Researchers often assume that possible worlds and times are represented in the syntax of natural languages. However, it has been noted that such a system can overgenerate. This paper proposes a constraint on systems where worlds and times are represented as situation pronouns. The Intersective Predicate Generalization, based on and extending work by R. Musan, states that two items composed via Predicate Modification, such as a noun and an intersective modifier, must be evaluated in the same world and time. To (...) explain this generalization, a rule of Situation Economy is advanced, which holds that structures must have the fewest number of situation pronouns possible. Since strong DPs require a situation pronoun to receive a de re reading, a restriction on the type of strong determiners is proposed, which supersedes Situation Economy in this case. Finally, the paper shows how the Situation Economy approach explains an unrelated phenomenon involving bare plurals and examines the connection between this new rule and the grammar of natural language in general. (shrink)

This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of two (...) arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics. (shrink)

According to the orthodox account developed by Kaplan, indexicals like I, you, and now invariably refer to elements of the context of speech. This essay argues that the orthodoxy is wrong. I, you, and the like are shifted by certain modal operators and hence can fail to refer to elements of the context, for example, I can fail to refer to the speaker. More precisely, indexicals are syntactically akin to logical variables. They can be free, in which case they work, (...) roughly, on the Kaplan model. But they can also be bound: this happens, in a systematic fashion, when they are in the scope of epistemic modals or attitude verbs. The new view has two interesting philosophical consequences. First, it vindicates a broadly Fregean perspective on referential expressions, essentially refuting the idea that indexicals are rigid designators. Second, it suggests a new picture of the interaction between context and linguistic meaning: compositional semantics does not need to look at the context and hence has no need for a context parameter. (shrink)

It is argued that propositions cannot be the compositional semantic values of sentences (in context) simply due to issues stemming from the compositional semantics of modal operators (or modal quantifiers). In particular, the fact that the arguments for double indexing generalize to multiple indexing exposes a fundamental tension in the default philosophical conception of semantic theory. This provides further motivation for making a distinction between two sentential semantic contents—what (Dummett 1973) called “ingredient sense” and “assertoric content”.

Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional semantics. I also describe (...) some properties of the logic that are interesting from a philosophical perspective, and apply it to the so-called nesting problem. (shrink)

This paper discusses the fallacies of combination and division as they are presented by Aristotle in chapter 4 of his Sophistici Elenchi. Aristotle's examples are concise, their discussion is unclear, and it is difficult to distinguish the cases of combination from those of division. I analyse the Aristotelian examples and the interpretations offered so far. I show that these interpretations suffer from a major defect: they fail to identify a common characteristic whereby the Aristotelian examples can be classified as instances (...) of combination or division. In my reconstruction of the examples, I repair this deficiency: I give a single pattern of explanation for the fallacy of combination and another (similar) pattern for the fallacy of division. Thus, it is possible to free Aristotle from the following charges: (i) he did not clearly distinguish between combination and division, and (ii) he reduced combination and division to a single fallacy. My explanation of the fallacies uses the notion of scope of an expression: in modern terminology, the fallacy of combination can be described as ?fallacy of the wide scope?, the fallacy of division as ?fallacy of the narrow scope? (shrink)

In Ockhamist branching-time logic [Prior 67], formulas are meant to be evaluated on a specified branch, or history, passing through the moment at hand. The linguistic counterpart of the manifoldness of future is a possibility operator which is read as `at some branch, or history (passing through the moment at hand)'. Both the bundled-trees semantics [Burgess 79] and the $\langle moment, history\rangle$ semantics [Thomason 84] for the possibility operator involve a quantification over sets of moments. The Ockhamist frames are (3-modal) (...) Kripke structures in which this second-order quantification is represented by a first-order quantification. The aim of the present paper is to investigate the notions of modal definability, validity, and axiomatizability concerning 3-modal frames which can be viewed as generalizations of Ockhamist frames. (shrink)

Saul Kripke's thesis that ordinary proper names are rigid designators is supported by widely shared intuitions about the occurrence of names in ordinary modal contexts. By those intuitions names are scopeless with respect to the modal expressions. That is, sentences in a pair like (a) Aristotle might have been fond of dogs, (b) Concerning Aristotle, it is true that he might have been fond of dogs will have the same truth value. The same does not in general hold for definite (...) descriptions. If one, like Kripke, accounts for this difference by means of the intensions of the names and the descriptions, the conclusion is that names do not in general have the same intension as any normal, identifying description. However, this difference can be accounted for alternatively by appeal to the semantics of the modal expressions. On the account we suggest, dubbed 'relational modality', simple singular terms, like proper names, contribute to modal contexts simply by their actual world reference, not by their descriptive content. That account turns out to be fully equivalent with the rigidity account when it comes to truth of modal and non-modal sentence (with respect to the actual world), and hence supports the same basic intuitions. Here we present the relational modality account and compare it with others, in particular Kripke's own. (shrink)

Standard models for model predicate logic consist of a Kripke frame whose worlds come equipped with relational structures. Both modal and two-sorted predicate logic are natural languages for speaking about such models. In this paper we compare their expressivity. We determine a fragment of the two-sorted language for which the modal language is expressively complete on S5-models. Decidable criteria for modal definability are presented.

Recent theories of agency (sees to it that) of Nuel Belnap and Michael Perloff are examined, particularly in the context of an early proposal of the author.

Theoria, Volume 88, Issue 2, Page 276-277, April 2022.

European Journal of Philosophy, Volume 30, Issue 2, Page 623-638, June 2022.

I develop a puzzle, the resolution of which, I argue, requires an unfamiliar distinction between two forms or senses of metaphysical modality, each bearing a different relationship to time. In one sense of ‘metaphysically possible’, it is metaphysically possible for it to be a time other than the time it is now; in another sense, this is not metaphysically possible.

According to indexical contextualism, the perspectival element of taste predicates and epistemic modals is part of the content expressed. According to nonindexicalism, the perspectival element must be conceived as a parameter in the circumstance of evaluation, which engenders “thin” or perspective-neutral semantic contents. Echoing Evans, thin contents have frequently been criticized. It is doubtful whether such coarse-grained quasi-propositions can do any meaningful work as objects of propositional attitudes. In this paper, I assess recent responses by Recanati, Kölbel, Lasersohn and MacFarlane (...) to the “incompleteness worry”. None of them manages to convince. Particular attention is devoted to an argument by John MacFarlane, which states that if perspectives must be part of the content, so must worlds, which would make intuitively contingent propositions necessary. I demonstrate that this attempt to defend thin content views such as nonindexical contextualism and relativism conflates two distinct notions of necessity, and that radical indexicalist accounts of semantics, such as Schaffer’s necessitarianism, are in fact quite plausible. (shrink)

We defend the thesis that every necessarily true proposition is always true. Since not every proposition that is always true is necessarily true, our thesis is at odds with theories of modality and time, such as those of Kit Fine and David Kaplan, which posit a fundamental symmetry between modal and tense operators. According to such theories, just as it is a contingent matter what is true at a given time, it is likewise a temporary matter what is true at (...) a given possible world; so a proposition that is now true at all worlds, and thus necessarily true, may yet at some past or future time be false in the actual world, and thus not always true. We reconstruct and criticize several lines of argument in favor of this picture, and then argue against the picture on the grounds that it is inconsistent with certain sorts of contingency in the structure of time. (shrink)

We consider a natural-language sentence that cannot be formally represented in a first-order language for epistemic two-dimensional semantics. We also prove this claim in the “Appendix” section. It turns out, however, that the most natural ways to repair the expressive inadequacy of the first-order language render moot the original philosophical motivation of formalizing a priori knowability as necessity along the diagonal.

The view that actually has a reading on which it is a two-dimensional indexical modal operator has some problems.

This paper supersedes an ealier version, entitled "A Non-Standard Semantics for Inexact Knowledge with Introspection", which appeared in the Proceedings of "Rationality and Knowledge". The definition of token semantics, in particular, has been modified, both for the single- and the multi-agent case.

This essay discusses some aspects of the logical behaviour of sentences in languages containing indexical and demonstrative expressions. After some preliminary remarks in section one, sections two and three focus on instances of logically true sentences that may be uttered falsely, and on cases of logically equivalent sentences whose utterances may have distinct truth-values. The logical and semantic problems taken into consideration include the validity of a Principle of Translation, the so-called ‘puzzle of addressing’, and examples related to measurement and (...) approximation. Section four discusses the complementary phenomenon of sentences that may presumably always be uttered truly, but that do not qualify as logically true. In particular, I argue against the widespread tendency to consider ‘I am here now’ or ‘I exist’ as truths of the logic of indexicals. (shrink)

This paper contributes to the debate about ‘tenseless languages’ by defending a tensed analysis of a superficially tenseless language. The language investigated is St’át’imcets (Lillooet Salish). I argue that although St’át’imcets lacks overt tense morphology, every finite clause in the language possesses a phonologically covert tense morpheme; this tense morpheme restricts the reference time to being non-future. Future interpretations, as well as ‘past future’ would-readings, are obtained by the combination of covert tense with an operator analogous to Abusch’s (1985) WOLL. (...) I offer St’át’imcets-internal evidence (of a kind not previously adduced) that the WOLL-like operator is modal in nature. It follows from the analysis presented here that there are only two (probably related) differences between St’át’imcets and English in the area of tense. The first is that St’át’imcets lacks tense morphemes which are pronounced. The second is that the St’át’imcets tense morpheme is semantically underspecified compared to English ones. In each of these respects, the St’át’imcets tense morpheme displays similar properties to pronouns, which may be covert and which may fail to distinguish person, number or gender. Along the way, I point out several striking and subtle similarities in the interpretive possibilities of St’át’imcets and English. I suggest that these similarities may reveal non-accidental properties of tense systems in natural language. I conclude with discussion of the implications of the analysis for cross-linguistic variation, learnability and the possible existence of tenseless languages. (shrink)

In this paper, we axiomatize the deontic logic in Fusco (2015), which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the restrictions (...) Fusco’s account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to “lift” a Kripke frame for a one-dimensional modal logic into two dimensions. (shrink)

When embedding data are used to argue against semantic theory A and in favor of semantic theory B, it is important to ask whether A could make sense of those data. It is possible to ask that question on a case-by-case basis. But suppose we could show that A can make sense of all the embedding data which B can possibly make sense of. This would, on the one hand, undermine arguments in favor of B over A on the basis (...) of embedding data. And, provided that the converse does not hold—that is, that A can make sense of strictly more embedding data than B can—it would also show that there is a precise sense in which B is more constrained than A, yielding a pro tanto simplicity-based consideration in favor of B. In this paper I develop tools which allow us to make comparisons of this kind, which I call comparisons of potential expressive power. I motivate the development of these tools by way of exploration of the recent debate about epistemic modals. Prominent theories which have been developed in response to embedding data turn out to be strictly less expressive than the standard relational theory, a fact which necessitates a reorientation in how to think about the choice between these theories. (shrink)

Some theories of conditionals maintain that the difference between indicative and subjunctive conditionals involves the standard temporal interpretation of past tense. I provide an argument against such theories. The argument is based on the claim that these views do not correctly predict the correspondence between tense marking and temporal interpretation in certain conditionals.

How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This paper proposes a model-theoretic framework for investigating the logic and semantics of that interaction. The framework is put forward in an ecumenical spirit: it is intended to be applicable to all theories of vagueness that express vagueness using a definiteness (or: determinacy) operator. We will show how (...) epistemicists, supervaluationists, and theorists of metaphysical vagueness like Barnes and Williams (2010) can interpret the framework.  We will also present a complete axiomatization of the logic we recommend to both epistemicists and local supervaluationists. . (shrink)

This paper proposes that a core semantic property of temporal locating adverbs is the ability to introduce a new time discourse referent. The core data comes from that same day in narrative discourse. I argue that unlike other previously studied temporal locating adverbs—which introduce a new time discourse referent and relate it to the speech time or a salient time introduced into the discourse context—that same day is ‘twice anaphoric’, i.e. it retrieves two salient times from the input context without (...) introducing one of its own. Moreover, I argue that the adverb currently is like that same day in not introducing a new time discourse referent. Unlike that same day, however, currently has both a deictic and an anaphoric usage analogous to on Sunday. The analysis that I propose is implemented within Compositional Discourse Representation Theory. It illustrates how adverbial meaning can be integrated within a more general theory of temporal interpretation. (shrink)

Lewis (The Journal of Philosophy, 65(5), 113–126, 1968) attempts to provide an account of modal talk in terms of the resources of counterpart theory, a first-order theory that eschews transworld identity. First, a regimentation of natural language modal claims into sentences of a formal first-order modal language L is assumed. Second, a translation scheme from L-sentences to sentences of the language of the theory is provided. According to Hazen (The Journal of Philosophy, 76(6), 319–338, 1979) and Fara & Williamson (Mind, (...) 114(453), 1–30, 2005), the account cannot handle certain natural language modal claims involving a notion of actuality. The challenge has two parts. First, in order to handle such claims, the initial formal modal language that natural language modal claims are regimented into must extend L with something like an actuality operator. Second, certain ways that Lewis’ translation scheme for L might be extended to accommodate an actuality operator are unacceptable. Meyer (Mind, 122(485), 27–42, 2013) attempts to defend Lewis’ approach. First, Meyer holds that in order to handle such claims, the formal modal language L$$^*$$ ∗ that we initially regiment our natural language claims into need not contain an actuality operator. Instead, we can make do with other resources. Next, Meyer provides an alternative translation scheme from L$$^*$$ ∗ -sentences to sentences of an enriched language of counterpart theory. Unfortunately, Meyer’s approach fails to provide an appropriate counterpart theoretic account of natural language modal claims. In this paper, I demonstrate that failure. (shrink)

The truth conditions of sentences with indexicals like ‘I’ and ‘here’ cannot be given directly, but only relative to a context of utterance. Something similar applies to questions: depending on the semantic framework, they are given truth conditions relative to an actual world, or support conditions instead of truth conditions. Two-dimensional semantics can capture the meaning of indexicals and shed light on notions like apriority, necessity and context-sensitivity. However, its scope is limited to statements, while indexicals also occur in questions. (...) Moreover, notions like apriority, necessity and context-sensitivity can also apply to questions. To capture these facts, the frameworks that have been proposed to account for questions need refinement. Two-dimensionality can be incorporated in question semantics in several ways. This paper argues that the correct way is to introduce support conditions at the level of characters, and develops a two-dimensional variant of both proposition-set approaches and relational approaches to question semantics. (shrink)

Jean Buridan developed his theory of consequence within a semantical framework compatible with what we now call token-based semantics. In his Treatise on Consequences and Sophismata, Buridan showed...

I examine notions of equivalence between logics (understood as languages interpreted model-theoretically) and develop two new ones that invoke not only the algebraic but also the string-theoretic structure of the underlying language. As an application, I show how to construe modal operator languages as what might be called typographical notational variants of _bona fide_ first-order languages.

It has long been known that the popular account of egocentric thoughts developed by David Lewis is in conflict with a natural account of communication, according to which successful communication requires the transmission of a thought content from speaker to hearer. In this paper, I discuss a number of proposed attempts to reconcile these two accounts of egocentric thought and communication. Each of them postulates two kinds of mental content, where one is egocentric, and the other is transmitted from speaker (...) to hearer in communication. I argue that Ninan’s account, which involves multi-centered contents, and Kölbel’s and Moss’s accounts, which postulate centered and uncentered proxy contents, respectively, are unsatisfactory. Therefore, I propose a two-dimensionalist account, according to which egocentric thoughts are represented by primary intensions, while the thoughts shared by speaker and hearer in cases of successful communication are represented by secondary intensions. Finally, I argue that aside from being able to reconcile Lewis’s account of egocentric thoughts with the natural account of communication, two-dimensionalism also provides the means for modeling agreement and disagreement. (shrink)

Kaplan (1989) famously claimed that monsters--operators that shift the context--do not exist in English and "could not be added to it". Several recent theorists have pointed out a range of data that seem to refute Kaplan's claim, but others (most explicitly Stalnaker 2014) have offered a principled argument that monsters are impossible. This paper interprets and resolves the dispute. Contra appearances, this is no dry, technical matter: it cuts to the heart of a deep disagreement about the fundamental structure of (...) a semantic theory. We argue that: (i) the interesting notion of a monster is not an operator that shifts some formal parameter, but rather an operator that shifts parameters that play a certain theoretical role; (ii) one cannot determine whether a given semantic theory allows monsters simply by looking at the formal semantics; (iii) theories which forbid shifting the formal "context" parameter are perfectly compatible with the existence of monsters (in the interesting sense). We explain and defend these claims by contrasting two kinds of semantic theory--Kaplan's (1989) and Lewis's (1980). (shrink)

The paper has two parts: First, I describe a relatively popular thesis in the philosophy of propositional attitudes, worthy of the name ‘taking tense seriously’; and I distinguish it from a family of views in the metaphysics of time, namely, the A-theories (or what are sometimes called ‘tensed theories of time’). Once the distinction is in focus, a skeptical worry arises. Some A-theorists maintain that the difference between past, present, and future, is to be drawn in terms of what exists: (...) growing-block theorists eschew ontological commitment to future entities; presentists, to future and past entities. Others think of themselves as A-theorists but exclude no past or future things from their ontology. The metaphysical skeptic suspects that their attempt to articulate an ‘eternalist’ version of the A-theory collapses into merely ‘taking tense seriously’– a thesis that does not imply the A-theory. The second half of the paper is the search for a stable eternalist A-theory. It includes discussion of temporary intrinsics, temporal parts, and truth. (shrink)

Modal realists should fashion their theory by postulating and taking seriously the modal equivalent of tense, or modal tense. This will give them a uniform way to respond to five different objections, one each by Skyrms, Quine, and Peacocke, and two by van Inwagen, and suggest a non-Lewisian path to modal realism.

This paper follows Part I of our essay on case-intensional first-order logic ). We introduce a framework of branching histories to take account of indeterminism. Our system BH-CIFOL adds structure to the cases, which in Part I formed just a set: a case in BH-CIFOL is a moment/history pair, specifying both an element of a partial ordering of moments and one of the total courses of events that that moment is part of. This framework allows us to define the familiar (...) Ockhamist temporal/modal connectives, most notably for past, future, and settledness. The novelty of our framework becomes visible in our discussion of substances in branching histories, i.e., in its first-order part. That discussion shows how the basic idea of tracing an individual thing from case to case via an absolute property is applicable in a branching histories framework. We stress the importance of keeping apart extensionality and moment-definiteness, and give a formal account of how the specification of natural sortals and natural qualities turns out to be a coordination task in BH-CIFOL. We also provide a detailed answer to Lewis’s well-known argument against branching histories, exposing the fallacy in that argument. (shrink)

This article surveys some of the key issues that arise when one tries to use tense logic as a metaphysical theory of the nature of time. Topics discussed include basic tense logic, tense logic and verb tense, the structure of the time series, instants of time, quantified tense logic, and the expressive resources of tense logic.

This paper presents a short survey of recent developments in stit theories, with an emphasis on combinations of stit and deontic logic, and those of stit and epistemic logic.

Natural language provides motivation for studying modal backwards-looking operators such as “now”, “then” and “actually” that evaluate their argument formula at some previously considered point instead of the current one. This paper investigates the expressive power over models of both propositional and first-order basic modal language enriched with such operators. Having defined an appropriate notion of bisimulation for first-order modal logic, I show that backwards-looking operators increase its expressive power quite mildly, contrary to beliefs widespread among philosophers of language and (...) formal semanticists. That in turn presents a strong argument for the use of operator-based systems in the semantics of natural language, instead of systems with explicit quantification over worlds and times that have become a de-facto standard for such applications. The popularity of such explicit-quantification systems is shown to be based on the misinterpretation of a claim by Cresswell, which led many philosophers and linguists to assume that introducing “now” and “then” is expressively equivalent to explicitly quantifying over worlds and times. (shrink)

One of the most gripping intuitions that people have about time is that it, in some sense “flows.” This sense of flow has been articulated in a number of ways, ranging from us moving into the future or the future rushing towards us, and there has been no shortage of metaphors and descriptions to characterize this sense of passage. Despite the many forms of the metaphor and its widespread occurrence, it has been argued that there is a deep conceptual problem (...) in any assumption that time “passes” or “flows.” The idea expressed by the metaphor is supposed to be incoherent. But is the idea expressed by this metaphor really incoherent? In this essay I will argue that, on one understanding of the metaphor, it is not. I’ll argue that the metaphor can be unpacked as representing three features of temporal experience, and while these features together appear to lead to paradox, I will argue that correctly handled they do not. (shrink)

Sensitivity to the extra-linguistic context, as exhibited by indexical and demonstrative expressions, and sensitivity to the linguistic context, as exhibited by, for example, anaphoric uses of third person pronouns, are regularly regarded as different and independent phenomena. The data on indexicals, demonstratives, and third person pronouns, however, call for a more unified notion of context and of context sensitivity. This paper aims to develop such a unified picture by generalizing the notion of anaphora to encompass extra-linguistic context dependency and generalizing (...) the notion of a structured discourse context so that contexts contain antecedents for expressions that refer to entities in the extra-linguistic context. (shrink)

Evans distinguishes between superficial necessity and deep necessity in his analysis of the contingent a priori. The distinction between these two notions of necessity is formalized by Davies and Humberstone through the addition of the operator Fixedly to Actuality Modal Logic (AML, S5A), where deep necessity is represented by the combination Fixedly Actually. Wehmeier’s Subjunctive Modal Logic (SML) provides an extension of the expressive capacity of ordinary modal predicate logic alternative to AML. I add Fixedly to SML and show that (...) in the system SML with Fixedly the distinction between deep and superficial necessity disappears. I conclude that the existence of the distinction between deep and superficial necessity, as well as the existence of the contingent a priori, cannot be asserted independently of the choice of background logic. (shrink)

I might summarize this section by saying that the English tenses, according to this analysis, form quite a motley group. PAST, PRES and FUT serve to relate reference time to speech time, while WOULD and USED-TO behave like Priorian operators, shifting the point of evaluation away from the reference time. HAVE also shifts the point of evaluation away from the reference time, but in a more complicated way. And FUT, in contrast to PRES and PAST, is a substitution operator, putting (...) the reference time of its clause in the plate of the speech time of subordinate clauses. (shrink)