2.1.1 A Nonstarter: Metaphysically Loaded Vocabulary

An intuitively plausible route to a language’s semantic commitments runs through overt category attributions (e.g. (7)) or class-existence statements (e.g. (8)). It additionally – or alternatively – runs through ‘ontological’ sortals (i.e. predicates like proposition and event in (9a); see Reference MoltmannMoltmann, 2022a; Reference VendlerVendler, 1967b, ch. 5). In what follows, I call the former route the ‘overt class’ strategy. The latter is called the ‘sortal’ strategy.

A first challenge for the ‘overt class’ strategy from (7)–(8) is that our ordinary-language use of nouns like fact and event may differ from that of the technical ontological terms ‘fact’ and ‘event’ (see Reference VendlerVendler, 1967a). This challenge is aggravated by the observation that these nouns may even be paraphrased away (see Reference MontagueMontague, 1969, 148, who has claimed that (10a) is equivalent to (10b)).Footnote ¹⁰

An at least equally problematic challenge to the ‘overt class’ strategy lies in the observation that ontological support from constructions like (7) and (8) is limited to a proper subset of those categories that are commonly assumed as part of the semantic ontology. In particular, while category-attribution sentences like (7) and class-existence statements like (8) are acceptable – if not very natural – for concrete entities like individual objects and events, they are deviant for the vast majority of abstract and higher-order objects (see (11) for some variously deviant examples). In what follows, I will use prefixed double superscript question marks (as in (11a)) to indicate that a sentence is semantically very odd or questionable. A single superscript question mark (as in (11b)) indicates that the sentence is semantically slightly or moderately odd.

(11)	a.	${}^{??}$ There are generalized quantifiers.
	b.	${}^{?}$ There are degrees/manners/times.

The ‘sortal’ strategy from (9) avoids the above problem by being applicable to concrete and abstract objects alike. However, this strategy is challenged by the observation (due to Reference PriorPrior, 1963, Reference Prior1971) that sentences with the syntactic form of (9a) are often not equivalent to their ‘sortal-free’ counterparts. Thus, while (12a) describes Sally as standing in the fearing relation to a propositional content (namely, that Fido barks), (12b) describes Sally as standing in the fearing relation to a propositional object (namely, the proposition – qua abstract object – that Fido barks; see Reference MoltmannMoltmann, 2003; Reference Moltmann2013a). Since they relate Sally to different attitudinal objects, (12a) and (12b) have different truth-conditions: In contrast to the truth-conditions for (12a), many of the conditions under which (12b) is true are rather contrived.

(12)	a.	Sally fears that Fido barks.	(Reference GüngörGüngör, 2022, ex. (3))
$̸\equiv$	b.	${}^{?}$ Sally fears the proposition that Fido barks.

Nonequivalences like the one in (12) can also be observed for sentences with non-sortal DPs (in (13) and (14): with the DPs ordinariness, a unicorn) and with DPs of the form ‘the property of [ ${}_{dp}$   ]’ (or ‘the generalized quantifier denoted by [ ${}_{dp}$   ]’; (see Reference MoltmannMoltmann, 2004; Reference Zimmermann, Brandt and FußZimmermann, 2006b; Reference D’AmbrosioD’Ambrosio, 2023). In particular, the result, (13b), of substituting the DP ordinariness in (13a) by the linguistic designator of its intuitive semantic value, i.e. the property of being ordinary, is semantically quite odd.

(13)	a.	Ordinariness is boring.	(Reference MoltmannMoltmann, 2004, ex. (12))
$̸\equiv$	b.	${}^{??}$ The property of being ordinary is boring.
(14)	a.	Sally seeks a unicorn.	(Reference D’AmbrosioD’Ambrosio, 2023, ex. (10))
$̸\equiv$	b.	${}^{??}$ Sally seeks the generalized quantifier denoted by ‘a unicorn’.

I will not dive into the possible sources of Prior’s puzzle here.Footnote ¹¹ For the present purposes, it suffices to point out that these nonequivalences reflect the difference between ordinary entities and semantic values (this point is forcefully made in Reference Zimmermann, Brandt and FußZimmermann, 2006b).

2.1.2 Syntactic and Semantic Categories

My previous discussion has suggested a close correspondence between grammatical and semantic/ontological categories. This suggestion is reflected – to a varying degree – in Reference VendlerVendler’s (1967b) lexical–syntactic investigation of semantic category distinctions (see Section 2.2), in Reference MontagueMontague’s (1970) assumption of a syntax–semantics homomorphism (see Reference JanssenJanssen, 1983; Reference Zimmermann, Ball and BrianZimmermann, 2018), and in Reference Klein and SagKlein and Sag’s (1985) method of type-driven interpretation (see Reference Heim and KratzerHeim & Kratzer, 1998, ch. 3). Specifically, Montague assumes that all elements of the same syntactic category are interpreted in the same semantic domain. This is achieved by combining a ‘semantic uniformity’ constraint on the interpretation of lexical items with a map between syntactic and semantic composition rules.Footnote ¹²

If Montague’s homomorphism were an isomorphism (such that each semantic domain would interpret the elements of exactly one syntactic category; see Figure 1a), the strategies that will be discussed in Sections 2.2–2.4 would provide an easy, reliable route to identifying a language’s semantic commitments (there: the commitments of a reasonably representative fragment of contemporary American English). In fact, the bijective relation between syntactic and semantic categories would make it possible to conduct the project of providing an ontology for natural language at the level of syntax alone, without moving to semantic interpretation.

Figure 1 The naїve (a), Montagovian (b), and flexible (c) view of the syntax–semantics relation.

However, even Montague did not defend such a straightforward picture of the syntax–semantics relation. In particular, Montague’s homomorphism is only surjective (i.e. ‘onto,’ as described in the penultimate paragraph), but not injective (‘one-to-one,’ in the sense described in the previous paragraph). As a result, a single semantic domain may provide the values of different syntactic categories. In Reference MontagueMontague (1970), this is the case for intransitive verbs (IVs; e.g. sleep) and common nouns (CNs; e.g. child), which are both interpreted as properties of individuals. It is also the case for verb phrase adverbs (IAVs; e.g. rapidly) and infinitive-complement verbs (IV//IV; e.g. try to). An illustration of Montague’s syntax–semantics relation is given in Figure 1b (adapted from Reference Liefke and HartmannLiefke & Hartmann, 2018, 319). In this figure, $E_k$ is the set of expressions of syntactic category  $k$ (where $k$ is a variable over categories); $D_k$ is the associated set of semantic values. T is the syntactic category of DPs and quantifier phrases; S is the syntactic category of declarative sentences. Arrows represent Montague’s syntax–semantics homomorphism.

The many-to-one relation between syntactic and semantic categories carries an important caveat for the strategies in Sections 2.2–2.3: Since there may be more syntactic than semantic categories, observing that a language (here: German) resists the grammaticality-preserving substitution of one expression (in (15a): German schlafen [‘sleep’]) by an expression from a different syntactic category (in (15b): Kind [‘child’]) does not, by itself, warrant the inference to two distinct ontological categories.Footnote ¹³ This holds at least so long as this distinction is not supported by other strategies for the identification of ontological categories, or by ontological intuitions (a fact exploited in Reference VendlerVendler, 1967a, Reference Vendler1967b). I will return to this point at the end of Section 2.2.

(15)	$\text{Matti}\left(\begin{array}{cccc}\text{a.}& \text{schl"{a}ft}.& (\text{transl.: Matti sleep-textsc{3sg.subj}.& \text{`Matti is sleeping.'})\\ \text{b.}& {}^{*}\text{Kind.}& (\text{translation: Matti child}& \text{`Matti is a child.'})\end{array}\right)$

It has often been held that Montague’s assumption of a surjective-only relation is undesirable from the point of view of simplicity (see, e.g. Reference CharlowCharlow, 2014; Reference HendriksHendriks, 1993, Reference Hendriks, Gutzmann, Matthewson, Meier, Rullmann and Zimmermann2020; Reference Partee, Groenendijk, de Jongh, Groenendijk and StokhofPartee, 1987): Since Montague’s theory of syntax, Cate-gorial Grammar, identifies syntactic categories via the result of combining its expressions with an expression from a different category, all categories but S and the extensionally empty category  $e$ (intuitively, the category of individual-denoting terms) are complex (see Reference GamutGamut, 1991, ch. 4.3; Reference van Benthemvan Benthem, 1991). For example, since DPs (Montague’s ‘terms’) combine with verb phrases (expressions of Montague’s category IV) to yield a sentence (Montague’s $t$ ; in Figure 1: category S), even referential DPs (e.g. Matti, the boy) are treated as members of a complex category.

As a result of the above, Montague’s syntax–semantics map will require interpreting referential DPs in the same semantic domain as quantifier phrases, that is, as generalized quantifiers. Obviously, this strategy of ‘generalizing to the worst case’ (Reference ParteePartee, 1983, 34) goes against the principle of simplicity (reason: generalized quantifiers are internally complex entities).Footnote ¹⁴ What may even be worse: It violates basic intuitions about meaning and reference. According to these intuitions, proper names contribute their individual referents to the meaning of the linguistic constructions in which they occur (see Section 1.1 and Section 2.2.4).

To obtain the simplest-possible semantic ontology, this Element follows the inverse to the above strategy, namely, ‘try simplest types first’ (Reference Partee, Rosner and JohnsonPartee, 1992, 115).Footnote ¹⁵ This strategy assumes that some subcategories (e.g. referential DPs) may allow for an interpretation as a simpler, less complex object (i.e. as an individual, associated with Montague’s empty category E, originally $e$ ; see Reference HendriksHendriks, 1993, Reference Hendriks, Gutzmann, Matthewson, Meier, Rullmann and Zimmermann2020). Such interpretations are obtained through a series of injective functions (called ‘type-shifters’) that map more complex entities to simpler entities while preserving their distinctness. An example of such a function is Reference Partee, Groenendijk, de Jongh, Groenendijk and StokhofPartee’s (1987) type-shifter lower, which sends a set of properties to the individual that exemplifies these properties. The syntax–semantics relation that results from this strategy is given in Figure 1c. In this figure, dotted arrows represent type-shifters. Dashed arrows represent the syntax–semantics relation that results from applying these type-shifters.

Arguably, not all linguistic expressions have their syntactic category written on their sleeve. This holds for example for the expression a woman in (16), which is ambiguous between the direct object of past-tense see and the subject of the gerundive small clause a woman swimming (for a more detailed discussion of this example, see Section 2.3).

To prevent ambiguities like the one in (16) from distorting our investigation of semantic ontology, I identify ‘syntax’ with Logical Form, LF.Footnote ¹⁶ For the present purposes, I take LF to be the level of syntactic analysis at which ambiguities like the one in (16) are resolved and at which wh-movement and quantifier raising (if any) have taken place. An example of one of the LFs of (16) is given in (17). There, a woman has been raised out of the scope of the verb see (enforcing a de re-reading). In this raising, a woman has received a binder index (here: 1) and has left a trace ( $t_1$ ) that has the same index as its binder. The square brackets around ‘ $t_1$ swimming’ indicate that this string is a syntactic constituent, identifying this reading with the small-clause reading.

(17)	$\left[\text{a woman}{]}_1\right[\text{John saw}\left[t_1\text{swimming}\right]]$

Arguably, working at the level of LF does not undo our observation that there is no royal road from syntax to semantics (and, hence, to ontology). This is so since a single constituent of an LF (e.g. a woman in some non-de re reading of (16)) may still be interpreted in different semantic domains (e.g. as an individual or a generalized quantifier).

In the following subsections, I will present several strategies for identifying a language’s ontological commitments that try to avoid the most obvious syntactic fallacies. These strategies are based on the semantic selection properties of natural language predicates (see Section 2.2), on the study of dedicated proforms (see Section 2.3), and on the identification of implicit semantic arguments (see Section 2.4). They prevent counterintuitive conclusions (to too many, or too few, ontological categories) by focusing on semantic selection and semantic deviance (rather than on syntactic selection and syntactic inacceptability; in Section 2.2), by testing each strategy across a robust range of different constructions (especially in Section 2.3), and by moving away from language use (including language-specific selection and lexicalization) to language modelling (in Section 2.4). The separation of these strategies largely follows Reference AsherAsher (1993), whose classification of abstract entities considers “data about distributional differences and predicate incompatibilities” (see my Section 2.2) alongside “examples concerning anaphora” (Section 2.3) and quantification (Section 2.4; Reference AsherAsher, 1993, 4; cf. Reference Rett and AltshulerRett, 2022).

2.2.1 Facts and Events

One of the best-known instances of the lexical strategy (due to Reference VendlerVendler, 1967a, Reference Vendler1967b, ch. 5) has focused on selectional differences between different nominalizations. Such nominalizations include nominal gerunds like (18a), verbal gerunds like (18c), and that-clause constructions like (18c):

(18)	a.	i. the singing of the song	(ing ${}_{\text{of}}$ )
		ii. John’s singing of the song	(POSS-ing ${}_{\text{of}}$ )
	b.	John’s singing the song	(POSS-ing)
	c.	that John was singing the song	(that-clause)

According to Vendler, only nominal gerunds combine with perception and action verbs (e.g. watch, listen to, imitate), time-dependent existence predicates (e.g. occur, take place, begin, last an hour), and manner adjectives (e.g. slow, sudden, gradual) (see (19)). Only that-clause constructions combine with truth-evaluating predicates (e.g. be true, be false), propositional attitude verbs (e.g. think, know, forget), and speech act verbs (e.g. state, claim) (see (21); cf. Reference AsherAsher, 1993, ch. 1). In contrast to nominal gerunds, that-clause constructions also combine with modal adjectives (e.g. possible, likely, good) and causal predicates (e.g. cause, make, be the result of; see (20a, c)). In this respect, they resemble verbal POSS-ing constructions (see (20b)).

(19)	$\left(\begin{array}{cc}\text{a.}& \text{The/John's singing of the song}\\ \text{b.}& {}^{??}\text{John's singing the song}\\ \text{c.}& {}^{??}\text{That John was singing the song}\end{array}\right)\text{~occurred at noon/was sudden/loud/lasted an hour.}$
(20)	$\left(\begin{array}{cc}\text{a.}& {}^{??}\text{The}{/}^{??}\text{John's singing of the song}\\ \text{b.}& \text{John's singing the song}\\ \text{c.}& \text{That John was singing the song}\end{array}\right)\text{~is unlikely/possible/made Mia blush.}$
(21)	$\text{Mia thinks}\left(\begin{array}{cc}\text{a.}& {}^{??}\text{the}{/}^{??}\text{John's singing of the song}\\ \text{b.}& {}^{??}\text{John's singing the song}\\ \text{c.}& \text{that John was singing the song}\end{array}\right)or:\text{is true/good.}$

The selectional difference between nominal and verbal gerunds is corroborated by the noun-like versus verb-like characteristics of these gerunds: unlike POSS-ing constructions (which require adverbial modification; see (22)), ing ${}_{\text{of}}$ and POSS-ing ${}_{\text{of}}$ constructions only allow for adjectival modification (see (23a)).Footnote ¹⁷ In contrast to their verbal counterparts (see (22b–c)), ing ${}_{\text{of}}$ and POSS-ing ${}_{\text{of}}$ constructions are incompatible with auxiliary verb constructions (see (23b)) and with negation (see (23c); Reference Grimm and McNallyGrimm & McNally, 2022):

(22)	a.	John’s singing the song beautifully
	b.	John’s having sung the song
	c.	John not singing/having sung the song
(23)	a.	John’s beautiful singing of the song
	b.	${}^{??}$ John’s having sung of the song
	c.	${}^{??}$ John’s not singing of the song

Vendler takes the different properties of nominal gerunds and POSS-ing constructions to suggest that these two kinds of gerunds are classified in different semantic categories. In particular, he assumes that nominal gerunds denote events, processes, and actions, while POSS-ing constructions denote facts or results (or, more generally, possibilities; see Reference GinzburgGinzburg, 2005, fn. 11). Vendler motivates this categorization with respect to the specific properties of the pre- dicates from (19) and (20): Since predicates like occur, take place, and begin express temporal properties, the semantic arguments of these predicates are temporal or temporally located objects, namely, events. Since predicates like possible and likely denote atemporal, modal, and causal properties, Vendler identifies their semantic arguments with facts (esp. Reference VendlerVendler, 1967b, 141–146; see also Reference AsherAsher, 1993, for some cases).Footnote ¹⁸

Note that the success of Vendler’s argument for the event/fact-distinction relies on the selectional restrictiveness of the embedding predicate: while restrictive predicates like occur and be possible can be used to argue for a distinction between events and facts (as evidenced by (19)–(20)), selectionally flexible predicates like surprise (which license both nominal gerunds and POSS-ing constructions) challenge such an argument (see (24a–b); based on Reference VendlerVendler, 1967b, 125–126).Footnote ¹⁹

(24)	$\left(\begin{array}{cc}\text{a.}& \text{John's singing of the song}\\ \text{b.}& \text{John's singing the song}\\ \text{c.}& \text{That John was singing the song}\end{array}\right)\text{~surprised me.}$

I will show in Section 2.2.2 that the choice of embedding predicate plays an important role in Vendler’s strategy for identifying semantic commitments: only selectionally restrictive predicates enable the identification of sufficiently fine-grained ontological categories. I will return to this point and discuss its extreme version in Section 2.2.4.

2.2.2 Questions

A parallel situation to the one in (24) can be observed for the ontological distinction between propositions and questions: Much work on the semantics of interrogatives distinguishes rogative predicates (i.e. predicates that only embed interrogative complements) like wonder (in (25b)) from anti-rogative predicates (i.e. predicates that only embed declarative complements) like think (in (25a); see e.g. Reference GrimshawGrimshaw, 1979; Reference LahiriLahiri, 2002). While the selectional difference between rogative and anti-rogative predicates supports the distinction between propositions and questions, the selectional flexibility of responsive (i.e. declarative- and interrogative-embedding) predicates like know (in (25c)) prima facie undermines it (see Reference Ciardelli, Roelofsen and TheilerCiardelli et al., 2017; Reference Theiler, Roelofsen and AloniTheiler et al., 2018):

(25)

$\text{Mia~}\left(\begin{array}{cccccc}\text{a.}& \text{thinks}& \{i.& \text{that},& {\text{ii.}}^{??}& \text{whether}\}\\ \text{b.}& \text{wonders}& \{i{.}^{??}& \text{that},& \text{ii.}& \text{whether}\}\\ \text{c.}& \text{knows}& \{i.& \text{that},& \text{ii.}& \text{whether}\}\end{array}\right)\text{~John was singing the song.}$

For further empirical support for the distinction between propositions, facts, and questions, the reader is referred to Reference GinzburgGinzburg (1995).

2.2.3 Propositions

Much of Vendler’s work discusses the semantic difference between facts and events. Reference VendlerVendler (1967a) complements this discussion with two arguments for a distinction between facts and propositions. The first of these arguments targets a difference in the licensing predicates for POSS-ing and that-clause constructions. The second argument targets a difference in the intensionality properties of embeddings under POSS-ing- and that-clause-licensing predicates.

Vendler’s first argument is based on the observation that only that-clause constructions felicitously combine with propositional attitude verbs (e.g. think, know) and with truth-evaluating predicates (see (21) and its surrounding discussion). Vendler’s second argument is based on the observation that the choice of embedding predicate affects the referential transparency of the sentence containing this predicate (Reference VendlerVendler, 1967a, 709–712; see Reference AsherAsher, 1993, 58): While propositional attitude verbs famously create opaque contexts (i.e. contexts in which the substitution of co-referential or truth-conditionally equivalent expressions does not necessarily preserve the truth of the original sentence; see, for example, Reference Frege and BeaneyFrege, 1997; Reference ForbesForbes, 2006; Reference QuineQuine, 1956), this is not the case for causal predicates. Specifically, in contrast to (26), substituting Jocasta for his [= Oedipus’] mother in (27) preserves the truth of the original sentence (see also Reference Davidson and DavidsonDavidson, 2001):Footnote ²⁰

(26)	a.	Oedipus knew that he was marrying Jocasta.
	b.	Jocasta is Oedipus’ mother.
$\nRightarrow$	c.	Oedipus knew that he was marrying his mother.	(invalid)
(27)	a.	The tragedy was caused by Oedipus’ marrying his mother.
	b.	Jocasta is Oedipus’ mother.
$\Rightarrow$	c.	The tragedy was caused by Oedipus’ marrying Jocasta.	(valid)

Newer literature supports the difference between propositions and facts by referring to the different cancellation behavior of non-factively embedded that-clauses and DPs of the form ‘the fact that [ ${}_{tp}$   ]’ (see e.g. Reference KastnerKastner, 2015). Thus, in contrast to the that-clause construction in (28a), the fact-DP in (28b) cannot be consistently negated. The non-negatability of fact-DPs straightforwardly extends to POSS-ing constructions (see (28c)), as Vendler’s analysis would lead one to expect.

(28)	a.	I explained that the building collapsed. (But it didn’t really.)
	b.	I explained the fact that the building collapsed. ( ${}^{\#}$ But it didn’t really.)
	c.	I explained the building’s collapsing. ( ${}^{\#}$ But the building didn’t really collapse.)

2.2.4 Individuals

Plausibly, Vendler’s selection-based strategy can also be applied to distinguish individuals from events (see Reference VendlerVendler, 1967b, 143–144). In particular, in contrast to ing ${}_{\text{of}}$ and POSS-ing ${}_{\text{of}}$ constructions, concrete referential DPs can combine with adjectives for visually perceivable properties (e.g. color, size, shape, and texture; see (29a)), with object-directed perception verbs (e.g. touch, look at; see (30a)), and with extensional transitive verbs like pull and kick (see (31a)). To show that the referents of concrete referential DPs also resist a co-categorization with facts and propositions, I include POSS-ing and that-clause constructions in the contrast from (29)–(31):

(29)	$\left(\begin{array}{cc}\text{a.}& \text{The/John's book}\\ \text{b.}& {}^{??}\text{The}{/}^{??}\text{John's singing (of) the song}\\ \text{c.}& {}^{??}\text{That John is singing the song}\end{array}\right)\text{is red/thin/smooth/dusty.}$
(30)	$\text{Sally touched/was looking at}\left(\begin{array}{cc}\text{a.}& \text{the/John's book}\\ \text{b.}& {}^{??}\text{the}{/}^{??}\text{John's singing (of) the song}\\ \text{c.}& {}^{??}\text{that John was singing the song}\end{array}\right).$
(31)	$\text{Paul pulled/kicked/tore apart}\left(\begin{array}{cc}\text{a.}& \text{the/John's book}\\ \text{b.}& {}^{??}\text{the}{/}^{??}\text{John's singing (of) the song}\\ \text{c.}& {}^{??}\text{that John was singing the song}\end{array}\right).$

Vendler observes that the above predicates share reference to (points in) space. Since he assumes that individual objects “are in a place, but $\dots$ do not take place at a certain time” ((Reference VendlerVendler, 1967b), 144), he identifies the denotations of concrete referential DPs with individuals (as opposed to events). The separation of individuals and events is supported by Reference MoltmannMoltmann’s (2020a) work on the ontological import of specific existential constructions. This work has found that different English existence predicates (e.g. exist, occur, obtain) select for semantic arguments from different ontological categories and with different spatial and/or temporal properties:

(32)	$\left(\begin{array}{cc}\text{a.}& \text{John's book}\\ \text{b.}& {}^{??}\text{The}{/}^{??}\text{John's singing of the song}\\ \text{c.}& {}^{??}\text{John's singing the song}\end{array}\right)\text{~exists.}$
(33)	$\left(\begin{array}{cc}\text{a.}& {}^{??}\text{John's book}\\ \text{b.}& \text{The/John's singing of the song}\\ \text{c.}& {}^{??}\text{John's singing the song}\end{array}\right)\text{occurred/happened/took place yesterday.}$

In particular, Reference MoltmannMoltmann (2020a) observes that, whereas “exist [only] applies to material and abstract objects” excluding events and facts (318), occur and obtain only select for events and, respectively, for facts. This observation warrants an analogous semantic categorization to the one from Reference VendlerVendler (1967a, Reference Vendler1967b). Reference Rett and AltshulerRett (2022) extends Vendler and Moltmann’s strategy by replacing existence predicates by (nominal, adjectival, and adverbial) modifiers (see also Reference RettRett, 2018). Such modifiers can be used to distinguish degrees (i.e. the semantic arguments of very; see (34a)) from kinds (i.e. the semantic arguments of endangered; see (34b)):

(34)	$\text{Emmy is very~}\left(\begin{array}{cc}\text{a.}& \text{tall.}\\ \text{b.}& {}^{??}\text{Javan rhinos/the Javan rhino.}\end{array}\right)$

Their successful distinction of ontological categories suggests that Vendler and Moltmann’s strategies can be extended to any selectionally restrictive predicates whatsoever. Such generalization would only exclude selectionally super-flexible predicates like remember, which combine with declarative and interrogative finite clauses, infinitival clauses, gerunds, and concrete referential DPs alike (see Reference LiefkeLiefke, 2021). However, this generalization results in a plethora of ontological categories that much exceed Bach’s ontological zoo. An example of such undesirable multiplication of ontological categories is given in (35). In this example, the difference in acceptability between (35a) and (35b/c) seems to indicate an ontological distinction between animate objects (see (35a)) and (concrete or abstract) inanimate objects (see (35b/c)). However, this distinction is not reflected in any mainstream semantic ontologies.

(35)	$\left(\begin{array}{cc}\text{a.}& \text{Paul's cat/The orchid in my office}\\ \text{b.}& {}^{??}\text{The book}{/}^{??}\text{Betty's wedding ring}\\ \text{c.}& {}^{??}\text{Pegasus}{/}^{??}\text{Matti's favorite color}\end{array}\right)\text{has genes/will eventually die.}$

To avoid both a return to an extreme version of Bach’s ontological zoo and the assumption of a single ontological category (as suggested by (24)/(25c); but see Reference Liefke and WerningLiefke & Werning, 2018; Reference SuttonSutton, 2024), it seems advisable to combine the selection-based strategy for the identification of ontological categories with other, different, strategies. One such strategy is presented in Section 2.3. This strategy uses morphological items that are dedicated to a particular semantic category (Reference Rett and AltshulerRett, 2022; see also Reference AsherAsher, 1993; Reference MoltmannMoltmann, 2013a). Since this strategy uses the same proform, namely, it, for reference to animate and inanimate objects (see (36)), it suggests their ontological co-classification.

(36)

$\left(\begin{array}{cc}\text{a.}& {\text{[Paul's cat]}}_i/{\text{[The orchid in my office]}}_i\\ \text{b.}& {\text{[The book]}}_i/{\text{[Betty's wedding ring]}}_i\\ \text{c.}& {\text{[Pegasus]}}_i/{\text{[Matti's favorite color]}}_i\end{array}\right)\begin{array}{c}\text{~is beautiful/awesome.}\\ {\text{Mia likes it}}_i\end{array}$

We will see in the next subsection that the pronoun it, in fact, enables reference to a much wider class of objects than just individuals. This is yet more motivation for the suggestion to combine strategies.

2.4.1 The Method: Indirect Interpretation

To obtain linguistic meanings, this Element will use Reference Montague, Hintikka, Suppes and MoravcsikMontague’s (1973) method of indirect interpretation. This method obtains the semantic values of natural language expressions indirectly, namely, by interpreting these expressions’ logical ‘translations’ in set-theoretic models (typically: models of some $n$ -sorted version, ${\text{TY}}_n$ , of Reference GallinGallin’s (1975) higher-order logic ${\text{TY}}_2$ ). The semantic interpretation of natural language thus proceeds in three steps:

1. (❶) analyze the syntax of a non-trivial natural language fragment (here: a fragment of contemporary American English; see Section 2.1.2);

2. (❷) develop a language ( $L$ ), model-theoretic domain ( $F$ ), and interpretation function ( $I$ ) for the interpreting logic (here: ${\text{TY}}_n$ );

3. (❸) provide a translation function, $⇝$ , (or, historically, a set of translation rules) that sends analyzed linguistic expressions to logical terms.

Figure 2 (adapted from Reference RoelofsenRoelofsen, 2008, 15) illustrates the interpretation, $I\left(\chi \right)$ , of a natural language expression $X$ via $X$ ’s translation into the logical term $\chi$ . To prime intuitions, this interpretation is illustrated on the example of the proper name Brutus from (44) (see (45)). In this example, brutus is an individual ${\text{TY}}_n$ constant that serves as the logical translation of the English proper name Brutus (such that Brutus $⇝$ brutus). Its interpretation, that is, $[=I(\text{brutus}\left)\right]$ , is an object in the domain of the designated ${\text{TY}}_n$ model.

Figure 2 The method of indirect interpretation.

Since the bulk of arguments for certain ontological categories is independent of the specific elements in the model’s domains (see Section 2.4.2–2.4.3 and Section 4), this Element will often stay at the level of logical translations (this level is printed as a darker box with a double frame in Figure 2). This option is not available for semantics like Reference Heim and KratzerHeim and Kratzer (1998), which interpret natural language expressions into logical models directly, without using an intermediary logical language. In the few instances where it is helpful to stay neutral between these competing approaches (e.g. in Section 1 and in Section 5.2), I introduce linguistic meanings through semantic brackets, $〚\cdot 〛$ , (such that $〚X〛=I\left(\chi \right)$ , where $X⇝\chi$ ).

My decision to adopt the method of indirect interpretation is motivated by its domain- and language-independence. I have already pointed out that a focus on logical translations obviates the use of specific set-theoretic models. As a result, this strategy avoids false ontological conclusions that may be brought in by our particular choice of model-theoretic domain(s). Since the Quinean strategy for identifying ontological commitments (see Section 2.4.2–2.4.3) is targeted at existentially quantified variables, it fits more squarely with our preferred ‘logical language’-based indirect interpretation strategy.

To avoid introducing too much complexity, I will not give a detailed specification of the translation function $⇝$ (see step (❸); Reference Heim and KratzerHeim & Kratzer, 1998, ch. 3.1; Reference Zimmermann and SternefeldZimmermann & Sternefeld, 2013).Footnote ²⁶ Instead, I will only assume that there is a principled way of translating complex linguistic expressions, which takes into account the logical translations of these expressions’ syntactic constituents.

To ease the reader into Quine’s strategy for identifying ontological commitments, I finish this subsection by surveying our ‘intermediate’ logical language, $L$ : This language assumes a fixed stock of variables and nonlogical constants. From these basic expressions, it obtains complex terms inductively through the usual connectives (i.e. $=$ , $\neg$ , $\wedge$ , $\vee$ , $\to$ ) and quantifiers ( $\forall$ , $\exists$ ), as well as through F(unctional) A(pplication) and lambda abstraction (for the denotation of functions). In virtue of FA, the application of a function term, $\text{B}$ , to a (suitably typed) argument term, $\text{A}$ , i.e. $\text{B}\left(\text{A}\right)$ , is also a $\text{TY}$ term.Footnote ²⁷ In particular, in (45a–c), functional application allows us to build an open formula, $\text{brutal}\left(e\right)$ , from the function term $\text{brutal}$ (which denotes the functional equivalent of a property of events) and the event variable  $e$ . In the next section, nonlogical constants (e.g. $\text{brutal}$ ) are given bold print. Variables (e.g. $e$ [event], $x$ [individual], and $w$ [possible world]) are written in italics.

2.4.2 Events

I have shown in Sections 2.2 and 2.3 that events serve as the intuitive referents of nominal gerunds and of certain proforms and quantifiers. A commitment to events is further supported by the observation that we need events to account for entailments like (44). These entailments are based on different instances of modifier-dropping (see (44a–d), due to Reference Parsons, Davidson and HarmanParsons, 1972; cf. Reference ColapintoColapinto, 2020). Because of their particular visual shape, these entailments are sometimes called ‘diamond entailments’ (Reference WynerWyner, 1994; see also Reference LandmanLandman, 2000).

(44)	a.	Brutus brutally stabbed Caesar on the forum at noon.
$\Rightarrow$	b.	Brutus brutally stabbed Caesar on the forum.	(temporal-PP drop)
$\Rightarrow$	c.	Brutus brutally stabbed Caesar.	(locative-PP drop)
$\Rightarrow$	d.	Brutus stabbed Caesar.	(adverb drop)

Reference Davidson and DavidsonDavidson (2001) has pointed out that, by interpreting verbs like stab in (44) as relations between events and their arguments, one can straightforwardly account for these entailments (namely, through conjunction elimination, as illustrated by the logical translations of (44a–d) in (45)).Footnote ²⁸ On his account, action verbs like stab have an additional argument slot for events. Adverbs like brutally are interpreted as properties of events. In (45), $e$ is a variable over events. ‘ $\text{stabbing}(e,\text{brutus}$ , $\text{caesar})$ ’ expresses that $e$ is a stabbing event by Brutus whose object (or ‘theme’) is Caesar.Footnote ²⁹ The functions loc (for ‘location’) and time (for ‘point in time’) describe the particular ways in which entities take part in an event.

(45)	a.	$\left(\exists e\right)\left[\text{stab}\right(e,\text{brutus},\text{caesar})\wedge \text{brutal}(e)\wedge \text{loc}(e)=\text{forum}\wedge \text{time}(e)=\text{noon}]$
	b.	$\left(\exists e\right)\left[\text{stab}\right(e,\text{brutus},\text{caesar})\wedge \text{brutal}(e)\wedge \text{loc}(e)=\text{forum}]$
	c.	$\left(\exists e\right)\left[\text{stab}\right(e,\text{brutus},\text{caesar})\wedge \text{brutal}(e\left)\right]$
	d.	$\left(\exists e\right)\left[\text{stab}\right(e,\text{brutus},\text{caesar}\left)\right]$

Since (45a–d) involve existential quantification over events, Davidson’s argument for events is close in spirit to Reference QuineQuine’s (1948) criterion of ontological commitment. This criterion assumes that “to be is $\dots$ to be the value of a variable” (Reference QuineQuine, 1948, 32), that is, to lie in the domain of (existential) quantification. Davidson acknowledges this connection to Quine when he remarks that “ontology is forced into the open only where the theory finds quantificational structure” (Reference DavidsonDavidson, 1977, 251).

The semantic commitment to events is further supported by the observation that existential quantification over events is required to account for the possibility of permuting adverbial modifiers (in (46): slowly and with a stick; see Reference LandmanLandman, 2000; Reference MoltmannMoltmann, 2007). It further accounts for the reference of anaphoric pronouns in sentences like (47) (Reference Davidson and DavidsonDavidson, 2001; see Asher 2003; Reference ColapintoColapinto, 2020), for the interpretation of aspect (in (48); see Reference KratzerKratzer, 1998), and for the intuitive truth- and entailment-conditions of experiential attitude reports (e.g. (49)–(50); see Reference HigginbothamHigginbotham, 1983, Reference Higginbotham and Barber2003; cf. Reference StephensonStephenson, 2010). In particular, unlike its that-clause counterpart, (50) is false in a scenario in which John has only been told that Mary was singing, but has not himself heard Mary sing. In (46b), ‘ $\text{instr}\left(e\right)$ ’ identifies the instrument that is used to perform the event  $e$ .

(46)	a. John walked slowly with a stick.	(Reference MoltmannMoltmann, 2007, 377, ex. (19))
$\equiv$	b. John walked with a stick slowly.
	$⇝\left(\exists e\right)\left[\text{walk}\right(e,\text{john})\wedge \text{slow}(e)\wedge \text{instr}(e)=\text{stick}]$
(47)	Ben fell (down the stairs). It happened at his workplace.
	$⇝\left(\exists e\right)\left[\text{fall}\right(e,\text{ben})\wedge \text{loc}(e)=\text{ben's-workplace}]$
(48)	Ralph is running.
	$⇝\lambda t\left(\exists e\right)[t\subseteq \text{time}(e)\wedge \text{run}(e,\text{ralph}\left)\right]$
(49)	a. John saw Mary leave.
	$⇝\left(\exists e\right)\left[\text{leave}\right(e,\text{mary})\wedge \text{see}(\text{john},e\left)\right]$
$\Rightarrow$	b. Mary left.	(Reference HigginbothamHigginbotham, 1983, 106–107)
	$⇝\left(\exists e\right)\left[\text{leave}\right(e,\text{mary}\left)\right]$
(50)	John remembers Mary singing.	(Reference Higginbotham and BarberHigginbotham, 2003, 505)
	( $̸\equiv$ John remembers that Mary was singing.)
	$⇝\left(\exists e\right)\left[\text{sing}\right(e,\text{mary})\wedge (\exists e^{\prime }\left)\right[\text{remember}(e^{\prime },\text{John},e)\left]\right]$

2.4.3 Possible Worlds

It is commonly assumed that an adequate treatment of modal expressions (e.g. auxiliaries like must or have to, and adverbs like necessarily or certainly) involves quantification over possible worlds (see Reference Knuuttila and ZaltaKnuuttila, 2003, who traces this idea back to medieval philosophy and to Leibniz). Following Reference HintikkaHintikka (1957) and Reference KripkeKripke (1959), nearly all contemporary semantic theories interpret modals through existential quantification (in the case of weak modals like may) or universal quantification over worlds (in the case of strong modals like must).Footnote ³⁰ A simple semantics that captures this idea is given in (51) (see Reference MontagueMontague, 1970).

(51)	a.	It may be raining in Bochum.  $⇝\left(\exists w\right)\left[\text{rain}\right(w,\text{bochum}\left)\right]$
	b.	It must be raining in Bochum.  $⇝\left(\forall w\right)\left[\text{rain}\right(w,\text{bochum}\left)\right]$

State-of-the-art semantics for modal expressions (which account for different flavors of modality, e.g. epistemic, deontic) likewise involve quantification over possible worlds. In these semantics (exemplified in (52), based on Reference von Fintel and Heimvon Fintel & Heim, 2021; see Reference Kratzer, von Stechow and WunderlichKratzer, 1991), $f$ is a ‘flavor’ function that projects a set of possible worlds from the anchor of the modal claim, $w$ .

(52)	a.	It may be raining in Bochum.
		$⇝\left(\exists w^{\prime }\right)\left[f\right(w\left)\right(w^{\prime })\wedge \text{rain}(w^{\prime },\text{bochum}\left)\right]$
	b.	It must be raining in Bochum.
		$⇝\left(\forall w^{\prime }\right)\left[f\right(w\left)\right(w^{\prime })\to \text{rain}(w^{\prime },\text{bochum}\left)\right]$

Like modals, propositional attitude predicates (e.g. believe, want) are often also interpreted as involving possible worlds (following Reference HintikkaHintikka, 1969; Reference MontagueMontague, 1970, Reference Montague, Hintikka, Suppes and Moravcsik1973). Intuitively, these predicates express relations between an individual agent (i.e. the semantic value of the predicate’s grammatical subject) and propositions/sets of possible worlds (i.e. the semantic value of the predicate’s complement; see Reference RussellRussell, 1905). The familiar semantics for these predicates (due to Reference HintikkaHintikka, 1969; see Reference von Fintel and Heimvon Fintel & Heim, 2021; Reference StalnakerStalnaker, 1978) involves partitioning the set of possible worlds into worlds (i.e. the agent’s attitudinal alternatives) that are compatible with the agent’s attitude and worlds that are incompatible with this attitude. It interprets the attitude predicate as a universal quantifier over the agent’s attitudinal alternatives. For the attitude report in (53a), the resulting semantics is given in (53b), where ${\text{DOX}}_{\text{bert},@}$ is the set of Bert’s doxastic [= belief-] alternatives in the actual world, @.

(53)	a.	Bert believes that Suzy is smart.
$⇝$	b.	$\lambda p\lambda x\left(\forall w\right)\left[{\text{DOX}}_{x,@}\right(w)\to p(w\left)\right](\text{bert},\lambda w^{\prime }.\text{smart}(w^{\prime },\text{suzy}))$
		$\equiv \left(\forall w\right)\left[{\text{DOX}}_{\text{bert},@}\right(w)\to \text{smart}(w,\text{suzy}\left)\right]$

The interpretation of attitude complements in terms of lambda abstraction over possible worlds (i.e. as sets of worlds; see the second line in (53a)) enables the modelling of entailment as set-theoretic inclusion (see Reference SinhababuSinhababu, 2015; Reference LiefkeLiefke, 2024). On this account, a sentence  $X$ entails another sentence, $Y$ , i.e. $X\Rightarrow Y$ , iff $〚X〛\subseteq 〚Y〛$ (Reference KacKac, 1992; Reference Keenan and FaltzKeenan & Faltz, 1985). This relation is exemplified by the sentences in (54):

(54)	a.	Suzy is smart and hardworking.
		$⇝\lambda w^{\prime }.\text{smart}(w^{\prime },\text{suzy})\wedge \text{hardworking}(w^{\prime },\text{suzy})$
$\Rightarrow$	b.	Suzy is smart.
		$⇝\lambda w^{\prime }.\text{smart}(w^{\prime },\text{suzy})$

Assuming that believe is upward monotonic in its complement position (such that, for all $p\subseteq q$ , any agent who believes  $p$ will also believe  $q$ ),Footnote ³¹ this account straightforwardly captures the validity of the inference in (55):

(55)	a. Bert believes that Suzy is smart and hardworking.
	$⇝\lambda p\lambda x\left(\forall w\right)\left[{\text{DOX}}_{x,@}\right(w)\to p(w\left)\right](\lambda w^{\prime }.\text{smart}(w^{\prime },\text{suzy})\wedge \text{hardworking}(w^{\prime },\text{suzy}))\left(\text{bert}\right)$
$\Rightarrow$	b. Bert believes that Suzy is smart.
	$⇝\lambda p\lambda x\left(\forall w\right)\left[{\text{DOX}}_{x,@}\right(w)\to p(w\left)\right](\lambda w^{\prime }.\text{smart}(w^{\prime },\text{suzy}))\left(\text{bert}\right)$

Abstracting over possible worlds also enables a uniform account of (propositional and objectual) intensionality, as I have shown in Reference LiefkeLiefke (2024) (see Reference MontagueMontague, 2007).

4.2.1 Manners

Some researchers have argued that Quine-style quantificational evidence like that from Section 2.4 can also be used to support a semantic commitment to manners. Specifically, the assumption of manners is supported by the observation that the uniform interpretation of adverbs as properties of events (along the lines of Reference Davidson and DavidsonDavidson, 2001) cannot account for the intuition that some adverbs (e.g. illegibly in (74)) modify a manner (see Reference Dik and KraakDik, 1975; Reference Schäfer, Bonami and HofherrSchäfer, 2008; Reference PiñónPiñón, 2008). This intuition is corroborated by the observation that (74a) admits a paraphrase through a construction of the form the way $\dots$ (see (74b)).

(74)	a.	John wrote illegibly.
		$⇝\left(\exists e\right)[\text{write}(e,\text{john})\wedge \left(\exists m\right)\left[\text{manner}\right(m,e)\wedge \text{illegible}(m\left)\right]]$
$\equiv$	b.	The way John wrote was illegible.

The Davidsonian treatment of manner adverbs as predicates of events further fails to account for the nonvalidity of inferences like (75) (Reference Parsons, Davidson and HarmanParsons, 1972, 131–133; see Reference Schäfer, Bonami and HofherrSchäfer, 2008). In the premise of this inference, i.e. (75a), painstakingly takes scope over intelligible (such that painstakingly does not specify the manner of John’s writing, but the manner of his writing illegibly; Reference SchäferSchäfer, 2006, 152). Since ‘manner-free’ semantics like Davidson’s cannot capture such scope effects, they predict – falsely – that (75) is equivalent to (76a) and, hence, entails (76b). By allowing quantification over manners  $m$  – and by adopting Reference EckardtEckardt’s (1998) notion of a complex ‘big event’ $e^{*}$  – manner-based semantics block the inference in (75) as desired (Reference Schäfer, Bonami and HofherrSchäfer, 2008). In (75), $m$ is a variable over manners; ‘ $\text{part-of}(e,e^{*})$ ’ expresses that the writing event  $e$ is (spatio-temporally and informationally) included in the big event $e^{*}$ .

(75)	a.	John painstakingly wrote illegibly.
		$[$ ‘That John wrote illegibly was painstaking’ $]$
		$⇝\left(\exists e^{*}\right)[\text{agent}(e,\text{john})\wedge \left(\exists e\right)\left[\text{part-of}\right(e,e^{*})\wedge \text{write}(e,\text{john})\wedge$
		$\left(\exists m\right)\left[\text{manner}\right(m,e)\wedge \text{illegible}(m)\wedge \text{painstaking}(e^{*}\left)\right]]]$
$\nRightarrow$	b.	${}^{??}$ John wrote painstakingly.

(76)	a.	${}^{??}$ John wrote painstakingly and illegibly.
		$⇝\left(\exists e\right)\left[\text{write}\right(e,\text{john})\wedge \text{painstaking}(e)\wedge \text{illegible}(e\left)\right]$
$\stackrel{?}{\Rightarrow }$	b.	${}^{??}$ John wrote painstakingly.
		$⇝\left(\exists e\right)\left[\text{write}\right(e,\text{john})\wedge \text{painstaking}(e\left)\right]$

Note that the existentially quantified manner  $m$ in (75) is still dependent on some event  $e$ . This observation could lead one to the following conjecture about a universal semantic typology: The semantic ontology of any language will include manners only if it includes events. I will discuss conjectures of this form in Section 4.5.

4.2.2 Degrees

In contrast to the above, a commitment to degrees is supported by the observation that degree-free semantics (which try to model comparative constructions without reference to degrees; see Reference McConnell-GinetMcConnell-Ginet, 1973; Reference KleinKlein, 1980; Reference Neeleman, van de Koot and DoetjesNeeleman et al., 2004)Footnote ³⁸ cannot easily account for explicit comparatives (Reference Rett and AltshulerRett, 2022, 286–289). The latter are constructions like (77a) and (77b) that contain the comparative morpheme -er or the equative morpheme as.

Degree-based approaches (e.g. (Reference Cresswell and ParteeCresswell, 1976; Reference von Stechowvon Stechow, 1984; Reference HeimHeim, 2000) model comparative constructions by interpreting gradable predicates like tall as relations between individuals and degrees. They assume that formulas of the form ‘ $\text{tall}(x,d)$ ’ are true iff the measure of  $x$ along the scale of height, ${\mu }_{\text{height}}\left(x\right)$ , is at least $d$ . Degree-based approaches treat comparative clauses as scope-taking expressions, where -er and as compare the maxima, $\text{max}\left(D\right)$ and $\text{max}\left(D^{\prime }\right)$ , of two sets of degrees, $D$ and  $D^{\prime }$ (see Reference LassiterLassiter, 2012). The degree-based interpretation of (77a) is given in (78):

(78)	Jane is taller than Bill.
	$⇝\text{max}(\lambda d.{\mu }_{\text{height}}(\text{jane})\ge d)>\text{max}(\lambda d.{\mu }_{\text{height}}(\text{bill})\ge d)$

Since (78) involves lambda-abstraction over degrees (see the terms ‘ $\lambda d.{\mu }_{\text{height}}(\dots )\ge d$ ’, which denote characteristic functions of sets of degrees), (78) prima facie provides an alternative to the Davidsonian/Quinean identification of ontological commitments from existential quantification. However, since degree-based approaches assume that degrees are downward monotone (such that anyone who is $d$ -tall is also $d^{\prime }$ -tall for all heights $d^{\prime }<d$ ; Reference LassiterLassiter, 2012, 567) – and since ‘ $\lambda d.{\mu }_{\text{height}}\left(\text{jane}\right)\ge d$ ’ is a definite description of a degree (namely, the highest degree to which Jane is tall) –, the interpretation in (78) is even equivalent to the interpretation in (79).