Truthmaker semantics for natural language: Attitude verbs, modals, and intensional transitive verbs

1 Introduction

Possible-worlds semantics certainly is the most common approach to the semantics of modals, and it is also a dominant approach to the semantics of attitude reports, at least in formal semantics in the tradition of Montague (Thomason 1974). While philosophers have discussed problems with possible-worlds semantics for quite some time, the approach continues to have a range of attractive features that have made it persevere as a central tool of analysis in formal semantics. First of all, possible-worlds semantics appears to have the very general advantage of allowing for a unified compositional semantics of intensional and extensional expressions of various sorts, in the tradition of Montague Grammar. In addition, possible-worlds semantics promised more specific advantages, such as being a suitable basis for accounting for various sorts of connections between modals and attitude reports, and for how utterances of sentences relate to the discourse context, which is standardly construed as a set of worlds, a context set (Stalnaker 1978, 1984, 2002).

The main shortcomings of possible-worlds semantics are well-known and derive from the fact that propositions construed as sets of possible worlds give too coarse-grained a notion of content. Thus, standard possible-worlds semantics does not distinguish the meanings of logically equivalent sentences and fails to account for the intuitive notions of subject matter and of partial content. The need for a more fine-grained notion of content, especially for attitude reports, was the motivation for an alternative, structured conception of content, replacing sets of worlds by structured propositions, commonly construed as n-tuples of objects or concepts (Cresswell 1985 and others). The structured-propositions view comes with its own problems, however (Hanks 2015; Jubien 2001; Moltmann 2003b, 2013a, 2013b; Soames 2010). For one thing, it raises serious conceptual problems (such as the problems of the unity of the proposition and of the arbitrariness of the order of propositional constituents). Moreover, it is tailored for attitude reports of a certain sort, but not modals, and it is harder to make use of for general semantic purposes, such as the semantic composition of complex expressions of different sorts.

A third approach to the semantics of attitude reports makes use of situations rather than entire worlds, an approach that also gives a more fine-grained notion of content, though of a different sort (Barwise and Perry 1983; Kratzer 2014). One recent version of a situation-based approach is truthmaker semantics, as developed by Fine (2012, 2014, 2017a, 2017b, 2017c, 2018a, 2018b). Truthmaker semantics is based on the relation of exact truthmaking or satisfaction between a situation or action and a sentence (as well as a corresponding relation of exact falsification or violation). Exact truthmaking holds between a situation and a sentence just in case the situation is wholly relevant for the truth of the sentence. Truthmaker semantics is able to distinguish contents of logically equivalent sentences and gives an immediate account of the notions of subject matter and of partial content. Truthmaker semantics has been applied to a range of semantic and logical topics. However, it has not been applied to natural language more generally and in particular not to the various sorts of intensional predicates in natural language.

This paper gives an outline of a development of truthmaker semantics that I call object-based truthmaker semantics. Object-based truthmaker semantics carries over the truthmaker-semantic notion of content, based on situations or actions in the role of exact truthmakers or satisfiers. However, it applies the truthmaking/satisfaction relation (and the corresponding falsification/violation relation) not just to sentences, but also to objects of a certain sort. For modal sentences and attitude reports those objects are what I call modal and attitudinal objects, entities quite distinct from propositions. Modal objects are entities like obligations, permissions, and needs; attitudinal objects are entities like claims, judgments, beliefs, requests, promises, decisions, intentions, desires, and hopes. Modal and attitudinal objects are typically (but not necessarily) the denotations of nominalizations of modal predicates or attitude verbs. They are characterized by a range of properties that jointly distinguish them from other categories of entities. Most importantly, they carry truth or satisfaction conditions, yet display properties of concreteness.

Object-based truthmaker semantics avoids the problems of possible-worlds semantics, yet aims to retain similar advantages, in particular in providing a unified semantics of modals and attitude reports. It also has specific advantages in being able to give a better account of certain sorts of modals in attitudinal contexts (harmonic modals), of the distinction between weak and strong permissions, of the semantics of response-stance verbs and factive verbs, and of the distinction between descriptive and performative modals.

Object-based truthmaker semantics can be extended to the semantics of intensional transitive verbs, such as look for and owe, and explain particular semantic phenomena involving them: the interpretation of weak quantificational NPs as complements and restrictions on the sharing of the semantic object associated with different intensional verbs. The application of object-based truthmaker semantics to intensional transitive verbs requires extending the domain of bearers of truthmaking conditions to entities such as searches, purchases, and debts. An additional motivation for object-based truthmaker semantics applied to intensional transitive verbs comes from the fact that entities like searches and purchases require a causal connection to their satisfaction situations. Overall, the semantics of intensional transitive verbs gives significant further support for object-based truthmaker semantics, as opposed to possible-worlds semantics or even sentence-based truthmaker semantics.

This paper will first give a general outline of object-based truthmaker semantics against the background of the standard semantic approaches to attitude reports and modals. Second, it will elaborate the ontology of modal and attitudinal objects and motivate their status as bearers of truthmaking or satisfaction conditions. Third, it will apply object-based truthmaker semantics to attitude reports and modal sentences of various sorts, to factive and response-stance verbs, and to intensional transitive verbs. The paper will focus on the general picture and just present the general ideas for a compositional semantic analysis of the relevant data, rather than fully elaborating such an analysis itself.

2 Standard views of propositional attitudes and modals

3 The attraction of the possible-worlds view of modals and propositional attitudes

The possible-worlds account of content is most plausible for implicit attitudes, such as implicit beliefs, including those of animals and small children, which can hardly involve any form of structured mental representation. In fact, it has been argued that such attitudes are ascribed on the basis of how an agent would act in counterfactual circumstances (possible worlds) (Stalnaker 1984). For implicit attitudes only the agent’s dispositions regarding particular circumstances matter, not the structure of a mental representation. The possible-worlds account of content is much less plausible for other attitudes, though, such as occurrent thought, or generally mental or illocutionary acts, which involve a more finely grained content (Cresswell 1985).

Possible-worlds semantics, however, has been attractive to formal semanticists for other reasons. First, possible-worlds semantics, it appears, allows for a unified compositional semantics of the sentential units (clausal complements or subjects or prejacents) associated with both attitudinal and modal predicates. Sentential units on that view always stand for sets of possible worlds, which are obtained compositionally from possible-world-based meanings of subsentential expressions.

Possible worlds have also played an important role for representing the common ground. The common ground is generally conceived as an unstructured content of what the interlocutors take for granted, as a set of worlds or context set. The common ground plays a central role in theories of presuppositions, in the so-called Satisfaction Theory of presupposition projection (Heim 1983). On the Satisfaction Theory, the presuppositions of a sentence S need to be true in the worlds of the common ground C (a set of worlds) in order for C to be updated with the proposition p expressed by S (a set of worlds) (which means intersecting p with C). Complex sentences such as conjunctions (and conditionals) involve complex conditions on updating. Updating a context set C with the utterance of a conjunction S & S’ consists in first intersecting C with the proposition expressed by S and then intersecting the result with the proposition expressed by S’.

In addition to the primary context set representing what is shared by the interlocutors, the common ground, various secondary context sets need to be distinguished, representing what the interlocutors take the content of a particular type of attitude of a particular agent to be. Thus, in a sequence John believes that it is raining. He believes that it will stop soon, the presupposition of it will stop soon needs to be true not in the worlds in the primary context set, but in the worlds compatible with what the interlocutors take to be John’s beliefs. The latter make up just one secondary context. Another secondary context may represent John’s fears, and yet another Bill’s beliefs. Further additions to the context set (or the context sets) are needed to account for updating with questions as well as with imperatives and performatively used deontic modals, that is, modals that put a requirement in place, rather than describing it, as on one reading of (6) below:^[3]

There are also particular connections among propositional attitudes and modals. I will focus on just two. One of them consists in that attitude or illocutionary act reports may permit particular inferences to modal sentences such as the inferences below:

For (7a) to be felicitous, though, John must have the right authority to set up an obligation by issuing a request.

Another connection between attitude reports and modals is certain occurrences of modals in embedded clauses exhibiting modal concord, ‘harmonic modals’, as Kratzer (2016) calls them. Harmonic modals are occurrences of modals in the complement clause of an attitude verb that appear to resume the modal force associated with the reported attitude, rather than contributing to a modal content of that attitude:

The harmonic use of the modal should in (8) matches the subjunctive mood in (9a) and contrasts with the non-harmonic use of must in (9b):

Again, possible-worlds semantics appears to be suited to capture this sort of connection between modals and propositional attitudes given that attitude verbs are basically treated as modal operators ranging over worlds and may range over the same worlds as a modal (Section 5.2).^[4]

4 The structured-propositions view and verbs of saying

Structured propositions have been proposed as an alternative to the conception of propositions as sets of worlds, giving a more fine-grained notion of content. A structured proposition is generally conceived of as an n-tuple consisting of the meanings of the elementary constituents. Thus, a simple type of structured proposition, as the meaning of the subject-predicate sentence Mary is happy, would be a pair consisting of a property (the property of being happy) and an object (Mary). With structured propositions as their meanings, two sentences that are logically equivalent, but involve significantly different syntactic structures, are distinguished, as are sentences that are about different objects or involve different properties. Though structured proposition appear more suited than sets of worlds for representing the content of propositional attitudes, structured propositions come with conceptual problems of their own, especially the problem of the unity of the proposition: truth conditions for structured propositions need to be stipulated and do not pertain to the nature of structured propositions as such (Hanks 2015; Jubien 2001; Moltmann 2013b, 2020; Soames 2010). Moreover, the structured-propositions view imposes a fineness of grain that is not generally considered needed for the semantics of modals and the semantics of various sorts of implicit attitudes, and sometimes even for explicit attitudes. For example, the order of disjuncts or of complements should not generally lead to a difference in the content of the reported attitude (John’s belief that Mary gave Joe a book is not necessarily distinct from John’s belief that Mary gave a book to Joe). Furthermore, if the objects of attitudes are construed as structured propositions, attitudes would lose their similarity to modals, which means that connections between attitudes and modals would be harder to account for.

Yet, it appears that for certain sorts of attitude reports a highly fine-grained, structured notion of content is unavoidable, namely those with verbs of saying.^[5] The sensitivity of verbs of saying to the syntactic structure and perhaps even choice of words in their complement can be enforced by the use of literally:

However, if for verbs of saying, the particular choice of words as well as the syntactic structure of the complement clause may matter, this may not so much motivate a particular conception of sentence meaning as such (structured propositions as opposed to sets of worlds). Rather it may motivate a view according to which the complement of verbs of saying contributes differently to the characterization of the reported attitude than the complement of other attitude verbs, namely by specifying the structure of the product of a locutionary act, rather than just providing a propositional content (or the truth or satisfaction conditions of the reported attitudinal object) (Moltmann 2017b). In what follows, therefore, I will set aside verbs of saying, as they arguably involve a rather different overall semantics than other attitude verbs.

5 Truthmaker semantics

Truthmaker semantics, as recently developed by Fine (2012, 2014, 2017a, 2017b, 2017c, 2018a, 2018b), gives a notion of content that is more fine-grained than that of possible-worlds semantics, but yet not as fine-grained as that of the structured-propositions view. In particular, the content of a sentence is not taken to reflect syntactic structure in the way a structured proposition does. The following is a very brief outline of Fine’s sentence-based truthmaker semantics, which should suffice for the present purposes.

Truthmaker semantics is based on situations (and actions) rather than entire worlds, as well as on the relation of exact truthmaking (or satisfaction) holding between situations (or actions) and sentences. A situation (or action) s stands in the relation ╟ of exact truthmaking (or exact satisfaction) to a sentence S just in case s is wholly relevant for the truth (or satisfaction) of S. This means that s should not include anything that fails to bear on the truth (or satisfaction) of S. A situation (or action) s is a falsifier (or violator) of a sentence S just in case s is wholly relevant for the falsity (or violation) of S.

The use of the notion of exact truthmaking distinguishes truthmaker semantics from older situation-based semantic theories such as that of Barwise and Perry (1983) and Kratzer (2014), which are based on the relation inexact truthmaking or verification between situations and sentences. The notion of an exact truthmaker of a sentence is distinct from that of a minimal situation supporting a sentence, a notion defined in terms of inexact truthmaking in Kratzer (2002, 2014. There are two important reasons for using the notion of an exact truthmaker rather than that of a minimal truthmaker (Fine 2017a). First, there are sentences that have exact verifiers, but lack minimal verifiers, for example there are infinitely many natural numbers.^[6] Second, a sentence such as it is windy or it is rainy and windy has two exact verifiers, a situation in which it is (just) windy and a situation in which it is (just) windy and rainy, but it would have only one minimal verifier (a situation in which it is windy) (Fine 2017a).

Situations are taken to be parts of worlds, and no further assumptions are made regarding their ontology beyond the roles they play within truthmaker semantics. Actions are a specific kind of situation, those that may comply with or violate imperative sentences, rather than making them true. The domain of situations divides into actual, possible, as well as impossible situations. Actual situations are part of the actual world; impossible situations are part of impossible worlds and would be truthmakers of contradictory sentences. The domain of situations is ordered by a part-whole relation < (a partial order) and is closed under fusion. Formally it forms a complete lattice.

The truthmaking/satisfaction relation ╟ applies to both declarative and imperative sentences: declarative sentences are made true by situations that are their exact truthmakers, imperatives are complied with by actions that are their exact satisfiers. The following standard conditions on the truthmaking of sentences with conjunctions, disjunctions, and existential quantification then hold, where ⊕ is the operation of fusion:^[7]

Truthmaker semantics assigns to sentences not only truthmakers or satisfiers, but also falsifiers or violators. Making use of the relation of (exact) falsification or violation allows a straightforward formulation of the truthmaking conditions of negative sentences: a truthmaker of ¬ S is a falsifier of S. With ╢ as the relation of (exact) falsification or violation, the condition on negation is given below:^[8]

Also complex sentences are assigned both verification and falsification conditions. For conjunctions and disjunctions, the falsification conditions are those below:

A sentence S then has as its meaning a pair <pos(S), neg(S)> consisting of a positive denotation, the set pos(S) of verifiers of S, and a negative denotation, the set neg(S) of falsifiers of S.

In truthmaker semantics, logically equivalent sentences will have different semantic values whenever they are about different things. Truthmaker semantics provides a straightforward account of the notion of subject matter of a sentence, namely as the fusion of its truthmakers or satisfiers. In truthmaker semantics, the contents of sentences thus are considerably more fine-grained than in possible-worlds semantics, which does not provide a reasonable notion of subject matter if sentence meanings are just taken to be sets of worlds (Yablo 2015). Truthmaker semantics, moreover, provides a straightforward account of the notion of partial content (Fine 2017a; Yablo 2015):

The notion of partial content is extremely well-reflected in the way we talk about content, including the contents of modal and attitudinal objects: part of the content of this sentence, part of John’s belief, part of John’s obligation all stand for a partial content (of a belief, a sentence, and a modal object). It is also reflected in the adverb partly when modifying attitude verbs (Section 9). Given the notion of partial content, that it is cold is part of John’s belief that it is raining and it is cold (since every situation in which it is just cold is part of a situation in which it is raining and it is cold, and every situation in which it is cold and it is raining has a situation as part in which it is just cold). However, that two is greater than one is not a part of that belief, unlike on a possible-worlds account of inference. Moreover, unlike on a possible-worlds account, that two is greater than one or it is cold need not be part John’s belief that it is cold given (14). For Fine (2018a), partial content also plays a central role for the validity of inferences. For example, it explains the invalidy of the inference with imperatives in (15), which is a problem for possible-worlds semantics (Ross’ paradox):

For Fine, p! implies q! only if q is a partial content of p, which is not the case in (15).

Truthmaker semantics as developed by Fine assigns content only to sentences and has not been developed so as to allow for an application to attitude reports and modals in general.^[9] An obvious way in which one might try to apply truthmaker semantics to attitude reports would be to take the truth-maker-based meaning of the embedded sentence to be the argument of the attitudinal relation. Thus, (16a) would have the logical form in (16b):

However, there are reasons why such an analysis would be unsatisfactory. One reason is that it could hardly be used to account for the connections between modals and attitude reports that this paper will discuss. Another reason is that (16b) would fall under the Relational Analysis of attitude reports, which is associated with a range of philosophical and linguistic difficulties, as will be discussed in the next section.

6 Problems for the Relational Analysis of attitude reports and the importance of modal and attitudinal objects

The Relational Analysis, on which attitude verbs take propositions as arguments, is compatible with more or less fine-grained notions of content: a proposition may be construed as a set of worlds or as a structured proposition of some sort. There are a range of philosophical and linguistic difficulties, however, for the Relational Analysis.^[10] I will just mention them briefly, since they are elaborated elsewhere in the literature and my own previous work.

1. The Relational Analysis fails to make a distinction (going back to Brentano) between the content and the object of an attitude, treating propositions as things agents have attitudes to, rather than as the contents of attitudes that agents engage in.

2. Abstract propositions raise a number of conceptual problems, which have been a major topic of debate in contemporary philosophy of language. They include the problem of the graspability of propositions, the problem of the unity of the proposition, and the problem of how propositions as abstract objects can be true or false (Hanks 2015; Jublien 2001; Moltmann 2013b, 2017a, 2020; Soames 2010).

3. The Relational Analysis has difficulty accounting for the Substitution Problem, the problem of the unacceptability of (17b) as an inference from (17a), and the Objectivization Effect, the semantic difference between (18a) and (18b) (Moltmann2013a, 2020):

1. The Relational Analysis has difficulties accounting for the semantics of nominal constructions, where the that-clause does not syntactically or semantically appear to act as an argument (Moulton 2015):

Semantically, the that-clause in (19) seems to stand for what the entire NP stands for (a request), rather than providing an object entering into a thematic relation to the noun request. Yet, the clausal complement would stand for a proposition and a proposition is not the same thing as a request. For example, a request can be complied with or ignored, but a proposition cannot (at least not in the same sense) (See Section 5.3).^[11]

1. The Relational Analysis does not get the semantics of what I call special quantifiers right (Moltmann 2013a, 2020, to appear). Special quantifiers (and pronouns), which include something, everything, that, and what, can take the position of clausal complements of attitude verbs. In that position, given the Relational Analysis, they should stand for propositions, but in fact they can only stand for attitudinal objects or kinds of them (Moltmann 2003a, 2003b, 2013a, 2013b, 2017a, to appear).

7 The ontology of modal and attitudinal objects

Object-based truthmaker semantics pursues an alternative to the propositions-based Relational Analysis of attitude reports and to the Quantificational Analysis of modal sentences.^[12] Object-based truthmaker semantics assigns very different logical forms to attitude reports and modal sentences than the standard approaches. On the standard view of attitude reports, clauses when embedded under an attitude verb act as singular terms standing for propositions. The present view is that such clauses act semantically as predicates of the attitudinal object associated with the attitude verb. The standard view is that modal predicates act as quantifiers over possible worlds and that what I will call the sentential unit associated with the modal predicate acts as the scope of such a quantifier (complement clause, subject clause, or prejacent). The present view is that the sentential unit semantically acts as a predicate of the relevant modal object. Clauses act as predicates of modal or attitudinal objects by giving their truthmaking or satisfaction conditions.^[13]

Object-based truthmaker semantics is based on a novel ontology of attitudinal and modal objects. Attitudinal and modal objects are part of the ontology implicit in natural language: they are referents of definite NPs whose heads are nominalizations of attitude verbs or modals (John’s belief that S, Mary’s claim that S, John’s obligation to VP), and they act as semantic values of special quantifiers and pronouns and as implicit arguments of predicates. The characteristic properties of attitudinal and modal objects are reflected in the semantics of those constructions, but also in various general intuitions we have about them.

Kinds of attitudinal and modal objects also play an important role. They act as referents of NPs of the sort the belief that S, the claim that S, the obligation to do X as well as semantic values of special quantifiers and pronouns. Two particular attitudinal objects (of the same sort) belong to the same kind just in case they are exactly or closely similar (‘are the same’), which means they are the same in content. If John’s belief is the same as Mary’s belief, John and Mary share a belief, and if John’s claim is the same as Mary’s, they made the same claim. Sharing a content thus means engaging either in attitudinal objects that are closely similar or in the same kind of attitudinal object.

Attitudinal objects are distinct from the more familiar ontological categories of actions and states. Attitudinal objects share characteristic properties that jointly distinguish them from actions (and states) and propositions. Moreover, they display properties that could hold neither of actions (and states) nor of propositions (which I will turn to shortly). Attitudinal objects divide into act-related attitudinal objects, which include judgments, decisions, claims, requests, promises, and state-related attitudinal objects such as beliefs, intentions, desires, and fears. Some attitudinal objects are products of acts in the sense of Twardowski’s (1911) distinction between actions and products. This arguably means that they are abstract artifacts in the sense of Thomasson’s (1999), which means that they lack a material or physical realization (Moltmann 2013b, 2017a). Thus, a claim is the (illocutionary) product of an act of claiming, a promise the (illocutionary) product of an act of promising, and a judgment the (cognitive) product of an act of judging. Attitudinal objects that are products of acts need not last longer than the act that produced them (Section 5.1).

Modal objects may be products of illocutionary acts, but need not be. Strong permissions are generally the products of illocutionary acts, but not so for weak permissions (Section 7.4). Modal objects share the characteristic properties of attitudinal objects and are sharply distinguished from states. But they can last longer than the act that produced them, and in fact they need not have come into existence at a particular point in time in the first place.

8 Motivations for object-based truthmaker semantics

There are a range of specific motivations for the use of modal and attitudinal objects in connection with truthmaker semantics. I will mention five of them.

9 Sentences as predicates of modal and attitudinal objects

We can now turn to the formal semantics of clauses as predicates of content bearers, that is, attitudinal or modal objects. For the semantics of attitude reports, I will make use of Davidsonian event semantics (Davidson 1967). That is, an attitude verb will have an additional argument position for events, acts, or states. I will assume, certainly simplifying, that there is a unique attitudinal object att-obj(e) associated with a Davidsonian event argument e of an attitude verb. The clausal complement of the attitude verb will then be predicated of the attitudinal object associated with the event argument, as in (25b) for (25a) below:

That is, (25a) means that there is an event e of claiming by John and that S holds of the attitudinal object associated with e (att-obj(e)). The semantics of attitude reports in (25b) is (almost) overtly reflected in the corresponding complex-predicate construction in (26), which involves explicit reference to an attitudinal object (or a kind of attitudinal object):

The fact that languages show an alternation between the simple and the complex-predicate construction further motivates the semantics in (25b) (Moltmann 2017a, 2018a).

Clausal modifiers of nominalizations of attitude verbs will be predicated of the attitudinal object described by the nominalization, as in (27b) for (27a):

Given the possibility of underspecification, the property that sentences as predicates of modal or attitudinal object express will consist in a partial specification of satisfaction conditions, as below, where ╟ is the relation of exact truthmaking or satisfaction now holding between situations or actions s and modal or attitudinal objects d (as well as sentences):

This simply means that the content of S is a partial content of the content of d in the sense of (14).

(28) cannot yet be adequate, though, since it would not allow distinguishing necessity and possibility semantically. Given (28), a permission (for Mary to enter the house) could be a modal object with the very same satisfaction conditions as an obligation (for Mary to enter the house). But the permission for Mary to enter the house is not an obligation for Mary to enter the house.

What distinguishes a permission from an obligation? Permissions allow for certain actions, those they permit. Obligations allow for certain actions, those that comply with them, but unlike permissions they also exclude certain actions, those that violate them. The permission for Mary to enter the house allows for actions of Mary entering the house, but does not exclude any other actions. By contrast, the obligation for Mary to enter the house allows for actions of Mary entering the house and excludes actions of Mary’s not doing so. This means that permissions have only satisfiers, whereas obligations have both satisfiers and violators.

Also illocutionary products are distinguished in that way. An offer or invitation has only satisfiers, but no violators. By contrast, a request or order has both satisfiers and violators.

This difference between modal forces requires modifying (28) by adding a condition on the falsification or violation of the modal or attitudinal object, namely that every falsifier of the sentence also be a falsifier or violator of the modal or attitudinal object. The modified meaning of a sentence S then is as follows, where the relation of falsification or violation ╢ now also obtains between actions or situations and modal or attitudinal objects (Moltmann 2018a):

That is, a sentence S expresses the property that holds of a modal or attitudinal object d just in case the content of S is a partial content of d and every falsifier of S is a violator of d, should there be a violator of d.

On this account, sentences conveying necessity and sentences conveying possibility will have exactly the same logical form; but they involve different sorts of modal or attitudinal objects with different satisfaction and violation conditions. This is given for (30a) and (30b) in (31a) and (31b) respectively, based on the same meaning of the complement clause (which is, syntactically simplified, taken to be Mary to leave the house):

In (31a) and (31b), the function att-obj maps the event argument of the verb onto the attitudinal object associated with that event, and the complement clause is predicated of that attitudinal object, with the property of (attitudinal or modal) objects in (29) as its meaning.

Similarly, modal sentences involve predication of the sentential unit associated with the modal predicate of the relevant modal object. Taking the modal object to be the event argument itself, (32a) and (33a) will then have the logical forms in (32b) and (33b) respectively:

In (32b) and (33b), the sentential units John to leave and Mary to take a walk will have the very same sort of property in (29) as their meaning and attribute that property to the respective modal objects, the need and the permission.

Unlike possible-worlds semantics, this gives an adequate account of strong (explicit) permissions (the only reading of Mary has permission to take a walk). If the modal object d is an explicit permission, the sentential unit will specify which sorts of actions will be exact satisfiers of d and not just what is true in some world compatible with what is obligatory. The latter may count as satisfiers only of a state of weak permission which is set up on the basis of what is obligatory, displaying the duality between permission and obligation (Moltmann 2018a).

There is a further important argument for the truthmaker account and against the possible-worlds account and that is that possible-worlds semantics would not permit a single property of clauses that could hold of attitudinal and modal objects of necessity and of possibility. Moulton (2015), who (following talks by Angelika Kratzer) proposes the property in (34a) as the meaning of that-clauses, based on the notion of the content cont(x_c) of a contextually determined content bearer x_c (e.g. an attitudinal object) in (34b):

One problem with this account is of course that it is based on possible worlds, leading to the usual problems of a too coarse-grained semantics for various sorts of attitudes. The second problem is that it treats content bearers with the force of possibility and content bearers with the force of necessity exactly the same. This makes it impossible to account for the connections between attitude reports and modals as mentioned earlier (see also Section 11.2). In fact, it is not clear how the account could apply to modals such as must, can, or need in the first place, since modals need not involve an object associated with a specific propositional content, for example when they convey weak permission or obligation.

10 The semantics of response-stance verbs and factive verbs

Not all attitude verbs have a semantics on which their clausal complement is just predicated of the attitudinal object associated with the event argument of the verb. With one class of attitude verbs, the clausal complement in addition serves as a predicate of a contextually given attitudinal object, which gives further support for the semantics of attitude reports based on attitudinal objects. The class of verbs consists in what Cattell (1978) called response-stance verbs and includes repeat, confirm, agree, and remind, as in the sentences below:

In general, response-stance verbs have a clausal complement that serves to characterize both the reported attitudinal object and a contextually given attitudinal object. Thus, in (35a) the complement clause gives the content of two attitudinal objects: John’s assertion (or perhaps just his act of saying) and a contextually given claim, which may be John’s or another person’s previous claim. In (35b), the clausal complement gives the satisfaction condition of John’s assertion as well as that of a previous assertion or acceptance with a much weaker illocutionary force. In (35c), the infinitival complement specifies actions as satisfiers of John’s statement of intent as well as, say, a previous request. In (35d), the complement clause gives the satisfaction conditions of Mary’s decision or intention that John’s locutionary act aims to trigger, as well as those of a previous thought, decision, or intention of Mary’s. The lexical meaning of the response-stance verb constrains the nature of the contextually given attitudinal object and its relation to the attitudinal object of the reported agent.

What is the logical form of a sentence with a response-stance verb? A first option is (36b) for (36a), where d is the contextually given attitudinal object:

However, this cannot be right because an act can be an act of agreeing not on its own, but only in relation to a contextually given speech act. A better option is (37), where agree is now a three-place predicate taking the contextually given attitudinal object d as a third argument:^[22]

There is specific support for (37), and that is the general substitutability of the clausal complement by an NP explicitly referring to the contextually given attitudinal object (plus sometimes a preposition):^[23]

Additional support for (37) comes from the reading of the modifier partly with response-stance verbs (Moltmann 2017c). With verbs such as mention and think, that is, with what Cattell (1978) calls volunteered-stance verbs, partly fails to have a reading on which it relates to the content of the clausal complement:

(39a) has a conceivable reading on which it means that John mentioned that part of the house needed to be renovated, and (39b) on which it means that John thinks that only some of the students are talented. But such readings are not available. By contrast, response-stance verbs do permit a reading of partly on which it relates to part of the content of the contextually given attitudinal object:

In (40a) partly means ‘part of the content of the claim that the house needs to be renovated’ (which may be that part of the house needs to be renovated). In (40b), partly picks out a partial content of the claim that the students are lazy, which may be that part of the students are lazy. The same sort of reading of partly is generally available with transitive verbs:

Given Davidsonian event semantics, the general meaning of partly can be taken to be that of a relation between an event e and a type of event E which holds just in case e instantiates part of E. The logical form of (41a) will then be as in (42a) and the one of (41b) as in (42b), where ^ is an abstractor for event types:

With a verb like eat, the part structure of the event is inherited from the part structure of the object argument. Analogously, with a verb like agree, the part structure of the event of agreeing is inherited from the partial-content-based part structure of the attitudinal object. Partly then says that the event argument of the verb instantiates part of the type of the event described by the VP.

Response-stance verbs pattern together with factive verbs with respect to their syntactic behavior (for example disallowing adjunct extraction) (Cattell 1978). Factive verbs also exhibit the same reading of partly:

In (43a, b), partly relates to part of the content of a fact (partial failure in (43a) and part of the students being lazy in (43b)). This further supports the same semantics for factive verbs as for response-stance verbs. But with factive verbs the clausal complement will characterize not an attitudinal object, but a fact -- in addition to characterizing the content of the described mental state or act.

The relevant notion of a fact should not be that of an actual situation in the sense of truthmaker semantics, on which a fact would be a fully specific part of the actual world. Rather it should be a notion of a non-worldly fact, which can be quantificational or disjunctive. Non-worldly facts exist independently of anyone’s mental attitudes and thus are not attitudinal objects. Yet, they do have a part structure based on partial content (given how partly is understood in (43a, b)). Non-worldly facts in the required sense are best conceived as modal objects, namely modal objects whose satisfiers are situations that are part of the actual world. Such a factive modal object can be obtained by mapping a sentence S true in a world w onto an object f_w(S), a modal object whose satisfiers are just the situations that are part of w and make S true:

Making use of factive modal objects, the logical form of a sentence with a factive verb such as (45a) will be as in (45b):

Note that reference to the entire actual world in the characterization of modal objects means that truthmaker semantics cannot do without the notion of a world as such.

To sum up, object-based truthmaker semantics can naturally be extended to response-stance verbs and factive verbs, by positing an additional verbal argument that is a contextually given attitudinal object or a factive modal object. In the reading of the modifier partly, those attitudinal or factive modal objects display a part structure based on partial content, which specifically supports the truthmaker-based approach.

11 Subject clauses

There are also good reasons to assume that clausal subjects with a predicate like is true or is correct give the content of a contextually given content-bearer (a claim, rumor, or suggestion) (Moltmann 2018b). Thus, a sentence like (46) is generally understood in such a way that that S serves to give the truth conditions of a contextually given attitudinal object, a claim or speculation:

Correct does not apply to propositions, referred to as such, but only to attitudinal objects such as claims (The proposition that S is correct hardly makes sense, as opposed to the claim that S is correct). This means that (46) has the logical form in (47), for the relevant contextually given attitudinal object d:

Other clausal subjects may instead be predicated of an object that is an implicit argument of the verb or closely related to it. Thus, the clausal subjects of is possible is best viewed as acting as a predicate of the modal object that is an implicit argument of the modal possible, as in (48b) for (48a):

Of course, a particular semantic role of a clausal subject will have to have a syntactic basis. But in the present context, the aim was simply to show the plausibility of clausal subjects serving particular semantic roles which are not that of standing for a proposition.

12 Object-based truthmaker semantics and connections between modals and propositional attitudes

13 The semantics of intensional transitive verbs

Object-based truthmaker semantics is particularly suited for the semantics of intensional transitive verbs, once it is expanded so as to include not just attitudinal and modal objects as bearers of truthmakers or satisfiers, but also objects like searches, purchases, and debts. Since those objects are associated with intensional transitive verbs, I will call them ‘intensional objects’, a term that is used differently in other contexts, but in the present context matches the choice of the terms ‘attitudinal object’ and ‘modal object’.

Object-based truthmaker semantics has two important advantages over possible-worlds semantics for the semantics of intensional transitive verbs. First, it can explain the particular readings of NPs with weak quantifiers (a, exactly two, at most etc) as complements of intensional transitive verbs. Second, it can account for the constraints on the sorts of ’semantic objects’ that different intensional verbs can share. An additional motivation comes from the observation that certain intensional object require a causal connection to their satisfiers, for example purchases.

First of all, a few clarificatory remarks about intensional transitive verbs in general. I take intensional transitive verbs to comprise a larger class of verbs than is common, including the following types of verbs (Moltmann 1997, 2008):

Verbs of possession allow for intensional readings involving a nonspecific reading of their complement, e.g. John offered Mary a glass of wine (but no particular one), John bought a bottle of wine on the internet (but no particular one), Bill owns half of the estate (but no particular half) (Moltmann 1997; Zimmermann 2001). An example of an intensional reading of recognize is John recognized a genius (when he saw his daughter calculate) and of hire, Mary hired an assistant (giving Bill his first job).

Also the verb find can be used as an intensional verbs, either as a verb of nomination (Mary found a secretary) or a verb of recognition (John found a wife). Need and look for share the same two intensional readings (John needs / is looking for a secretary / a wife), in addition to an object-related one (John needs / is looking for a pen).

The general criterion for the intensionality of intensional transitive verbs is not lack of existence-entailment or failure of substitutivity, but rather a particular nonspecific reading of complements with weak quantifiers (on which they could not take scope over the verb) (Moltmann 1997; Zimmermann 2001). What is also characteristic of intensional transitive verbs is that they involve particular semantic objects which special quantifiers (something, what, the same thing etc.) range over when they are in the object position of intensional transitive verbs. I will call those objects ‘variable satisfiers’,

14 Summary

Possible-worlds semantics has been a dominant approach in formal semantics, despite its obvious shortcomings. Possible-worlds semantics appeared to have particular advantages for the pursuit of compositional semantics of natural language, allowing for a unified compositional semantics of a great range of constructions in a context of discourse and in particular for a unified semantics of modals and attitude reports. The most serious overall shortcoming of possible-worlds semantics is that it fails to give a sufficiently fine-grained notion of content. Truthmaker semantics with its central notion of a situation as an exact truthmaker of a sentence presents a more fine-grained notion of content, and its sentence-based version has been applied to a range of issues that present difficulties for the possible-worlds account.

Object-based truthmaker semantics extends sentence-based truthmaker semantics by applying the truthmaking relation not just to sentences, but also to attitudinal objects as well as the related categories of modal and intensional objects. It connects truthmaker semantics to the ontology of the mind as well as social objects such as obligations and permissions (entities on a par with laws), purchases, offers, and debts.

There are more specific motivations for object-based truthmaker semantics. One of them is the dependence of truthmakers on modal and attitudinal objects, which manifests itself in the distinction between weak and strong permissions, the possibility of underspecification of the content of the attitudinal, modal, or intensional object by the complement clause, sentential unit or NP complement, as well as causal or other connections in some cases between an object and its satisfiers.

The paper has outlined a semantics of attitude reports and modals on which a sentence embedded under an attitude verb semantically acts as a predicate of the attitudinal object associated with the verb, and the sentential unit associated with a modal as a predicate of the modal object that is an implicit argument of the modal. This semantics is (almost) overtly reflected in complex predicates of the sort make the claim, which often alternate with simple predicates like claim.

The semantics of attitude reports is able to overcome a range of difficulties for the standard proposition-based Relational Analysis, which include empirical and conceptual difficulties for the Relational Analysis as such as well as difficulties with the notion of an abstract proposition and the involvement of propositions in the semantics of attitude reports.

Of course, the paper has given only a very general outline of object-based truthmaker semantics, which invites various elaborations of empirical and formal detail, as well as more thorough comparisons with standard approaches for particular applications.