplace predicate constant, \(P\) is a 1place predicate constant and \(x\) is a variable, then \(I_{{\left\langle {w, t} \right\rangle }} \left( {Q_{\lambda x.P\left( x \right)}^{i} } \right) \in {\mathcal{P}}\left( {\left\{ {\left\langle {d_{1} , \ldots ,d_{i} , \ldots ,d_{n} } \right\rangle \in I_{{\left\langle {w, t} \right\rangle }} \left( Q \right):d_{i} \in I_{{\left\langle {w, t} \right\rangle }} \left( P \right)} \right\}} \right).\)
A modified predicate is still a predicate—it is interpreted as a subset of the extension of the predicate being modified, a set of ordered ntuples of objects of a domain. However, there is an additional condition: it should be such a set of ntuples that every ith element in ntuples fulfills the descriptive content φ with respect to the time and world of evaluation. This condition is needed to avoid the unintuitive consequence that an ntuple could belong to the extension of a modified predicate, despite the fact that the ith element in the ntuple does not fulfill the descriptive content which modifies the predicate. In that way the interpretation of a modified predicate is related to the extension of the predicate being modified (we get Drop from Definition 2 which is a response to Szabó’s semantic objection).^{14}
In such a way somebody could have a property \(\varphi\) but not a property ‘\(\varphi \, as \,\psi\)’ or could have a property ‘\(\varphi \,as\, \psi\)’ but not a property \(\varphi\) in any other way (to be \(\varphi \, only\, as \, \psi\)). For example, the extension of the modified predicate ‘to give an interview as a boxer’ is a subset of people who gives an interview. Intuitively we could say about Madonna that she belongs to the set of people who gives an interview (\(GI\)) but not to the subset of those who give interviews as a boxer Open image in new window . Intuitively, we could say about Michael Phelps that he took part in the Olympic Games (PO) but only as a swimmer (PO _{ swimmer }), so we would not find him in any other subset of people taking part in the Olympic Games, Open image in new window .^{15} Also if somebody has a property \(\varphi\) and a property \(\psi\), we could not conclude that that he has a property ‘\(\varphi \, as\, \psi\)’ (by NonEntailment). The failure of making such a conclusion was noticed by Aristotle (On Interpretation XI 20b 35): ‘Thus, again, whereas, if a man is both good and a shoemaker, we cannot combine the two propositions and say simply that he is a good shoemaker.’
Modifiers are closed under conjunction.
Definition 3
If \(Q\) is a nplace predicate constant, \(x\) is a variable, and \((\lambda x . \varphi),\,(\lambda x . \psi)\) are modifiers, then \(I_{{\left\langle {w, t} \right\rangle }} \left( {Q_{{\lambda x . \left( {\varphi \wedge \psi } \right)}}^{i} } \right) = I_{{\left\langle {w, t} \right\rangle }} \left( {Q_{\lambda x . \varphi }^{i} } \right) \cap I_{{\left\langle {w, t} \right\rangle }} \left( {Q_{\lambda x . \psi }^{i} } \right)\).
In a similar way, modifiers could be closed under disjunction but I do not add such a definition. I need to say that the generalized logic of modified predicates seems to be a hard nut to crack. One of the puzzling things that comes to mind is a definition of a modifier’s negation (‘but now I am visiting your school not as a police officer’). You cannot define it simply as \(I_{{\left\langle {w, t} \right\rangle }} \left( {Q_{\lambda x . \sim\varphi }^{i} } \right) = I_{{\left\langle {w, t} \right\rangle }} \left( Q \right){ \setminus }I_{{\left\langle {w, t} \right\rangle }} \left( {Q_{\lambda x . \varphi }^{i} } \right)\), because such a definition excludes the possibility for somebody who does \(Q\, as\, \varphi\) to do \(Q\, not\, as\, \varphi\) simultaneously (‘I came to your school as a police officer but also I came to your school not as a police officer—as a father of one of the pupils’). You cannot define the modifier’s negation also as \(I_{{\left\langle {w, t} \right\rangle }} \left( {Q_{\lambda x . \sim\varphi }^{i} } \right) = {\mathcal{P}}\left( {I_{{\left\langle {w, t} \right\rangle }} \left( Q \right)} \right){ \setminus }I_{{\left\langle {w, t} \right\rangle }} \left( {Q_{\lambda x . \varphi }^{i} } \right)\), because you will have exactly the same consequence in case the extension of \(Q\) is a singleton (thanks to Leszek Wroński for discussion here). If you subtract any nonempty set from the family of subsets of \(Q\), you will have the empty set, so it will be impossible for someone to do \(Q\, as\, \varphi\) and to do \(Q\, not\, as\, \varphi\) simultaneously. Maybe in order to define what does it mean that somebody does \(Q\, not\, as\, P\) it would be better to follow the intuition that it means that somebody does \(Q\) in some other way R, where R ≠ P.
The other puzzling thing besides modifier negation is modification by a predicate abstracted from a formula with temporal operators (‘She blessed him as a future sonin law’ [as somebody who would be a soninlaw], ‘As a former police officer [as somebody who was a police officer], he investigated quickly which kid scratched the car’). In a standard way a formula prefixed with a temporal operator is satisfied in a model iff the model satisfies the formula without the temporal operator with respect to a new timeparameter (shifted by the temporal operator). Such a definition is compositional—we drop the temporal operator and check if the formula without it is satisfied in a new timeparameter. It is clear that the compositionality is lost in the case of formulas with predicates modified by a predicate abstracted from a formula with a temporal operator. Intuitively, a guy who, as a former police officer, now investigates who scratched the car may have nothing in common with guys who at some time in the past investigated as police officers who scratched the car. You cannot simply, as before, shift a time parameter and check the truthconditions of a formula without a temporal operator.
In my examples I have mentioned mainly asphrases used as adjuncts of manner (‘I will use the rest of the olive oil as a base for a salad dressing’) but besides expressing a manner asphrases could be used to express time (‘Ann was fat as a child’), reason (‘As a firefighter, John was asked to help in the rescue action’) and purpose (‘They hired him as a launching engineer’). Maybe asphrases could be used to express other characteristics of action or state named by a predicate and it is not clear if the analysis proposed here covers all types of use. For certain it doesn’t cover asphrases used as adjunct of comparison (‘He is in his midforties but his mother still treats him as a child’, ‘He used a spoon as a beer bottle opener’). Understood in the most classical way, a comparison is an act of comparing thing A to thing B under respect C. Comparing A to B we are not saying that A is B (contrary to Definition 2 requirements). Intuitively, when we say ‘Your knife is blunt because you often use it as screwdriver and as a tent peg’ we do not say that some particular knife is a screwdriver and is a tent peg (and, as a consequence, should belong to extensions of these predicates). All we are saying is that this particular knife is often used in a similar way as screwdrivers are used and in a similar way as tent pegs are used. So we can’t use the semantics proposed here to analyze such examples because otherwise all objects such as a screwdriver, a tent peg, a knife, a sharpened ferule, etc. would belong to the extension of ‘a screwdriver’/’a tent peg’ predicates, which is unintuitive consequence. It seems to me that in case of asphrases used as an adjunct of comparison we should give up the requirement that the object taking the ith argumentplace should belong to the extension of a modifying predicate (in such a way asphrases used as an adjunct of comparison may be analyzed in the same manner as adverbs in Clark’s semantics).
5 Modification of a predicate by the descriptive content of a proper name
As I noted earlier, the phenomenon of substitution failure is quite widespread and seems to concern not only names but other corefering NPs, such as group terms, plural terms, natural kind terms and definite descriptions. All these expressions possess a descriptive content that determines an expression’s reference.^{16} As we have seen, sentences like (1) and (2), except of exemplifying the substitution failure, are ambiguous between modified and unmodified readings. This regular ambiguity provides evidence that the descriptive content of a nominal phrase except for determining its extension functions as truthconditionally relevant adjuncts and constitute an additional contribution to the truthconditions (so I entirely agree with Szabó’s proposal on this point). Regularity and truthconditional relevance in its turn shows that the descriptive content is not suggested or implicated. I agree with Forbes (2006: 158) that the asphrase invokes the mode of presentation connected with an expression and propose to treat this ‘ways of giving’ in a similar way as adverbs are treated—as predicates modifiers.
 (3′)

Cassius Clay was never beaten.
 (3″)

Cassius Clay was never beaten as Cassius Clay.
 (3‴)

Cassius Clay was never beaten as such.
Despite being a descriptivist (in my opinion speakers do associate definite descriptions with a proper name), I do not take the phenomenon of predicate modification by the descriptive content of proper names as an argument in favor of the descriptive theory of reference fixing. If you prefer another theory of names you could also accept the phenomenon of predicate modification by descriptive content of names—for example you can hold that descriptions are contained in mental files connected with names and used by speakers to modify predicates but nevertheless the descriptions do not semantically determine name’s reference. Over the next two pages I will outline a way in which proper names could be formally represented. This formal representation is compatible with descriptive thesis about reference determination, that is, with thesis that the reference of a name is semantically determined via satisfaction of descriptive properties. This means that the interpretation of a term which formally represents a proper name depends on the interpretation of a description which, in turn, depends on the interpretation of the predicates it contains. If you do not accept descriptivism you can find a way to connect sets of descriptions with names without an interpretation dependency. Note that the majority of model domains contain no speakers, and that is why I will leave aside all epistemic objections raised against descriptivism and concern on modal and circularity objections only. I am not defending descriptivism in this paper and epistemic objections stay unanswered here (I answered them in Poller (under review b)).
I represent proper names formally as special terms which I call ‘nameterms’. Such terms are rigid but semantically complex and receive their interpretation via a special sort of definite descriptions. I will briefly outline the idea behind such formal representation (a full version of the formal representation of proper names in accordance with the descriptive theory of reference can be found in (Poller 2014). Let me start from iotaterms. In a standard way they are built via applying a \({\iota}\)operator to a formula \({\varphi }\) and designate with respect to a parameter of evaluation if there is only one object which fulfills \({\varphi }\) in a set assigned to the evaluation parameter (otherwise iotaterms fail to designate, Fitting and Mendelsohn 1998: 254, 104). Iotaterms designate contingently with respect to possible worlds but if you add time as another point of evaluation, iotaterms would also designate contingently with respect to times. For example, take ‘the Pope’. It designates different people with respect to different times in our world (or fails to designate). This expression does not designate somebody in particular unless you add ‘present’ to it, getting ‘the present Pope’, or you express a time explicitly (e.g. ‘the Pope in 1967’). ‘The present Pope’, ‘the Pope in 1967’ expressions designate exactly one and the same person (if designates at all) with respect to a possible world and any time. So by ‘a definite description’ I understand a special kind of iotaterms of the form \(\iota x.[_{i} ]\varphi\), where ‘[\({_i}\)]’ is a notational variant of \({\mathbf{then}}_{i}\) operator (‘true at \(t_{i}\)’) taken after (Rini and Cresswell 2012). The time operator [\({_i}\)] fixes a time of evaluation, so for any world \({w}\), time \({t}\) and assignment \({g}\) \(I_{{\left\langle {w, t} \right\rangle }}^{g} \left( {\iota x.[_{i} ]\varphi } \right) = I_{{\left\langle {w, t_{i} } \right\rangle }}^{g} \left( {\iota x.\varphi } \right)\). In other words, a definite description \(\iota x.[_{i} ]\varphi\) designates with respect to any time \({t}\) the object designated by iotaterm \(\iota x.\varphi\) with respect to time \({t_{i}}\). I will call definite descriptions \(\iota x.[_{i} ]\varphi\) actual with respect to \({t_{i}}\).
As we know from the previous section the account of modified predicates presented here is not general, so our most complicated modifier could be a predicate abstracted out of a conjunction of atomic formulas with one free variable. That is why I can use only some of definite descriptions \(\iota x.[_{i} ]\varphi\). To represent proper names formally we need a language \({\mathcal{L}}\) with a set of distinguished predicates \({\left(N_{1},\,N_{2},\,N_{3},\,\ldots\right)}\) which we will read as ‘called \({\alpha}\)’, where ‘\({\alpha}\)’ is a string of sounds or an inscription [arguments supporting such view on verbs of naming could be found in (Geurts 1997: 326–328), see also (Matushansky 2008: 578, 580–581)]. I will use symbol ‘\(!x. \varphi\)’ for iotaterms \(\iota x.\varphi\) with only one variable \({x}\) which occurs free in \({\varphi}\). All descriptions \(!x.[_{i} ]\varphi\) which we connect with a nameterm have a form of \(!x.[_{i} ]\left( {N_{j} \left( x \right) \wedge Q\left( x \right)} \right)\), where ‘\({N_{j}}\)’ is a distinguished predicate and ‘\({Q}\)’ is a 1place undistinguished, e.g. ‘the (present) president called [obama]’. A set of such descriptions will be called ‘\({{\Gamma }}_{{\mathcal{L}}}\)’ (see Sect. 7, Def.VI.S(a)). We avoid Kripke’s circularity argument by treating [obama] as a physical object (a sound or an inscription) which belongs to a model domain, not to a language. It is used as a mark to distinguish somebody (cf. Mill 1889/2011: 41), but the property of ‘being called [obama]’ is not sufficient to determine the reference because a lot of people are called so.
Now I will return to the question of modification. I let nameterms occupy an argument position of predicate abstracts only, \((\lambda x. \varphi)(n)\). Let me add some syntactic definitions (I will present them here in a simplified manner, see Def. V.R13, R17, R18, R22 in Sect. 7):
5.1 Syntax
Definition 4
If \({n}\) is a nameterm, then \({n}\) is a modifier;
Definition 5
If \(\left( {\lambda x.\,Q\left( {y_{1} , \ldots ,y_{m} } \right)} \right)\), \(\left( {\lambda x.\sim\,Q\left( {y_{1} , \ldots ,y_{m} } \right)} \right)\) are predicate abstracts and \({n}\) is a naming term, then \((\lambda x.Q\left( {y_{1} , \ldots , y_{m} } \right))_{n}^{i}\), \(\left( {\lambda x.\sim\,Q\left( {y_{1} , \ldots ,y_{m} } \right)} \right)_{n}^{i}\) are predicates abstracts modified by \({n}\) on ith argumentplace of \({Q}\) (where \(1\leq\, i\leq\, m\));
Definition 6
If \(\left( {\lambda x.\varphi } \right)_{n}^{i} \) is a modified predicate abstract and \({n}\) is a nameterm, then \(\left( {\lambda x.\varphi } \right)_{n}^{i}\,\left(n\right) \) is a formula.
Note that in case a predicate abstract is modified by a nameterm, such a predicate and a nameterm could form a formula iff the nameterm occupying an argument place is the same as modifying nameterm. As I noticed earlier, sentences as (3′) could be paraphrased as (3‴) with the anaphoric pronoun such (cf. ‘Lex fears Superman as such’, Forbes 2006: 158). Treating this case of anaphora in the most classical way, namely as a phenomenon of the interpretation dependence of occurrence of one expression on the interpretation of an occurrence of another expression, it is natural to suppose that the anaphoric pronoun takes as an antecedent an occurrence of the expression explicitly expressed in the same sentence (a proper name) which is the most salient occurrence of an expression.
Definition 7
\({\mathfrak{M}}^{{ \le g w t_{j} }} { \vDash }\left( {\lambda x.\varphi } \right)_{n}^{i} \left( n \right)\) iff there is a description \(!y. [_{j} ]\psi \in \pi_{1} \left( {h^{ \le } \left( {n,w} \right)} \right)\), such that \({\mathfrak{M}}^{{ \le g w t_{j} }} { \vDash }\left( {\lambda x.\varphi } \right)_{\lambda y.\psi }^{i} \left( n \right)\).
 (5)

Lukashenko is not blacklisted (as such)
 (5′)

\(\left( {\lambda x.\sim\,V\left( x \right)} \right)_{n} \left( n \right)\)
 (5″)

\(\sim\,\left( {\lambda x.V\left( x \right)} \right)_{n} \left( n \right).\)
I am grateful to an anonymous referee for calling my attention to sentences with modified predicate of identity, ‘to be identical as \(\varphi\)’. From a technical point of view, there is nothing in semantics presented here which restrains you from choosing any subset of extension of identity predicate as a representation of extension ‘to be identical as \(\varphi\)’ predicate (e.g. you can choose a proper subset, an empty set or the whole set of pairs \(\left\langle {d, \,d} \right\rangle\) such that \(d\) is \(\varphi\)). Could something, taken as \(\varphi\), not be identical with itself (e.g. taken as \(\psi\)) or not?—At this stage the notion needs further investigation and thus I leave it open. However, I think that an interpretation ‘to be identical as being called \(\alpha\)’ is simply a set of pairs \(\left\langle {d, \,d} \right\rangle\) such that \(d\) is called \(\alpha\), and that is why I share the referee’s intuition that there is no true reading of sentences such as ‘Muhammad Ali is not (identical with) Cassius Clay (as such)’. Let me show that there is no true reading of negated sentences with a predicate of identity modified by a descriptive content of a proper name (assuming that an interpretation of ‘to be identical as being called \(\alpha\)’ is simply a set of pairs \(\left\langle {d, \,d} \right\rangle\) such that \(d\) is called \(\alpha\)). As I mentioned earlier, sentences with predicates modified by a descriptive content of proper names and negation are ambiguous between two readings. One of the readings says that there is a description \(!x.[_{i} ]\varphi\) in the set of descriptions associated with ‘Muhammad Ali’, such that it is true about Ali that he as \(\varphi\) is not identical with Cassius Clay. Formula \(\varphi\) is a conjunction \(called \left[ {muhammad \,ali} \right]\left( x \right) \wedge Q\left( x \right)\), where \(Q\) is an atomic predicate true of Ali/Cassius. By definition modifiers are closed under conjunction so for ‘Ali is not identical with Cassius Clay as being called [muhammad ali] and \(Q\),’ to be true it should be so that Ali is not identical with Cassius Clay as being called [muhammad ali]. Yet this contradicts with our assumption—it is highly doubtful that an interpretation of predicates ‘to be identical as being called \(\alpha\)’ differs from the set of pairs \(\left\langle {d, \,d} \right\rangle\) such that \(d\) is called \(\alpha\). The other reading says that there is no description in the set of descriptions associated with ‘Muhammad Ali’ such that it is true about Ali that he is identical with Cassius Clay in any way. This reading is clearly false for the same reason. Both readings emerge as being false which means that sentences of the form NN is MM as such, where NN and MM are coreferential names, are true according to this account (under the assumption that an interpretation of ‘to be identical as being called \(\alpha\)’ is simply a set of pairs \(\left\langle {d, d} \right\rangle\) such that is called \(\alpha\)).
6 Concluding remarks
I raise the hypothesis that sentences with proper names as [Name][Predicate] are ambiguous between two readings, (I) and (II),
\(\left( {\text{I}} \right)\quad \left[ {Name} \right]\left[ {Predicate} \right]\),
\(\left( {\text{II}} \right) \quad\left[ {Name} \right]\underbrace {\left[{Predicate}\right]}_{{{\bf{modified}}\, {\bf{by}} \,\left[{Name} \right]}}.\)
 (6)

The papal nuncio supported an anarchist protest
 (7)

Romain Gary won the Prix Goncourt in 1975
 (8)

Romain Gary was the only person who won the Prix Goncourt twice
 (7′)

\({\mathbf{P}}\left( {\lambda x.W\left( x \right)} \right)\left( n \right)\)—‘a certain person, Romain Gary, won the Prix Goncourt in 1975′;
 (7″)

\({\mathbf{P}}\left( {\lambda x.W\left( x \right)} \right)_{n} \left( n \right)\)—‘a certain person, Romain Gary, won the Prix Goncourt in 1975 (as Romain Gary)’
The substitution of coreferential names in simple sentences could fail, because the different descriptive content of proper names modifies the main predicate differently, so in effect sentences could have different truth conditions. The double truth conditions of different readings (simple and modified) are responsible for the mixed intuitions which speakers feel about such examples. The raised hypothesis about the additional truthconditional relevance of descriptive content associated with a proper name allows one to explain why speakers associate a descriptive content with a proper name—using the descriptive content as adjuncts, they could express propositions that could not be expressed in any other way (without asphrases), for example ‘Romain Gary won the Prix Goncourt twice but only once as Romain Gary’.
In Appendix I will present a formal machinery [languages \({\mathcal{L}}\) and \({\mathcal{L}}^{ + }\) (without and with nameterms)] and prove some useful statements.
Footnotes
 1.
A scope of a negation is without importance here because it does not affect truthconditions—assuming that the descriptions designate, formula (2) and its variant with a negation in wide scope have exactly the same truthconditions.
 2.
Similarly all examples with terms other than proper names and descriptions could also be paraphrased with asphrases: ‘The judges are on strike as judges’/‘The hangmen, as hangmen, are not on strike’ (Landman 1989: 729–730); ‘Water is often dirty but H_{2}O as such is never dirty’, ‘The statue is made of copper but the copper as such isn’t made of anything’ (Szabó 2003: 388), ‘Lex fears Superman as such’, ‘Lex fears Clark, not as such but as Superman’ (Forbes 2006: 158, 159).
 3.
(Carlson 2003: 1231): ‘A wide variety of other anaphoric forms, beyond personal pronouns and temporal anaphora, make reference to an extensive array of other types of things. […] Other forms take as antecedents phrases that are not NPs. […] ‘such’ takes a modifier […] If intelligent students attend college, such students usually do very well.’ (Landman and Morzycki 2003: 140–141): ‘Such, then, can be interpreted as a property of individuals that realize a contextually supplied kind.’ Landman (2006: 56): ‘As observed above, examples like the following […] suggest an account of such as a property variable, as such appears to pick up the reference of a preceding adjective […]’. The view that such is anaphoric to kinds is due to Carlson (1980: 230–236). Arguments supporting the claim that such behaves syntactically and semantically as an adjective and not as adjectival phrase could be found in Siegel (1994: 482) and in Wood (2002: 91).
 4.
Forbes (2006) proposed a solution of The Superman Puzzle based on a semantics of ‘as such’ phrases. According to him, in cases of intuitive substitution failure, simple sentences with proper names such as ‘Lex fears Superman’ should be understood as containing a covert prepositional phrase ‘Lex fears Superman as such’ (2006: 157–158). Forbes treats the such pronoun as a case of logophora (a special case of anaphora in which an expression serving as antecedent is taken itself as a referent of an anaphoric pronoun, 2006: 155, 158), but contrary to him I think that such is adjectivally anaphoric.
 5.
Arguments in favor of this view are given by Szabó (2003: 395–397).
 6.
By ‘modification’ I understand here a syntactical relation defined as follows (Carnie 2006: 85): ‘If an XP (that is, a phrase with some category X) modifies some head Y, then XP must be a sister to Y (i.e., a daughter to YP).’ Strictly speaking, modifying position for adjuncts on a tree is not to be a sister to N, V, A or P but to N′, V′, A′ or P′ (Carnie 2006: 162), which constitutes the main syntactical difference between adjuncts and complements. However I will leave aside this difference in tree position between complements and adjuncts (so I will present adjuncts in simplified manner as ‘sisters’ to ‘V’ on the trees below).
 7.
Besides the standard predicate modifiers Clark proposed the semantics for modifiers that he called ‘fictionalizers’ and ‘negators’ (1970: 329). The characteristic feature of such ‘falsifiers’ is that the intersection of two extensions—of initial predicate (‘Ming vase’) and of it being modified by a falsifier (‘a fake Ming vase’)—is an empty set. The proposition of analyzing expressions as ‘fake’, ‘mythical’, ‘simulated’ in a different way is due to Twardowski (1927). In this paper I will consider only standard modifiers and leave ‘falsifiers’ aside [more can be found in Poli (1991), Cocchiarella (2005), van der Schaar (2013)].
 8.
 9.
A similar treatment can be found in (McConnellGinet 1982).
 10.
Katz (2008: 229) takes cases like these as supplying the claim that state verbs (contrary to events verbs) could be restricted from Drop.
 11.
This picture is taken from von Fintel, Kai. 24.903 Language and its Structure III: Semantics and Pragmatics, Spring 2005. (MIT OpenCourseWare: Massachusetts Institute of Technology), http://ocw.mit.edu/courses/linguisticsandphilosophy/24903languageanditsstructureiiisemanticsandpragmaticsspring2005 (Accessed 26 May, 2014). License: Creative Commons BYNCSA.
 12.
It seems that in natural language asphrases could be iterated and could modify a modified predicate on the same argument place or on different argument place. Consider for example: ‘Teryl Austin has been confirmed as being hired as the Lions new defensive coordinator’ (example from ‘World News’, accessed 11 July, 2014; http://article.wn.com/view/2014/01/18/Lions_hire_Teryl_Austin_as_defensive_coordinator_retain_8_fr/). Intuitively, it is not only the case that Teryl Austin has been confirmed as being hired and as being the Lions new defensive coordinator (conjunction of modifiers), but he has been confirmed as being hired as the Lions new defensive coordinator (modification of a predicate confirmed by the already modified predicate hired as a defensive coordinator). Also a predicate could be modified on several argumentplaces, e.g., ‘As a cardiologist, I refuse to buy you a box of Havana cigars as a birthday gift’.
 13.
I will preserve the intuition that a modified predicate abstract \(\left( {\lambda x.Q\left( {z_{1} , \ldots ,z_{n} } \right)} \right)_{\lambda y.\psi }^{i}\) and a predicate abstracted from a formula with a modified predicate \(\left( {\lambda x.Q_{\lambda y.\psi }^{i} \left( {z_{1} , \ldots ,z_{n} } \right)} \right)\) are one and the same predicate (so you can take a modifier ‘in and out’ of a predicate abstract, see Theorem I in Sect. 8).
 14.
Note that the interpretation of \(Q_{P}\) and \(P_{Q}\) predicates could differ. In case of \(I(Q_{P} )\) and \(I\left( {P_{Q} } \right)\) we have the same requirement that their extension should be a subset of \(I\left( Q \right) \cap I\left( P \right)\) set. Nothing restrains these sets from being different. But, assuming a mereology of states (as Szabó did), you would get quite an unintuitive result. Let me briefly explain. What does it mean on Szabó’s (2003) account that somebody, say \(d\), belongs to \(I(Q_{P} )\) and \(I\left( {P_{Q} } \right)\)? This means [2003: 404 def. (51b)] that there are two states, \(s\) and \(s^{\prime}\), such that \(d\) is agent of both of them and \(P\left( s \right),\,Q\left( {s^{\prime}} \right)\) are true. Moreover, because \(d \in I\left( {P_{Q} } \right)\), it should be so that \(s\) is a part of \(s^{\prime}\). In a similar way, because \(d \in I\left( {Q_{P} } \right)\), it also should be so that \(s^{\prime}\) is a part of \(s\). This means that \(s\) and \(s^{\prime}\) is one and the same state. I find this consequence quite unwelcome. Imagine that Jones is sentenced as a taxdodger and as a prisoner he does not pay taxes. So his state \(s\) if being a prisoner is a part of his state \(s^{\prime}\) of being a taxes nonpayer. In a similar way, his state \(s^{\prime}\) is a part of state \(s\). This means that his state \(s\) of being a prisoner and his state \(s^{\prime}\) of being a nonpayer of taxes is one and the same state. This means in turn that every predicate true of \(s\) should also be true of \(s^{\prime}\). Imagine that Jones is a convinced anarchist and is unhappy to be imprisoned but is happy not to pay taxes. So he is both in a happy and an unhappy state. Assuming a mereology of states, Szabó was trying to avoid such a dilemma (2003: 400), but as we see, the dilemma still remains. Compare a similar example: ‘As a suspect, Jones refuses to make a statement’/‘As refusing to make a statement, Jones becomes a suspect’. On Szabó’s account Jones’s refusingtomakeastatement state and becomingasuspect state should be one and the same state but intuitively these states are two different states.
 15.
I assume in this example that it is only possible to take part in the Olympic Games as an athlete of some kind.
 16.
An anonymous referee drew my attention to possible extension of the proposed account to indexicals. It seems, however, that there is no straightforward way to extend this account to sentences with indexicals, e.g. ‘He (pointing at young Cassius Clay’s photo in a newspaper) was never beaten but he (pointing at Muhammad Ali in another photo) was beaten five times’. Contrary to sentences with other coreferential NPs this is not a descriptive content of indexicals which is used as an adjunct (e.g. ‘male individual’ for ‘he’) because that is stable and thus could not modify the same predicate differently. The descriptive content which is used as an adjunct in this example is a contextually salient property (different in two acts of demonstration) possessed by a referent of an indexical, e.g. ‘a boxer named [cassius clay]’, ‘a boxer named [muhammad ali]’. Firstly, it is unclear how one could extract such a property (should it be a description at all?), and secondly it is far from obvious how one should semantically connect such a property with an indexical. On the other hand, once the property is extracted and by ‘He (pointing) was never beaten but he (pointing) was beaten five times’ one understands something like ‘He, as a boxer named [cassius clay], was never beaten but he, as a boxer named [muhammad ali] was beaten five times’ or something like ‘He was never beaten before 1964 but he was beaten five times after 1964’, one can use the analysis of predicate modification presented here.
 17.
Compare Kripke’s remark about rigidity and scopes of alethic modalities in (1980: 12 footnote 15). Fitting and Mendelsohn (1998: 217) characterize a term’s rigidity as the equality of the broad scope to the narrow scope reading.
Notes
Acknowledgements
I am especially indebted to Katarzyna KijaniaPlacek who provided advice and encouragement at every step of the preparation of this paper. I owe many thanks also to Professor Adam Olszewski for his remarks about the formal semantics presented here. I have also benefited greatly from many discussions with members of Department of Epistemology, Institute of Philosophy, Jagiellonian University and especially with Professor Tomasz Placek, Leszek Wroński, Jacek Wawer, Juliusz Doboszewski and Maja (Sherlock) Białek. A version of this paper was presented at the PhiLang 2013 conference held at the University of Łódź (09.05.–11.05.2013) and I would like to thank all of the audience for their valuable comments on this occasion and especially to Stefano Predelli, Tadeusz Ciecierski and Krzysztof Posłajko. This project was supported by the Ministry of Science and Higher Education of Poland, DEC2012/05/N/HS1/01429.
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