9.0 Questions and Answers

The goal of this chapter is to discuss which basic semantic entities should be included in formal semantic theory, and on which principles we should include or exclude them. While some framework-internal assumptions in formal semantics are hotly debated, the matter of how many and which basic entities a theory assumes is largely treated as a matter of personal taste or convenience. It will be useful for linguists to have a common standard for introducing and constraining basic entities in their frameworks, so they can better understand and model natural language semantics. Philosophers will find this discussion useful for the same reason, and also to learn more about the possible formalism that can model natural language, and what consequences these conclusions have for metaphysics or the philosophy of science.

The issue of which entities are basic has been building momentum for decades, as some semanticists have presented empirical motivations for proliferating types (to include e.g. degrees and events) while others have presented empirical motivations for reducing or combining them (e.g. to situations). But the issue has really gained a toehold in recent work arguing that specific languages can differ in which basic entities they employ; in particular, that languages seem to differ in whether their semantic representation must include degrees (Bochnak Reference Bochnak2015b).

This chapter presents the most prominent empirical motivations for proliferating types (to include e.g. events) and reducing them (to combine e.g. events and worlds). Effectively, arguments in favor of type-proliferation identify distinct morphology for quantifiers or proforms ranging over different types, and that failing to include a distinct type or entity could predict incorrect truth conditions. Arguments in favor of type-collapsing emphasize languages or phenomena in which morphology seems to be shared across putative type domains, and constructions for which the meaning of one putative type of entity is intrinsically tied to the meaning of another, related putative type of entity. I end by concluding that the arguments for type-proliferation are slightly more compelling in terms of empirical coverage and diachronic considerations.

I conclude this chapter by arguing that type-collapsing arguments are each individually compelling but inconsistent as an aggregate. It remains to be seen whether a semantic theory with minimal basic types could satisfy the wide variety of distinct empirical constraints placed on it by type-collapsing arguments across different empirical phenomena.

9.1 Introduction

The goal of this chapter is to discuss which basic semantic entities we should include in our formal semantic ontology, and on which principles we should include them (cf. Bach Reference Bach1986b). The vast majority of formal theories employ individuals as a basic type and primitive; these theories model quantification over, modification of, and reference to individuals in the metalanguage. But many theories include additional types or entities, including possible worlds, but also less common ones like vectors. Some papers have argued that types should be constrained or reduced; others that they should be proliferated. I’ll present some representative arguments on both sides and suggest a path forward in evaluating them against one another.

Standard Montagovian semantics employs individuals as a basic type, but in practice, some theorists embrace many more basic types. Champollion (Reference Champollion2010) uses at least five (differentiating between degrees, numbers and intervals) in just an extensional semantics; Bittner (Reference Bittner2003) uses seven (differentiating between animate and inanimate entities); and Landman (Reference Landman2006) assumes nine basic entities, differentiating between kinds, events, and event-kinds. In contrast, others have taken for granted that the adoption of different types should be constrained by Ockham’s Razor, and have posed and taken up the challenge of eliminating as many as mathematically possible. Thomason (Reference Thomason1980) argued that possible worlds aren’t necessary to model propositional attitudes, and Partee (Reference Partee2009) and Keenan (Reference Keenan and Bianchi2015, Reference Keenan2018) propose doing away with individuals as a basic semantic type.

As a semanticist, I take semantic adequacy to be the primary goal of a formal semantic theory. But a metasemantic concern about modeling the right entities – or at least the right quantity of entities – seems like a plausible secondary goal. This is highlighted by the reductio ad absurdum put forth in Ritchie (Reference Ritchie2016), which depends on the principle that equally semantically adequate treatments should have equal voice in determining the ontological commitments carried by natural language theory. If there are indeterminately many – or even multiple – semantic formalisms that postulate a distinct set of entities, we cannot hope for a principled relationship between semantic theory and ontology.

There are, as far as I can tell, three logically possible positions to take regarding basic entities in a semantic model:Footnote ¹

1. (1) Type Reductionism

1. (2) Type Ersatzism

1. (3) Type Proliferationalism

The difference between Type Ersatzism and Type Proliferationalism is a subtle one, reminiscent of selectional restrictions on verbs and adjectives, illustrated in (1).

1. (1)

   a.	*Jane met.	number restriction
   b.	*She’s a bachelor.	gender restriction
   c.	*The plant tried to grow.	animacy restriction
   d.	*Jane bounced the cloud.	(solid-)state restriction
   e.	*The piece of paper is fat.	(three-)dimension restriction

The predicates are picky about what sorts of arguments they take. Example (1a) is ungrammatical because intransitive meet requires that its subject denote a plurality; (1b) is ungrammatical because the adjective bachelor can only be predicated of males. It’s standardly assumed that these are all predicates of individuals; they can be modeled as denoting partial functions from the subclass of entities that satisfy the relevant selectional restriction. This is something like a Type Ersatzism approach; it treats different kinds of entity within the same type. In contrast, a Type Proliferationalism approach might assign different types to singular and plural entities, male and female entities, etc.

Example (2) illustrates this difference between Type Ersatzism and Type Flexibility for the adjectival modifier very (and some contextually valued standard s); the former involves individuals, type e, and requires a partial function to model the fact that very must modify something gradable (*very student); the latter involves entities other than individuals – degrees of type d – and thus does not require a partial function.

1. (2)

   a.	Type Ersatzism: $〚\text{very}〛=\lambda P_{〈e,t〉}\lambda x_e:\mathtt{\text{degree}}\left(x\right).P\left(x\right)\wedge x>s$
   b.	Type Flexibility: $〚\text{very}〛=\lambda D_{〈d,t〉}\lambda d_d.D\left(d\right)\wedge d>s$

I’ll end this section with some ground-clearing. First, I restrict myself to the discussion of basic types – not complex ones – because I assume that the latter come for free, in every formal model, via type formation. This is despite the interesting empirical arguments that some complex types (e.g. quantifiers) are unavailable in some languages (e.g. St’át’imcets, which I take to be a separate discussion, Matthewson Reference Matthewson, Newmeyer and Preston2014), and also despite the fact that the same arguments used to differentiate between basic and complex entities (Link Reference Link, Bäuerle, Schwarze and von Stechow1983) might also be useful in differentiating between two basic entities.

And while considerations of economy and parsimony are certainly relevant when it comes to evaluating theories, these considerations presume empirical equivalence (i.e. Can semantic theories that presume different basic semantic entities account for the same natural language data?). And since it is this empirical equivalence that I will be discussing, I will treat considerations of economy and parsimony as secondary to the discussion at hand.Footnote ²

When I discuss the question of how many basic entities or types there are, I view the issue as regarding the semanticist’s toolbox, rather than a given speaker’s i-language. In particular, if some language were to have what we decide to be irrefutable evidence that the semantic modeling of that language requires e.g. degrees as a basic entity, then this is sufficient evidence that there are degrees in the semantic ontology, but not sufficient evidence that there are degrees in every human being’s i-language. This is compatible with the possibility that some languages do not require degrees in their semantic modeling, or even should not be modeled using degrees, as has been argued for Washo (Bochnak Reference Bochnak2015b) and some other languages.

Finally, there is one diagnostic for basic semantic entities that I will not use: I will not assume that the presence of a referring expression over a particular sort of thing privileges that thing as an entity (cf. Schlenker Reference Schlenker2006). More broadly, I will focus on linguistic tests that don’t involve categories of words whose inventory is potentially infinite; this is the standard lexical vs. functional distinction. It seems as though we can coin a referring expression for anything, really, at least in particular contexts – e.g. Twin Earth (Putnam Reference Putnam1973) – and so it is a trivial test.

9.2 Metasemantic Arguments

Before I turn to empirical arguments made in favor of proliferating or collapsing types, I’ll briefly present two instances of semanticists directly addressing the question of how many basic entities the ontology should include, and discuss why their claims don’t seem to completely settle the issue.

In his 2006 paper, Philippe Schlenker observes that “Reference to individuals, times and worlds is uniformly effected through generalized quantifiers, definite descriptions, and pronouns” (Reference Schlenker2006: 504). He interpreted this observation as evidence that there is a single type, $\xi$, ranging over an 〈individual, time, world〉 triple.

As argued above, there is no limit on the sort of entity that can be referred to with a name or definite description, given the innovativeness of natural language. And, as we’ll see below, it seems clear that there are types of entities other than individuals, times and worlds (namely degrees, events, and/or situations) that are associated with quantifiers and proforms as well. So if Schlenker’s criteria are necessary and sufficient for differentiated basic entities – and he provides no arguments that they are, especially as he considers them members of a triple – they lead to a more inclusive ontology than he advocates for.

In her 2003 paper, Maria Bittner adopted a similar perspective. She advocates for a Ty-7 formal semantics, including worlds, times, places, events, states, animate individuals, and inanimate individuals as basic entities. What’s more, she meaningfully differentiates between basic types – like states and events – and derived or complex types, like processes and habits, which she takes to denote partial functions. Bittner’s criterion for a basic type (see also Bittner Reference Bittner2006, Reference Bittner2014) is whether entities of that sort participate in anaphora in a language, and thereby whether a dynamic model of that language requires a separate discourse stack for that type.Footnote ³

However, Bittner herself acknowledges that discourse reference can be to complex types (or, rather, to the basic components of a complex type): “In general, simple episodic discourse involves only simple types of drefs – the seven basic sorts (possibilities $\omega ≔𝐰t$, agentive entities α, non-agentive entities β, events ε, states σ, times τ, and places π or else simple functions (mostly processes ε …)” (Reference Bittner2003: 645). She specifies, of discourse referents to processes, “Formally, these are ε-dependencies, mapping each stage of the process, except the last, to the next stage” (Reference Bittner2003: 641).

So perhaps the ability of a proform or anaphor in a language to refer to an entity is a necessary but not sufficient condition for its being a basic type, as it could be anaphoric on a subcomponent of a complex entity. The result is a very robust and comprehensive crosslinguistic ontology, but one with no clear, reliable way of differentiating between basic and complex or derived types.

In the next section, I present several prominent empirical arguments that natural language semantics needs to include a given entity as basic.

9.3 Type-Proliferation Arguments

Across the formal semantics literature, there have been a number of implicit and explicit arguments for a number of different non-individual entities. I have summarized the most prominent ones in Table 9.1.Footnote ⁴

The empirical arguments for adding different types or entities to the semantic ontology have been very similar, and they fall into two broad categories. First, there is morphological evidence: arguments that a given language has functional items that seem dedicated to particular, nonindividual domains. Second, there is semantic evidence in the form of arguments from semantic adequacy: phenomena that seem to be able to be modeled only in a formalism that includes nonindividuals. For several familiar nonindividual entities, I will review some prominent arguments in favor of their inclusion in the semantic ontology.

9.4 Type-Collapsing Arguments

In contrast to those who have advocated for adding basic entities to the semantic ontology are those who have argued that basic entities should be collapsed or eliminated. These arguments, too, come in two forms: those from morphological cues and those from semantic convergence.

9.5 Concluding Summary and Discussion

Proponents of both proliferating types and collapsing them seem to care about the same sorts of things, which makes it easy at least in principle to compare the two perspectives. They care about capturing truth conditions (either making the theory sufficiently fine-grained or preventing it from being too fine-grained). And they take seriously the morphological cues of the language (explaining either the use of the same functional morpheme for more than one putative type, or two different functional morphemes for a single putative type).

Luckily, linguistic theory has something to say about the morphological arguments; specifically, it seems to have principled answers to the question: What’s more compelling, differentiated morphology or syncretic morphology? Loosely speaking, studies of grammatical change have suggested that it’s more likely natural language would co-opt function words for different entities than it would innovate different function words for the same entity. First, when languages add morphemes, especially via borrowing, they either tend not to be, or cannot be, functional morphemes (Thomason Reference Thomason2001). So the typical process by which we see lexical growth in a language generally does not extend to functional items, which has been the focus of the morphological arguments discussed here.

Second, functional items like proforms are more likely to converge over time (cf. Norde Reference Norde2009), via processes like analogical change (Hock Reference Hock, Joseph and Janda2005) or syncretism (Baerman et al. Reference Baerman, Brown and Corbett2005). Bußmann (Reference Bußmann1996) characterizes the former as the “diachronic process by which conceptually related linguistic units are made similar (or identical) in form … often regarded as the result of the move towards economy of form” (p. 21). Syncretism is a term for this sort of process when it affects inflectional paradigms, exemplified in Table 9.2.

In terms of semantic arguments, the question of what is more important, a powerful theory or a restrictive one, transcends discussions of semantic ontology and even linguistics. But there is an important difference between the two approaches in the consistency of their conclusions. The arguments for proliferating types seem to lead to consistent conclusions, crosslinguistically, possibly trivally. And they also result in an attractive (albeit incomplete) universal typology: {individuals, times, worlds} $<$ {degrees} (for instance).

The arguments for collapsing types, on the other hand, seem more inconsistent. Consider events: should they be type-assimilated with individuals, as suggested by individual/event polysemy (Bach Reference Bach1986a; Krifka Reference Krifka1990)? Or should they be associated with possible worlds and locations, as the situation semanticists have argued? And consider degrees: are they more like vectors (Schwarzschild Reference Schwarzschild and Snider2013; Rett Reference Rett2015), or are they more like manners and kinds (Anderson Reference Anderson2016)? While these empirical arguments are compelling in isolation, amalgamating them in a single semantic theory seems problematic.

I’ll close by reiterating that none of these arguments appear to be able to differentiate between Type Flexibility – a semantics with numerous basic types – and Type Ersatzism, with a single type that differentiates between e.g. individuals and events at some subtype level. I know of no empirical argument that can do this. Instead, I hope to have presented a wide variety of existing arguments for leaning towards Type Reductionalism and for leaning towards Type Flexibility/Ersatzism, and I have tentatively argued that the latter are more morphologically plausible and semantically consistent.

10.0 Questions and Answers

Philosophers have long been interested in questions of ontology, but from a metaphysical point of view.Footnote * In semantics, it is the philosophical versions of ontological primitives that are used in the construction of the nonlinguistic side of the meaning equation, and which inform the structure of semantic theories. The starting point of this chapter is the idea that metaphysical ontologies are inappropriate when it comes to natural language semantics. Moreover, the claim is not only that ontologies motivated by studying the structure of natural language are superior as a basis for building a natural language semantics, but also that the nature of those ontologies is an important intermediary in the more overarching metaphysical discussion (see also Rett, this volume). In other words, given that we use language to reason about the world, the metaphysical questions cannot be sensibly answered without being explicit about the ontological intermediates required by language.

There is much recent work in philosophy of language in the area of natural language ontology (Moltmann Reference Moltmann2017; Fine Reference Fine2014; Hinzen Reference Hinzen2016), which is reinvigorating a strand of (heretical) philosophy that questions the hegemony of Quine, Carnap, and Lewis in motivating the building blocks of meaning. On the linguistics side, recent work by e.g. Potts, Henderson, is attempting to extend the dominant frameworks to accommodate phenomena and modalities of expression that are deeply integrated in human linguistic expression, but which are not so easily accommodated within the traditional, classical model (Potts Reference Potts, Barker and Jacobson2007; Henderson Reference Henderson2015; Gehrke & McNally Reference Gehrke and McNally2015).

A detailed compositional treatment of natural language semantics distinguished by an emphasis on the lexical primes and category types that we can show have psychological reality as primes of memory and computation.

As with all empirical questions that require a close study of natural language phenomena, the question is always the extent to which the evidence from a single language generalizes crosslinguistically. In other words, which of the natural classes of syntactic and semantic primes are universal/cognitively unavoidable within natural language systems, and which are more linguistically parochial and contingent.

10.1 Ontology and the Problem with Truth

Consider the following three sentences of English.

1. (1)

   a.	John closed the door.
   b.	John is closing the door.
   c.	The door is closed.

These three sentences all use forms of the same ‘verb’ in English, close, and that verb contributes to the semantics of what is being said in an important and systematic way, as indeed all scholars of meaning in language would concede. It is natural to associate the meaning of the verb close with all the situations that are ‘closing’ events. However, there is something interestingly different about the three cases. While in (1a), the verb meaning can be elucidated in terms of the situations in which it could be said to be true, namely actual closing events, the verb meanings in (1b) and (1c) are not so straightforward to describe in this way. This is because the situations in which we would judge (1b) to be true are not literally ‘closing’ events in the sense that if John stops half way then what he has done is not ‘close the door’. Nevertheless, what he is doing must be sufficiently similar to a fulfilled ‘closing’ event for it to justify the use of that particular verb, and the situation so described must somehow perceptually and cognitively evoke actual closing events as their organic continuation. The task then becomes how we describe in a formal and precise way what it means to evoke a ‘closing’ event even if it never comes to fruition.

The problem with (1c) is essentially the converse. The verbal form used here is closed, the past participle, and it is systematically and paradigmatically part of the same verbal item as in (a) and (b). Situations that make (1c) true are those in which the door is in a particular kind of state, specifically, the state it would be in if somebody had performed a ‘closing’ event on it. But it is easy to see that no such ‘closing’. event need actually have transpired for (1c) to be true – the door could have been manufactured closed, for all we know. The task here is the temporal inverse of the task in the progressive case – how do we describe in a formal and precise way what it means to be the potential outcome of a ‘closing’ event without making reference to that closing event itself as a primitive.

The problem for both cases reflects choices that have been made in the ontology of how we talk about semantics in linguistics: we choose the actualized event of closing as the primitive with respect to which the subparts of ‘criterial activity’ and ‘criterial result’ should be defined. The reason that the actualized event of ‘closing’ is chosen as the primitive here is because it has a clear and transparent role of truth-making for natural language expressions using the close lexical verb. However, every language I have ever worked on or seen discussed has, in addition to its finite verbal forms, at least one related verbal form which is used in nonfinite contexts, often several. In many cases, these nonfinite forms are at least as morphologically simple, sometimes more so, than the finite inflected forms of the same verb. As we have seen, these nonfinite forms create complexities for the articulation of truth conditions for even the simplest of sentences containing them. Specifically, these ‘simple’ forms have classically been treated by invoking possible worlds as an addition to the ontology required for describing natural language meanings (Lewis Reference Lewis1973, Reference Lewis1986). This allows the event of ‘closing’ to live not just in the real world, but in all worlds imaginable, counterfactual, hypothetical and future. With this toolbox we can talk directly of events that could have happened even though they actually didn’t, or which might come to pass if things continued normally.

In this chapter, I will argue that choosing the actualized event, the truthmaker, as the primitive of our semantic theory, while successful and elegant for some descriptive purposes, fails to make sense of natural language in the sense that it gives us no purchase on the details and specifics of what has elsewhere been called natural language ontology. This question has been a central concern in the work of e.g. Friederike Moltmann (see Moltmann Reference Moltmann2017, Reference Moltmann2020 for summaries of the area). In this article I will be fully endorsing her position that natural language ontology is an important domain within ‘descriptive metaphysics’ (using the term from Strawson Reference Strawson1959), which is distinct from the kind of foundational metaphysics that the philosophical tradition tends to engage itself in. This project analyses the ontological commitments implicit in natural language(s) itself, one of the most pervasive and important reflections of our human engagement with the world. As Fine (Reference Fine2017) argues, there is even a case to be made that progress in foundational metaphysics relies on a close and nuanced understanding of the descriptive metaphysics involved in natural language ontologies. But even if that were not the case, as a linguist, it seems to me that the project of natural language ontology is crucial if we are to understand the compositional products of meaning and meaning-building in language, and the mechanisms by which it is embedded in our cognition and cognitive processing more generally. The spare and elegant axiomatization of semantic descriptions anchored just in truth and reference to particulars simply does not do justice to content and partial and incremental contents that we see in language. Exploring natural language ontology in its own right, taking the internal evidence as primary is a prerequisite to getting this kind of deeper understanding.

In other words, I will be arguing that the ontological categories that we require for understanding the domain of natural language meaning (“its properties and the relations between them”), cannot and should not be identified with external objects in the world or the nature of being, and certainly cannot be explicated in terms of the latter’s ontology. Anchoring all denotations in the primitives of extensional reality justified by some kind of foundational metaphysics, ends up ‘flattening out’ and making opaque the different ways in which such meanings are built up. The internal pieces of compositional meaning in such a system are reverse engineered from their connections to metaphysically justified primitives, and are not taken as evidence of natural language ontological primitives. Of course I would not deny that we clearly want to understand the use of language to ‘say things about the world’, and that a good theory of utterance meaning must ultimately anchor itself in a truth-making relation to situations in the world (Fine Reference Fine2014). What I do deny is that natural language meanings for the lexical and functional formatives of a particular linguistic code should be stated directly extensionally. While we sometimes use meanings to build truth-evaluable thoughts or refer to things in the world, the meanings of lexical items themselves are the cognitive precursors of those acts (see Pietroski Reference Pietroski2018).

The central empirical, descriptive ground in this chapter will be ‘nonfinite verbal forms’ as illustrated briefly in this introduction. In Section 10.2, I take the example of the English participle in -ing and discuss its ‘meaning’ in terms of the classic imperfective paradox that it gives rise to in the English progressive construction. In Section 10.3, I take on a slightly less well discussed case of the same sort of paradox, this time involving the English participle in ‑en/ed the passive/perfect. In Section 10.4, I provide an overarching diagnosis of the problem and in Section 10.5 I lay out the structure of the solution. As indicated in my introductory paragraph, the solution will require a rather different set of grounding assumptions than those we have become accustomed to over the past 40 years.

10.2 V-ing: The Imperfective Paradox

I start with the English participle in -ing, productively formable from every single verb in the language and ubiquitous in the speech of children and adults alike.

1. (2)

   (a)	John is singing.
   (b)	Mary is riding her bike.

It turns out that even these most basic of English sentences involve a troubling paradox that becomes visible particularly when a verb with a natural telos is chosen. To see the problem, let us compare the simple past tense of the verb cross in (3a) with the past progressive using the -ing participle in (3b).

1. (3)

   (a)	John crossed the street.
   (b)	John was crossing the street.

Difficulties that arise when one attempts to express the truth conditions of the English progressive in terms of the truth conditions of the verb it is based on. Bennett and Partee (Reference Bennett and Partee1972) noticed that you could not give a semantics of the progressive that said it was ‘true at a proper subinterval of the interval at which the nonprogressivized sentence is true’. This is because if you say that, you commit yourself to John actually getting across the street at some future time.

10.3 V-en: The Paradox of Target States

We turn now to the other major nonfinite form in English, the ed/en-participle found in the passive (and perfect) constructions. I will abstract away from its use in the dynamic constructions (eventive passive and perfect) and concentrate on the stative use of this participle, since this is where the paradox emerges (but see Ramchand Reference Ramchand2018 for an account of the participle that encompasses all three uses).

Even confining ourselves to the stative use, in the literature a number of different types of stative participle have been claimed to exist. In Embick (Reference Embick2004), these are called ‘resultative’ vs. ‘stative’ participles (although they are both actually stative, as he acknowledges). In Kratzer (Reference Kratzer2000) a ‘resultant state’ vs. a ‘target state’ passive participle are distinguished. In fact, these two authors are not making precisely the same distinction with these labels, so we cannot simply choose our terminology here. In the case of Embick, what is important in distinguishing the two classes is the presence or absence of ‘event implications’: resultative stative participles have event implications, ‘pure stative’ participles do not. In the case of Kratzer, what is important for the label is the relationship of the stative meaning to the meaning of the verb as a whole: ‘target state’ participles denote a state which is already an internal component of the verbal denotation; ‘resultant state’ participles denote a state that holds forever by virtue of the event in question having occurred, as in the distinction originally proposed by Parsons (Reference Parsons1990) for the perfect. Each of these distinctions comes with its own set of diagnostics. In fact, as we will see, it is not the case that target state participles are the non-event-implicating participles and resultant state participles are the event-denoting participles. Rather, target state participles can be both event-implicating and non-event-implicating in the relevant sense, while resultant state participles are only event-implicating.Footnote ⁶

The point I am interested in here is in what is meant by ‘event implications’. Let us consider first the following diagnostic, as proposed by Embick (Reference Embick2004).

1. (15)

   a.	The door was built open.
   b.	*The door was built opened.

According to Embick and much subsequent work, the problem with (15b) is that the state of being ‘opened’ simply cannot be true in the world unless there has been a prior event of ‘opening’, i.e. it is not something that can be one of the door’s properties before anything has happened to it. This is not true of the underived adjective open, which can be true regardless of how that state so described came about. In the case of open, there is an underived adjective which has the non-event-implicating reading, effectively blocking that interpretation for the participial form. But in English, there are many participles in en/ed which do in fact allow this kind of reading. Consider the participle closed.

In other words, it is perfectly sensible to describe a door as ‘closed’ even if that particular state was never actually preceded by a ‘closing’ eventuality. What is important to note about this situation is that the nature of the state described by the participle closed is in fact related in an intimate and organic way to the verbal concept close – the state we are describing is one that would typically result from an action of ‘closing’. To give another example, one can describe a drawn object as a ‘flattened cube’ because it has exactly the configuration of lines and angles that you would get if you took a three dimensional cube and flattened it symmetrically. There is no implication that it is a cube that has been flattened, just that it can be accurately described as such. The description is crucially dependent on a knowledge of what it means to ‘flatten’ something, but not on the actual existence of such an event.

The criterion of event implications in the literature that stems from Embick’s original distinction refers to the property of entailing the previous instantiation of an event particular. Thus, target states do not have event implications in Embick’s sense, but they are conceptually related to the corresponding dynamic event and thus give rise to what I will call the ‘resultative paradox’ – they describe the result of an event, which in fact did not have to happen to produce it.

Can Kratzer’s distinction between ‘resultant state participles’ and ‘target state participles’ get us out of the resultative paradox? Unfortunately not. Kratzer distinguishes between ‘resultant state’ participles and ‘target state’ participles, but as Embick (Reference Embick2004) points out, the phrasal target state reading that she analyses and gives a denotation always has event implications of necessity, since it requires existentially binding the Davidsonian event variable corresponding to the verb. It is only a pure adjectival reading that corresponds to the ‘pure state’ reading in Embick’s terms. The denotation for the adjective cool vs. the target state cooled from Kratzer, cited in Embick (Reference Embick2004) is given below in (17).

1. (17)

   a.	$\mathit{\text{cool}}:\lambda \mathrm{x}\lambda \mathrm{s}\left[\text{cool}\left(\mathrm{x}\right)\left(\mathrm{s}\right)\right]$
   b.	$cooled\text{:}\lambda \text{x}\lambda \text{s}\exists \text{e}[\text{cool}(\text{x})(\text{s})\wedge {\text{s=f}}_{target}(\text{e})]$

We can see that in the case of the non-event-implicating reading of closed and flattened given above, this definition has the unwanted eventuality entailments built in to it and simply won’t do the job. However, Kratzer’s denotation for the target states is importantly correct in one respect, namely that the verb that gives rise to the target state includes specific conceptual information corresponding to the result state that the participle eventually denotes.

The resultant state passives in Kratzer (Reference Kratzer2000), on the other hand, are the ones where there is no readily available state in the denotation of the verb’s meaning. Instead, the state that the participle denotes is the state that Parsons (Reference Parsons1990) calls the ‘resultant state’. The definition from Parsons is given in (18).

1. (18)

   Resultant states

   “For every event e that culminates, there is a corresponding state that holds forever after. This is ‘the state of e’s having culminated,’ which I call the ‘Resultant state of e,’ or ‘e’s Rstate.’ If Mary eats lunch, then there is a state that holds forever after: The state of Mary’s having eaten lunch.”

Kratzer’s diagnostic to distinguish resultant states in this sense from the others (the target states and the pure adjectives) is the incompatibility with the adverb immer noch-‘still’. This is because the definition of resultant state means that the state persists indefinitely for ever after the event is over, and therefore trivially the adverb ‘still’ cannot meaningfully be applied to it.Footnote ⁷ The resultant state passives given by Kratzer (Reference Kratzer2000) are shown below in (19).

1. (19)

   a.	Das	Theorem	ist	(*immer noch)	bewiesen.
   	The	theorem	is	(*still)	proven.
   	? ‘The theorem is (*still) proven.’
   b.	Der	Briefkasten	ist	(*immer noch)	geleert.
   	The	mail box	is	(*still)	emptied.
   	? ‘The mailbox is emptied.’
   c.	Die	Gäste	sind	(*immer noch)	begrüsst.
   	The	guests	are	(*still)	greeted.
   	? ‘The guests are greeted.’
   d.	Die	Töpfe	sind	(*immer noch)	abgespült.
   	The	pots	are	(*still)	washed up
   	? ‘The pots are washed up.’

Kratzer (Reference Kratzer2000)’s semantics for the resultant state does not produce a property of events, but rather a property of times directly. However, it is important to note that her semantics for both the target state and the resultant state require actualization and have real event implications, since for her events are instantiated particulars. So with respect to event implications, target state passives and resultant state passives are on a par. The only difference is the way in which that state is constructed.

The Target State passive participle, the one that is compatible with immer noch ‘still’, has a strong constraint imposed on it. For these to be formed, the verb in question must contain a caused result state in its denotation. Kratzer (Reference Kratzer2000) diagnoses this by the fact that a ‘for’-phrase is felicitous as a measure of the duration of that caused state. It is precisely these verbs that form good target state passives with immer noch, Kratzer argues, that consist of an activity portion and a final state. It is this ‘final state’ that ends up being the denotation of the formed up participle.

If we consider the denotation Kratzer assumes for the target state verb aufpumpen ‘pump up’, we see that it contains the representation of a caused final state.

1. (20)

   das Boot aufpump- - ‘pump up the boat’

   $\lambda \mathrm{s}\lambda \mathrm{e}\left[\text{pump}\left(\mathrm{e}\right)\wedge \text{event}\left(\mathrm{e}\right)\wedge \text{inflated}\left(\text{the}\text{boat}\right)\left(\mathrm{s}\right)\wedge \text{cause}\left(\mathrm{s}\right)\left(\mathrm{e}\right)\right]$

According to Kratzer’s semantics, the output of the stativizer -en/ed is a predicate of states, exactly the one that is inside the verb’s complex event semantics. The external event variable (the ‘process’ variable in my terms), is existentially bound.

1. (21)

   $\text{Stativizer}:\lambda \mathrm{R}\lambda \mathrm{s}\exists \mathrm{e}\mathrm{R}\left(\mathrm{s}\right)\left(\mathrm{e}\right)$

   $\text{Output}:\lambda \mathrm{s}\exists \mathrm{e}[\text{pump}\left(\mathrm{e}\right)\wedge \text{event}(\mathrm{e}\wedge \text{inflated}\left(\text{the}‐\text{boat}\right)\left(\mathrm{s}\right)\wedge \text{cause}\left(\mathrm{s}\right)\left(\mathrm{e}\right)]$

So the participle morphology in Kratzer’s system does not do very much work except to existentially bind the ‘Davidsonian’ event, and also to license the absence of verbal inflection. Since in the vast majority of cases, ‘a pumped up’ state is actually preceded by a ‘pumping up’, Kratzer does not notice or address the resultative paradox. But it is a fact that the target state stative participles, defined in terms of being a subpart of the whole verb’s event decomposition, are precisely the ones where the resultative paradox emerges. Once again, the existence of the meaning in question is conceptually dependent on knowledge of the whole event description corresponding to the verb, but this cannot be cashed out in terms of actual events.

Going back to the case of the ‘closed door’. To describe the truth conditions precisely, we would have to make reference to possible worlds, counterfactual worlds in this case, preceding the current moment, which would contain dynamic subparts of the event of ‘closing’ that culminate in the final state of ‘closedness’ in the actual world. We must find a continuation branch from a previous possible world into the present, even though in fact, that previous possible world is not the real one. This is all that is required to felicitously refer to something as ‘closed’. Most times when we use the stative participle, there is in fact a dynamic act of ‘closing’ that leads to it, but this does not appear to be necessary. Although I do not know if anyone has stated the semantics in exactly these terms before, I would contend that the case of pure stative participles of the non-event-implicating kind, what we are seeing in the resultative paradox is in fact the perfective counterpart of the ‘imperfective paradox’, and would require the equivalent move to the possible worlds toolbox.

10.4 Diagnosis

The discussion of the meaning of these two core nonfinite verbal forms in English (and I have no reason to believe that trying to understand participles in any other language would be any easier), has led us to seemingly unresolvable paradoxes, which I have argued cannot actually be defused by helping ourselves to a model invoking possible worlds. Moreover, the paradox in question is actually the same one, and has the same ultimate cause – it results from attempting to express essentially internalist compositional ingredients in externalist terms.

Chomsky (Reference Chomsky1995) argues convincingly to my mind that reference and truth are themselves mystical notions, and that the attempt to fill out some materialist agenda closing the gap between mind and body by bypassing the mental in favor of external reality fails to do justice to the reality and structuredness of mental representations.

In other words, by starting from the assumption that sentences denote truth or falsity and that meanings of lexical items are functions from entities to truth values, or some recursive type associated with those extensional primitives, one effectively begs the question. In other words, it tells us nothing about what precisely the cognitive ingredients are, and how human minds combine them to create these complex truth-evaluable expressive acts.

I wish to argue that the difficulties described above in characterizing the meanings of perfectly ordinary elements of natural language should be evidence that we need to rethink the very foundation of our formal theories of semantics, and abandon truth as the language in which we explicate meanings of natural language formatives. We do need to preserve an indirect relationship with truth-making, via the explication of the pragmatically enriched sentence or proposition, but we should simply abandon the idea that ‘meanings’ of language ingredients are stated directly in terms of truth conditions. This heretical position has been argued for by others, most particularly Paul Pietroski in a series of articles and books and most recently in Pietroski (Reference Pietroski2018). Problems with the truth-conditional approach to natural language meanings are well known, but often ignored strategically because of the payoffs gained in getting a robust theory of semantics off the ground. It is time to revisit those problems and reassess the foundations.

10.5 Towards a Natural Language Ontology for Meaning

I contend that we cannot just acknowledge the flaws the current system and use that wisdom to deploy the system carefully and circumspectly. All the puzzles and paradoxes are the same, all the dead ends have the same deep problem at their heart. All the technical solutions contain the same self-defeating trick (structure the possible world space in an increasingly elaborate, context-sensitive way, often depending on the actual words used in building the construction). This shows that we really have not understood the meanings of words in a way that is helping us to solve the compositional issues.

The bottom line here is that we can grant that formal semantics is a computational theory (in the sense of Marr Reference Marr1982) of meaning and still hold it to certain standards of correctness. Even if successful in its own terms, correctness needs to be understood at least partly in terms of a theory’s potential to inform and constrain theories of representation and algorithm. The current theory, even when wielded by extremely intelligent and knowledgeable linguists ends up forcing us into dead ends and paradoxes. All of which could be avoided by dropping the empirically undermotivated assumption that meanings are immediately extensional.

And it’s not so bad actually to have had 50 years of this particular tradition of formal semantic theorizing. There is a lot we know that we did not know before. In concentrating on the externally verifiable truth conditions of sentences, we have a sort of E-semantics (in the sense of Chomsky’s E-Language) descriptively in place, that can form the foundation for an I-semantics of language, if we are willing to take the next step.

In the case of Pietroski, he proposes that we think of Meanings as instructions to fetch a potentially polysemous network of concepts, and further that Meanings are confined to a restricted version of monadic predication (M predicates) and dyadic predication (D Predicates). They combine in ways that are severely restricted compared to the full combinatorical power of the type-based approach using functions. These are defined so as to ensure that the meaning of two joined meanings properly includes those individual pieces.Footnote ⁹ Pietroski defines two basic semantic combinatoric operations: M Predicates combine with M Predicates by M junction and M predicates combine with D predicates by D junction.

I welcome the Pietroskian critique of truth, which is close to my own position, but I think that the meanings of nonfinite verbal forms which formed the empirical heart of this chapter tell us something important about what needs to be added to natural language ontologies to get a satisfying account of partial contents and compositionality at the sentence internal level. In what is left of this chapter, I will briefly lay out my own formal solution to the paradox of maintaining the identity of descriptive content across formatives in the absence of actuality implications. To anticipate, the surprising new addition to the ontology required by natural language for the expression of complex meanings will be the linguistic symbol itself.

The starting intuition follows an old line of thought most forcefully articulated in Barwise and Perry (Reference Barwise and Perry1983) concerning the reusability of the sign. For human language to get off the ground, and because of the reusability of the signs of natural language, we need to have (i) common possession of symbols that are abstractions over the different actual situations encountered in the learning phase, and (ii) a speaker to deploy those symbols as a means of characterizing new situations in the world as she comes across them. Put in this way, we can see an important logical separation between the symbols, or elements stored in declarative memory with their rich web of associational content, and the external world which the speaker is using those symbols to describe. Because symbols are reusable they cannot be tied to a particular time and place, and they cannot be overly rigidly tied to particular worldly particulars. Polysemy and flexibility must be seen as features of the symbolic inventory not bugs. Thus symbols, because they are stored as abstractions or generalizations over particulars function as types rather than tokens, although crucially they are not ‘kind level’ in the formal semantic sense as being literally built from particulars, as in some attempts to capture this intuition. To be sure, the process of acquisition must involve the experiencing of particulars, but symbols are then stored and used in the system as abstract associational bundles, in much the same way that the cognitive scientists have assumed and maybe even best implemented in terms of a vector semantics (see Rett, this volume for more discussion). How then can we move from this psychologically plausible internalist conception to a formal semantics describing real-world objects and situations, and how can we model it computationally? Intuitively, the bridge is made by understanding that the symbol is to be literally deployed by a speaker at a particular place and time in order to describe a new real-world particular in the human being’s flow of experience. To do this, symbols must literally become objects in the ontology themselves, artifacts of human language.

I thus propose a radically different computational theory of meaning composition: this logical architecture seeks to reconcile internalist conceptions of meaning with the well-established formal foundations of an externally grounded theory of meaning. I argue for a view whereby the symbol is reified in the formal system and then explicitly deployed via an act of communication. The separation of the act of communication from the symbol itself allows for an internalist conception of the symbol qua symbol to be embedded within an extensionalist semantics for the content that is created after deployment in a context.

In Ramchand (Reference Ramchand2018), I argued that typological meaning layering in the verbal domain and was part of an argument against purely extensional meanings of lexical items (see also Pietroski Reference Pietroski2018). Here I take the idea further and propose that lexical items (items stored in declarative memory) are the reusable symbols whose meaning needs to be represented nonextensionally (internalistically). Functional items, on the other hand, contribute information that is directly relevant to reference in the world and the instantiation of situations (see Figure 10.1).

Figure 10.1 Meaning layers of the Symbol-within-Reference model

To bridge the internalist–externalist divide (chasm, one might say), information about the context of utterance (via an event variable corresponding to the very act of communication) must be used to mediate the internal representation and the externalist one and gives rise to a second zone where externalist content is structured and manipulated.

So in brief, the symbol is deployed by a user in a communicative context, giving rise to content that actually says something about the external world. Actual reference only occurs in the second step, crucially mediated by the speaker, the here and the now. This general architecture is represented schematically in Figure 10.2.

Figure 10.2 Information composition in the (Sym)Ref model

This is different from the standard classical semantic formalism where the most primitive denotations are couched in terms of objectual referents and truth, while intensional concepts have to be built by generalizing these denotations over possible worlds. The present model inverts the primitive-derived distinction found there, and structures the system around a primitive abstract and essence-like core with referential objectual and instantiational facts built up on top of that.

Formal semantic theories as we know them sit squarely in the domain of ‘computational theories’ in the sense of Marr (Reference Marr1982) and as such are independent of the nitty gritty of minds and brains that might implement them, and Marr’s work has been widely read in linguistics as a plea for and a legitimization of this level of scientific theorizing. But Marr was interested ultimately in understanding the functioning of our internalized systems in creating behaviors in response to stimuli, and notationally equivalent computational theories could nevertheless be distinguished by how well they help us understand the other, more algorithmic levels. His model included both an internal representation (the primal sketch) fed directly by light stimulus, and a final 3-D representation of our cognitive uptake. For Marr also, there is crucially a role for the subjective perspective in between the two (what Marr called the 2 1/2-D level), which in a sense allows the transition from the primal sketch to the objectual 3-D representation. In my own system, the reification of the utterance event and the parameters of context c that it brings with it performs the same cognitive function as the folding in of the subjective perspective in Marr’s own algorithm. I do not think it is an accident that the two systems mirror each other in this way. Marr’s own proposed computational system, which was designed to interface with a more algorithmic understanding of visual perception in the mind is a blueprint for cognitive neuroscience more generally. The idea that explicit information about the Self, or Origo is necessary to convert the stimulus into the information necessary to build an objectual 3-D representation is echoed in my claim that the reification of the utterance context is necessary to convert abstract symbolic content into representations with truth-conditional import. This model of meaning puts the identity of the anchoring information, consciousness of Self and the cognitive appreciation of the fact of other minds at the heart of the creative construction and comprehension of meaning respectively, and it makes different predictions for the role of context in the time course of complex meaning construction than other models of meaning.

In logical and philosophical terms, the picture above is a more Kaplanian (Kaplan Reference Kaplan, Almog and Wettstein1989) view of context as mediator between character and content, but it is at odds with the more classical formal semantic strategy of integrating context after linguistic form has been processed. This means that no current theoretical semantic proposals incorporate it – it would require a formal rift between symbol and symbol deployer in the build-up of the compositional system. Conversely, cognitive and internalist theories of meaning struggle with dealing with the aboutness of language and with reliable facts about how speakers judge entailment. In addition, cognitive theories do not concern themselves centrally with the structural meaning that arises procedurally from hierarchical syntactic structure. So far neither view has succeeded in building a genuinely algorithmic theory of meaning composition in the brain, which to my mind must deal with both of these kinds of phenomena.

Because it is the symbol that is being combined and manipulated in the earliest zone of compositional combination, we are not yet dealing with actual events in the world, but with complex concept combination. At this level of formal composition, we need to be manipulating elements of a new domain ${\mathrm{D}}_{\mu }$ which we add to the model, following Potts (Reference Potts, Barker and Jacobson2007), which is essentially the domain of well-formed linguistic symbols, possibly nonatomic, of type µ. To do this formally we need to add to the usual model, a domain which is the domain of well-formed linguistic objects. I will assume that these linguistic objects are triples, consisting of a < phonological information, syntactic features/information, semantic representation >, very similar to what is assumed in the psycholinguistic literature as a structured associational bundle. So we could think of the denotation of the English verbal symbol run as an ordered triple as in (27).

where we represent the content of the third, semantic, position in terms of a (necessarily incomplete) set of properties of events to indicate that it is a shorthand for a certain abstraction of cognitive properties, a meaning contribution which is partial on the one hand when it comes to describing an event in the world since it lacks temporal and locational specifications, but also potentially excessive and irrelevant on the other in that it includes ‘irrelevant’ and associational information as well (including the fact that meetings can ‘run’ as well as things like water and trains). This triple is also the piece of information that is stored in declarative memory, and which indeed may turn out to be most satisfactorily represented through vector semantic notation, as suggested by e.g. Baggio (Reference Baggio2018).

The point is that the internal structure of the elements in the domain ${\mathrm{D}}_{\mu }$ include a semantic contribution, which can in principle be filled in with whatever associational and incomplete meaning contributions turn out to be psycholinguistically and neurologically justified. Crucially, we do not need to state the meaning member of the triple in terms of the kinds of extensional formulas that formal semantics traffics in. To reiterate, the reason we have the freedom to place an internalist conception of meaning in this part of the ‘denotation’ for the symbol run is because ‘meaning’ in the internalist sense is encapsulated away from the formal computation. The encapsulation is effected by reifying the symbol itself as an object of the ontology. The symbol itself is an artifact of human communicative life, and it is an object in the domain of reference as much as a book, or a piece of string.

Importantly, the ‘meanings’ of the symbols of ${\mathrm{D}}_{\mu }$ need to be devoid of temporal or worldly information. They form the hierarchically inner core which is then clothed with the contingent information of time, place, and world, to link descriptions to actual particulars. True, the symbols of a person’s language are acquired through actual experience of the world, both sensory and cognitive, but they are, importantly, abstractions over the particular instantiations exposed to. The result (which may be fine tuned over the life of the speaker) is a partial description of essential properties for the event that, on grounds of reusability, are necessarily devoid of information related to the particularity of the instantiation (time, place and the reference of the participants). Humans possess an inventory of symbols, which are then consciously deployed in multiple situations. It is reusability, this third factor property of the symbolic system itself that leads to temporal and spatial, and referential information being represented morphosyntactically external to the memorized sign (the topic of Ramchand’s Reference Ramchand2018 monograph).

Now, let us imagine that conceptual content is associated to symbols we store in declarative memory, and that it can be combined by simple processes of primitive semantic combination to create complex concepts. We can call this Stage-One-Semantics for convenience. It is going to be an open question exactly what the possibilities and limits of internal concept combination are, but the hypothesis is going to be that it is qualitatively different from the next stages.

The reification of the symbol qua symbol in the computational representation is what allows us to embed the internalist intuition in the clothing of an externalist computational paradigm. Once the symbolic layer (possibly complex) has been constructed, these partial descriptions (properties of symbols) can be converted into formal properties of events that are identical to the kinds of denotations we are used to from formal semantics. To do this, Stage-One-Semantics must be followed by the integration of meaning corresponding to the Origo, the speaker in the here and the now, in order to convert abstract conceptual content into actual claims about the world. This is done by means of an explicit deployment operation. Our starting point is the innovation proposed in Henderson (Reference Henderson2015) who needs it to incorporate ideophonic, or depictive content into the descriptive system. The conversion operator (called QUOTE) by Henderson, combines with a complex symbol, notated u in (28) below, and a demonstration event d, to produce a property of events. The predicate ${\mathrm{TH}}_d$ relates the demonstration event d to the symbol being deployed, u. The DEMO predicate relates d and a general event variable e, saying that d ‘demonstrates’ or has certain structural properties in common with e.

I propose to carry the QUOTE function over to the general case, proposing that the reusable essential symbolic content of any perfectly ordinary sign is the equivalent of Henderson’s ideophone. In other words, a symbol, as reconceived this way, is a hyper-conventionalized ‘ideophone’ used to invoke and describe an event, with a higher proportion of descriptive as opposed to depictive content. In order to make this fully general, though, we need to replace Henderson’s DEMO predicate with what I will call CONVEY, and replace the exotic idea of a demonstration event with the ordinary garden variety utterance act itself. Thus, Ramchandian externalization operator would have the following general form.

1. (28)

   The Deployment of Symbolic Content

   $\lambda \mathrm{d}\lambda \mathrm{e}\exists \mathrm{u}$ [Utterance(d)] & ‘u is the symbolic content of d’ & convey(d,e)

   Property of of an utterance event d and event e, which has $\mathrm{u}\left(\in {\mathrm{D}}_{\mu }\right)$ as its theme, and where d deploys u to convey e.

To build the externalized representation, I follow Champollion (Reference Champollion2015) in closing the event variable low, at the point of inclusion of the deployment act of communication, introducing a variable over spatiotemporal properies of eventualities. In other words, these are now properties of fully objectual eventive particulars.

1. (29)

   The Externalized Representation

   $\lambda \mathrm{f}\lambda \mathrm{d}\exists \mathrm{e}\exists \mathrm{u}$ [Utterance(d) & ‘u is the symbolic content of d’ & convey(d,e) & f(d,e)]

   Where f is a variable representing spatiotemporal/worldly properties of events which I propose is a complex property relating d and e. Put another way, f is a property of events e, anchored in d.

In other words, this is now a property of a communication event d and event e in the world, where d deploys the (possibly complex) symbol $\mathrm{u}\left(\in {\mathrm{D}}_{\mu }\right)$ in order to convey e. Truth-conditional content is created only after deployment in a context by a speaker. This corresponds to the idea of demonstration in the gestural and ideophonic literature. The novelty of this model is that the symbol is always in some sense ‘demonstrated’, whether that symbol is conventional or possesses some iconic properties.

It is only at the point where an externalized denotation has been built up that what linguists term functional items, or grammatical words, can be integrated with the message. Here I am thinking about functional items like the determiner the or the past tense marker -ed in English. These items have the semantic property that they are related to extensional meanings, or in simpler terms they involve actual reference to entities in the world. The very earliest studies of aphasias and language disorders show a robust double dissociation between function words and richly contentful lexical items. Both of these kinds of items have a ‘semantics’, in my view, but of a radically different kind. The meanings of lexical items are associational and abstract, while lexical items clothed in function words have truly referential meanings. Formal semantic theories with their insistence on extensional denotations for everything including lexical items like dog and run are not in a position to make a distinction in these terms. Because it builds in meaning layering explicitly into the formal semantic account of meaning, with an internalist compositional core embedded within an outward-looking externalist representation, I have referred to the framework outlined above as the Symbol-within-Reference model of meaning composition. This is different from the standard classical semantic formalism where the most primitive denotations are couched in terms of objectual referents and truth, while intensional concepts have to be built by generalizing these denotations over possible worlds. The present model inverts the primitive-derived distinction found there, and structures the system around a primitive abstract and essence-like core with referential objectual and instantiational facts built up on top of that.Footnote ¹⁰ When it comes to holistic meaning, there is an additional layer of downstream inferencing based on whole sentence meaning, and conversational assumptions, but this is not directly my concern here.

A reviewer rightly asks how a model such as the Symbol-within-Reference model helps us with the problem of explicating the truth conditions of sentences containing the progressive, for example. For example, the present model allows us to state the relationship between ing forms and root forms of the same verbal symbol in terms of a ‘criterial state with the ‘same’ cognitive recognizers’, thus defusing the immediate imperfective paradox. However, we still do need an explanation of why sentences containing accomplishment verbs give rise to a failure of entailment between the progressivized version and the simple past verb, while activity verbs do allow such an entailment. I fully agree that this is part of our responsibility as semanticists, and elsewhere I have discussed how this theory does allow us to have an account of the empirical facts as just stated (Ramchand Reference Ramchand2018). The central idea here is that although the ‘meanings’ of lexical uninflected verbs are not stated in terms of truth conditions directly, propositions that contain them do have truthmakers, and there are principles that systematically relate the use of these lexical items to the truthmakers of the sentences that contain them. For example, the principles of Taylor (Reference Taylor1977) constitute a theory of how stative vs. activity vs. accomplishment lexical verbs produce different kinds of entailments when clothed in temporal information. This theory, plus the claim that the progressive operator creates a derived state, combine to provide an account of why “John is building the house.” does not entail “John built a house” while “John is running.” does seem to entail “John ran.” at least under certain contextual conditions. It is important to underline that the agenda I am pursuing here does not entail an abandonment of the principle of truth-making in explicating what people take to be what propositions ‘mean’. I am proposing that lexical items and certain operations over them are primitive meaning ingredients in a natural language ontology and occur as cognitive precursors to truth-making.

The lesson of nonfinite verbal forms is that language is telling us something quite specific about natural language ontology, namely that the ‘meanings’ of lexical roots must be stated in a way that is neutral with respect to finiteness. Finite inflection is what anchors the use of the verb to a particular event in a particular world at a particular time. Nonfinite verbs very transparently do not have any such direct entailments, and therefore throw up technical complications for semantic theories rooted in extensional denotations. But internal structuring of complex meaning in natural language shows us that we need to have a common meaning ingredient for both finite and nonfinite verbal forms that is simple and primitive. If I am right, that common meaning ingredient must be stated in nonexternalist terms.

10.6 Conclusion

We started on this journey by noticing the repeating paradoxes thrown up by truth theories, exemplified here by the attempt to relate the denotations of nonfinite verbal forms to the finite verbal counterparts. I have insisted that the job of semantics is to understand the ontology of natural language and how it then relates to truth-making. Natural language ontology forces us to acknowledge that meaning ingredients are not directly extensional. This, combined with typological facts about meaning layering in all natural languages, suggests a layered architecture for natural language semantics involving the integration of internalist and externalist-anchored ingredients, mediated by the utterance context.

While there is something important about establishing the connection to truth-making, there is nothing in the logic of how we got here that says we have to state natural language ingredients in terms of functions which take extensional primitives as their inputs and truth values as their final output. The theory we currently have is essentially reverse engineering based on externally verifiable behavior, which denies any role to internal representations. It is akin to constructing a theory of the sound system of human languages by relating objective acoustic primitives of the message to the articulatory primitives that produce that message, without passing through a mode of organization and internal representation in terms of abstract phonemes. In addition, such a theory has no way of modeling the kind of ‘partial content’ that I think actual linguistic forms traffic in. And as Pietroski (Reference Pietroski2018) points out, for natural language, there is no logical necessity for our truth-evaluability to be so direct. Rather, we need to see how sentences constructed systematically by natural language, eventually end up building something that is truth-evaluable, but this does not mean that meanings themselves, the linguistic ingredients of sentence, are extensions.

Finally, this sort of study of nonfinite verbal forms in natural language is important because of how it can inform both linguistics and philosophy. I endorse the position of Fine (Reference Fine2017) and Moltmann (Reference Moltmann2020), who argue that the descriptive work of natural language ontologies is an important stepping stone to both the understanding of the human mind, and for any subsequent theorizing about foundational metaphysics.