Individuals as sets of perspectives

Timothée Bernard, Philippe de Groote

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Timothée Bernard, Philippe de Groote. Individuals as sets of perspectives. LENLS21 - 21st International Workshop of Logic and Engineering of Natural Language Semantics, Nagoya University, Nov 2025, Nagoya, Japan. hal-05482006

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Individuals as sets of perspectives

Timothée Bernard

Philippe de Groote

Université Paris Cité, CNRS, LLF

Université de Lorraine, CNRS, Inria, LORIA

timothee.bernard@u-paris.fr

philippe.degroote@loria.fr

**Introduction.** It is commonly acknowledged that the substitution of co-referential expressions within the scope of a propositional attitude verb is not valid. (This is one of Frege's famous puzzles.) By contrast, widespread is the assumption that substitution of co-referential expressions is valid in simple sentences. The data put forward by Saul (1997), however, cast doubt on this assumption. Since Clark Kent and Superman are the same individual, (1) seems true, but for each of the minimal pairs in (2), the first sentence seems true while the second seems false.

(1) Superman is Clark Kent.

(2) a. (i) Clark Kent went into the phone booth, and Superman came out.

(ii) *Clark Kent went into the phone booth, and Clark Kent came out.

b. (i) Superman was more successful with women than Clark Kent.

(ii) *Superman was more successful with women than Superman.

In what follows, we propose to take these intuitions seriously and to provide a fully compositional system that correctly predicts the corresponding truth values, without resorting to pragmatic. This system is based of the non-standard notion of *perspectives*, which are intuitively ways of viewing an individual. Marie Curie as a scientist, Marie Curie as a woman, Marie Curie as the recipient of the 1903 Nobel Prize in Physics, etc., are all perspectives on Marie Curie. These perspectives are *perspectives on* an individual rather than *perspectives from* a point of view, and thus differ from the notion of perspective discussed for instance by Lasersohn (2016) but are conceptually closer to Fine (1982)'s *qua-objects*. To theorise certain relations such as that between an object and the matter that constitutes it, Fine postulates qua-objects such as Socrates qua philosopher, and for a statue and the matter that constitutes it, that matter qua statue.

Our proposal relies on the idea that, although Clark Kent and Superman are intuitively the same individual, they correspond to two distinct (though not disjoint) sets of perspectives. And just as the properties of an individual may vary across worlds (e.g. Marie might have been shorter had she eaten less soup as a child), the perspectives associated with a proper name also vary across worlds (in a world where Marie Curie never took an interest in science, she would lack a scientist perspective).

**Perspectives as the counterparts of events in the nominal domain.** In previous work (de Groote and Bernard, 2025a), following Larson (1998), we argued that a parallel in inference patterns between verb-adverb and noun-adjective combinations should be extended to the level of formalisation by applying a Davidsonian-like treatment to the nominal domain.

More precisely, (3a) does not entail (3b) and (4a) does not entail (4b).

(3) a. Marie dances beautifully and Marie sings.

b. Marie sings beautifully.

(4) a. Marie is a beautiful dancer and Marie is a singer.

b. Marie is a beautiful singer.

The lack of entailment from (3a) to (3b) is accounted for in event semantics, following Davidson (1967), by the hypothesis that an event mediates between a verb, its possible adverbial, and
its subject. In the neo-Davidsonian tradition (Parsons, 1990), the meaning of (3a) is typically represented by (5a), which, as expected, does not entail (5b), the meaning of (3b).

$$ (5) \quad \begin{array}{l} \text{a. } (\exists e_1. \mathit{dance}(e_1) \land \mathit{ag}(e_1) = \mathit{Marie} \land \mathit{beautiful}(e_1)) \land (\exists e_2. \mathit{sing}(e_2) \land \mathit{ag}(e_2) = \mathit{Marie}) \\ \text{b. } \exists e. \mathit{sing}(e) \land \mathit{ag}(e) = \mathit{Marie} \land \mathit{beautiful}(e) \end{array} $$

Similarly, we argued that the lack of entailment from (4a) to (4b) is due to the existence of a perspective mediating between a name and the noun and adjective used to describe it. We represented the meaning of (4a) as formula (6a) and that of (4b) as (6b), where $p > x$ indicates that $p$ is a perspective on individual $x$. Larson (1998) suggests a similar but more complex analysis, with actions introduced by a *generic quantifier* (Chierchia, 1995) rather than perspectives introduced by a standard existential quantifier.

$$ (6) \quad \begin{array}{l} \text{a. } (\exists p_1. \mathit{dancer}(p_1) \land p_1 > \mathit{Marie} \land \mathit{beautiful}(p_1)) \land (\exists p_2. \mathit{singer}(p_2) \land p_2 > \mathit{Marie}) \\ \text{b. } \exists p. \mathit{singer}(p) \land p > \mathit{Marie} \land \mathit{beautiful}(p) \end{array} $$

In our previous work, we took intersective adjectives (e.g. *Polish*, *kind*) to lexicalise predicates of individuals, and subsubcessive adjectives (e.g. *skilful*) to lexicalise predicates of perspectives. The system predicted the usual inference patterns without introducing predicate modifiers or invoking the notion of intension as in Montague (1970)'s solution.

In subsequent work (de Groote and Bernard, 2025b), we also proposed to view possible worlds as sets of eventualities, which we take to include not only the usual ones (states and events) but also perspectives, resulting in analyses such as:

(7) a. Marie is a skilful journalist.

$$ \text{b. } \lambda w. \exists x. \exists p. p \in w \land \mathit{journalist}(p) \land \mathit{skilful}(p) \land p > x \land \mathit{Marie} = x $$

(8) a. A journalist is sleeping.

$$ \text{b. } \lambda w. \exists x. \exists p. p \in w \land \mathit{journalist}(p) \land p > x \land \exists e. e \in w \land \mathit{sleep}(e) \land \mathit{ag}(e) = x $$

This previous system, however, is somewhat unsatisfactory, in that (1) is analysed as the term $\lambda w. (Superman = Clark Kent)$, which is a tautology in some models and a contradiction in all others, whereas sentence (1) is neither. Below, we propose a treatment of proper names that accounts for all of the examples above, and leads us to reconsider some aspects of our theory and to clarify the distinction between perspectives and states.

**Names as sets of perspectives.** The core idea defended here is that proper names lexicalise sets of perspectives rather than individuals. Intuitively, if two set-of-perspectives individuals share one or more perspectives (in a world $w$), they are the same individual (in that world $w$). We assume that the actual existence of an individual corresponds to the existence of a *material* perspective, and that if two set-of-perspectives individuals share perspectives, then they share at least their material perspective. On this view, identity statements can be contingents (at least in an epistemic sense), because two set-of-perspectives individuals may share perspectives in some but not all worlds.

In standard formal semantics, individuals (in a broad sense including persons and objects) are treated as primitive, with constants and variables of type $e$ in the logical language. Here, we propose to dispense with the type $e$. We consider instead perspectives to be primitive, and that certain sets of perspectives are perceived or conceptualised as wholes: these sets of perspectives *are* the individuals. Individuals thus emerge from the notion of perspectives. Explaining why some sets of perspectives but not others constitute individuals — this is related to how we decompose the universe, typically along criteria of spatio-temporal continuity — is out of the scope of this abstract. Instead, we develop our proposal on the basis of this assumption.
Formally, in addition to the type *t* for truth values, we posit a single type *v* for events, states, and perspectives. Each model defines a domain *D*<sub>v</sub>, of which a subset *P* ⊆ *D*<sub>v</sub> is the set of perspectives, and a set of set-of-perspectives individuals *I* ⊆ P(*P*). This set *I* essentially serves (i) to interpret constants of type ⟨v,t⟩ lexicalised by proper names (e.g. *Marie*) and (ii) as the domain of the quantifiers (∃x, ∀x) introduced by quantified noun phrases (e.g. *a journalist*). Another subset *W* ⊆ P(*D*<sub>v</sub>) specifies the worlds of the model: a world is seen as the set of events, states, and perspectives that occur or obtain in it. Classically, worlds satisfy a maximality condition (they are complete; nothing can be added to them, and in particular, no world is strictly contained within another), though we will not formalise this condition here.

As mentioned above, we impose the two following constraints on individuals and worlds:

(9) $\forall x \in I. \forall w \in W. \forall p_1, p_2 \in x. (p_1, p_2 \in w \land \mathit{material}(p_1) \land \mathit{material}(p_2)) \rightarrow (p_1 = p_2)$
(Each individual contains at most one material perspective per world.)

(10) $\forall x_1, x_2 \in I. \forall w \in W. ((x_1 \cap x_2 \cap w) \neq \emptyset) \rightarrow (\exists p. \mathit{material}(p) \land p \in (x_1 \cap x_2 \cap w))$
(If in a world two individuals share perspectives, their material perspective is among them.)

We analyse (1) above as (11):

(11) $\lambda w. \exists p \in (\mathit{Clark Kent} \cap \mathit{Superman} \cap w)$

In the Superman fiction world *w*, Superman and Clark Kent are the same person and therefore share at least one perspective. But things could have turned out different, and Superman could have been, say, the photographer Peter Parker rather than the journalist Clark Kent. Such a possibility implies the truth of (12a), analysed as (12b), where *May*(*w*) is interpreted as the set of worlds accessible from *w* (à la Kripke).

(12) a. Peter Parker may be Superman.

b. $\lambda w. \exists w' \in May(w). \exists p. p \in (Peter Parker \cap Superman \cap w')$

We analyse (13a) as (13b) and (14a) as (14b). In *w*, Clark Kent — but not Superman — is associated with a journalist perspective, so (13a) and (14a) are predicted true and false respectively.

(13) a. Clark Kent is a journalist.

b. $\lambda w. \exists p. p \in (\mathit{Clark Kent} \cap w) \land \mathit{journalist}(p)$

(14) a. Superman is a journalist.

b. $\lambda w. \exists p. p \in (Superman \cap w) \land \mathit{journalist}(p)$

Verbal predicates are usually taken to be sortal, unlike adverbial predicates, in the sense that an event satisfying *sing* cannot also satisfy *dance*, though it may satisfy *beautiful* or another adverbial predicate. We assume that not only nouns but also intersective adjectives lexicalise sortal predicates, and thus that the composition of an intersective adjective with a noun describe two perspectives. Our system correctly predicts the equivalence between (15a) and (16a).

(15) a. Marie is a Polish scientist.

b. $\lambda w. \exists p_1, p_2. p_1, p_2 \in (Marie \cap w) \land Polish(p_1) \land scientist(p_2)$

(16) a. Marie is Polish and Marie is a scientist.

b. $\lambda w. (\exists p_1. p_1 \in (Marie \cap w) \land Polish(p_1)) \land (\exists p_2. p_2 \in (Marie \cap w) \land scientist(p_2))$

The neo-Davidsonian tradition treats thematic roles as relations (often functional) between
events and individuals. Consider, for example, (5a) and (5b), where *ag* is a function from events to individuals. To understand how to model thematic roles in a system where individuals are construed as sets of perspectives, let us turn to the sentence *Marie left*. If Marie left, we can intuitively view her as the agent of a leaving-event (*e*), as in the traditional picture (*ag*(*e*) = *Marie*). But this paraphrase also immediately provides us with an analysis in terms of perspectives; just as the possibility of viewing Marie as a physicist signals, in our view, the existence of a physicist perspective, the possibility of viewing Marie as the agent of an event *e* signals the existence of an agent-of-*e* perspective. We therefore introduce, for each thematic role, a function from events to perspectives. For an event *e*, *ag*(*e*) ∈ *Marie* indicates that *ag*(*e*) is the perspective on Marie as agent of *e*. Accordingly, we analyse *Marie sang beautifully* as:

$$ (17) \quad \lambda w. \exists e \in w. \mathit{sing}(e) \wedge \mathit{beautiful}(e) \wedge \mathit{ag}(e) \in \mathit{Marie} $$

**Compositional implementation.** The fragment of English that we develop here, shown in Figure 1, follows several principles of Champollion (2015)'s quantificational event semantics. In particular, the grammar is directly compositional (i.e. it does not assume a separate level of Logical Form; Jacobson 2012); verb entries contain an existential event quantifier; information can be transmitted from higher to lower nodes in the syntactic tree (and thus under the quantifier introduced by the verb) through a continuation-based system (see the *f* variables), which is ultimately closed off by a covert [closure] operator at the root (where ⊤ denotes a tautology); thematic roles are treated as covert operators, such as [ag], which combine with the arguments of verbs. Two adjacent constituents combine, depending on their types, by functional application, by generalised conjunction ⊓, or by continuation application @.

In line with a fairly standard view (Rothstein, 2004), we assume that the copula is semantically vacuous, as is the article *a* in noun phrases used as predicates, and that, in identity statements (such as *Clark Kent is Superman*), the copula triggers a type-shift (here *ϕ*) of the post-copular DP (*Superman*). A sample of derivations is shown in Figure 2.

<figure><img src="image_2.png" /><figcaption>Figure 1: The compositional fragment.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2: Some derivations.</figcaption></figure>
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