The paper is an investigation into the concept of actuality from the standpoint of the philosophy of language. It is argued that expressions such as 'actually' and 'in fact' are not indexicals like 'here' and 'now'; when e.g. 'Snow is actually white' is uttered in a world, what proposition is conveyed does not depend on the world. Nor are such expressions ambiguous. The paper makes a suggestion about the role that 'actually' and its cognates do play. It is also argued (...) that the sentence ⌜Actually S ⌝ expresses a necessary truth only if S itself expresses one. In order to capture the necessitation of the proposition expressed in ⌜Actually S ⌝, it is not sufficient to prefix the word 'necessarily'. (shrink)

The paper is an investigation into the concept of actuality from the standpoint of the philosophy of language. It is argued that expressions such as ‘actually’ and ‘in fact’ are not indexicals like ‘here’ and ‘now’; when e.g. ‘Snow is actually white’ is uttered in a world, what proposition is conveyed does not depend on the world. Nor are such expressions ambiguous. The paper makes a suggestion about the role that ‘actually’ and its cognates do play. It is also argued (...) that the sentence ⌜Actually S⌝ expresses a necessary truth only if S itself expresses one. In order to capture the necessitation of the proposition expressed in ⌜Actually S⌝, it is not sufficient to prefix the word ‘necessarily’. (shrink)

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)

. Fresh evidence from Free Choice Items (FCIs) in French question the current perception of the class. The role of some standard distinctions found in the literature is weakened or put in a new perspective. The distinction between universal and existential is no longer an intrinsic property of FCIs. Similarly, the opposition between variation-based vs intension-based analyses is relativized. We show that the regime of free choiceness can be characterized by an abstract constraint, that we call Non-Individuation (NI), and which (...) can be satisfied in different ways that match current distinctions. NI says that the information conveyed by a sentence containing a FCI should not be reducible to a referential situation, that is a situation in which particular individuals satisfy the sentence in the current world. The widely used resource of modal variation becomes a particular scenario of free-choiceness, not its essence. In fact, we show that under certain conditions, FCIs can occur in episodic, non-modal sentences, a fact that NI can accommodate. We also discuss more fine-grained aspects of the semantics of FCIs, such as their emotional colour. (. . .) the tripod fell spontaneously, because, though it stood on its feet so as to serve for a seat, it did not fall so as to serve for a seat. Aristotle, Physics II,6. (shrink)

We show that the actuality operator A is redundant in any propositional modal logic characterized by a class of Kripke models (respectively, neighborhood models). Specifically, we prove that for every formula ${\phi}$ in the propositional modal language with A, there is a formula ${\psi}$ not containing A such that ${\phi}$ and ${\psi}$ are materially equivalent at the actual world in every Kripke model (respectively, neighborhood model). Inspection of the proofs leads to corresponding proof-theoretic results concerning the eliminability of the actuality (...) operator in the actuality extension of any normal propositional modal logic and of any “classical” modal logic. As an application, we provide an alternative proof of a result of Williamson’s to the effect that the compound operator A□ behaves, in any normal logic between T and S5, like the simple necessity operator □ in S5. (shrink)

Does general validity or real world validity better represent the intuitive notion of logical truth for sentential modal languages with an actuality connective? In (Philosophical Studies 130:436–459, 2006) I argued in favor of general validity, and I criticized the arguments of Zalta (Journal of Philosophy 85:57–74, 1988) for real world validity. But in Nelson and Zalta (Philosophical Studies 157:153–162, 2012) Michael Nelson and Edward Zalta criticize my arguments and claim to have established the superiority of real world validity. Section 1 (...) of the present paper introduces the problem and sets out the basic issues. In Sect. 2 I consider three of Nelson and Zalta’s arguments and find all of them deficient. In Sect. 3 I note that Nelson and Zalta direct much of their criticism at a phrase (‘true at a world from the point of view of some distinct world as actual’) I used only inessentially in Hanson (Philosophical Studies 130:436–459, 2006), and that their account of the philosophical foundations of modal semantics leaves them ill equipped to account for the plausibility of modal logics weaker than S5. Along the way I make several general suggestions for ways in which philosophical discussions of logical matters–especially, but not limited to, discussions of truth and logical truth for languages containing modal and indexical terms–might be facilitated and made more productive. (shrink)

The traditional view that all logical truths are metaphysically necessary has come under attack in recent years. The contrary claim is prominent in David Kaplan’s work on demonstratives, and Edward Zalta has argued that logical truths that are not necessary appear in modal languages supplemented only with some device for making reference to the actual world (and thus independently of whether demonstratives like ‘I’, ‘here’, and ‘now’ are present). If this latter claim can be sustained, it strikes close to the (...) heart of the traditional view. I begin this paper by discussing and refuting Zalta’s argument in the context of a language for propositional modal logic with an actuality connective (section 1). This involves showing that his argument in favor of real world validity his preferred explication of logical truth, is fallacious. Next (section 2) I argue for an alternative explication of logical truth called general validity. Since the rule of necessitation preserves general validity, the argument of section 2 provides a reason for affirming the traditional view. Finally (section 3) I show that the intuitive idea behind the discredited notion of real world validity finds legitimate expression in an object language connective for deep necessity. (shrink)

We provide a Hilbert-style axiomatization of the logic of , as well as a two-dimensional semantics with respect to which our logics are sound and complete. Our completeness results are quite general, pertaining to all such actuality logics that extend a normal and canonical modal basis. We also show that our logics have the strong finite model property and permit straightforward first-order extensions.

Two-dimensional semantics, which can represent the distinction between a priority and necessity, has wielded considerable influence in the philosophy of language. In this paper, I axiomatize the dagger operator of Stalnaker’s “Assertion” in the formal context of two-dimensional modal logic. The language contains modalities of actuality, necessity, and a priority, but is also able to represent diagonalization, a conceptually important operation in a variety of contexts, including models of the relative a priori and a posteriori often appealed to Bayesian and (...) Gricean contexts. Finally, I sketch the prospects for extending this two-dimensional upgrade to other kinds of modal logics for natural language. (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)

Our concern here is with the extent to which the expressive equivalence of Wehmeier’s Subjunctive Modal Language and the Actuality Modal Language is sensitive to the choice of background modal logic. In particular we will show that, when we are enriching quantified modal logics weaker than S5, AML is strictly expressively stronger than SML, this result following from general considerations regarding the relationship between operators and predicate markers. This would seem to complicate arguments given in favour of SML which rely (...) upon its being expressively equivalent to AML. (shrink)

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. It is practically relevant because it makes it possible to use a decision procedure for the guarded fragment in order to decide regular grammar logics with (...) converse. The class of regular grammar logics includes numerous logics from various application domains. A consequence of the translation is that the general satisfiability problem for every regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Other logics that can be translated into GF2 include nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed-point operators. (shrink)

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. It is practically relevant because it makes it possible to use a decision procedure for the guarded fragment in order to decide regular grammar logics with (...) converse. The class of regular grammar logics includes numerous logics from various application domains. A consequence of the translation is that the general satisfiability problem for every regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Other logics that can be translated into GF2 include nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed-point operators. (shrink)

In this paper, I motivate the addition of an actuality operator to relevant logics. Straightforward ways of doing this are in tension with standard motivations for relevant logics, but I show how to add the operator in a way that permits one to maintain the intuitions behind relevant logics. I close by exploring some of the philosophical consequences of the addition.