In this paper I argue for a non-referential interpretation of some uses of indexicals embedded under epistemic modals. The so-called descriptive uses of indexicals come in several types and it is argued that those embedded within the scope of modal operators do not require non-referential interpretation, provided the modality is interpreted as epistemic. I endeavor to show that even if we allow an epistemic interpretation of modalities, the resulting interpretation will still be inadequate as long as we retain a (...) referential interpretation of indexicals. I then propose an analysis of descriptive indexicals that combines an epistemic interpretation of modality with a non-referential interpretation of indexicals. (shrink)

In the present study, cross-modal (i.e., across sensory modalities such as smell and sound) iconicity (i.e., resemblance) and indexicality (i.e., contiguity) in lexical sensory and emotional signs in Finnish Sign Language will be considered from an articulatory perspective (i.e., the production of signs). Such cross-modal iconicity has not been extensively studied previously, so here, with the help of cognitive semiotics, I aim to carefully describe the cross-modal patterns observed across 118 signs, including 60 sensory signs and 58 emotional signs. (...) The analysis is framed within the theoretical model of Semiotic Hierarchy, which entails a non-reductionist view of meaning. In addition, a pheno-methodological triangulation will be applied: phenomenology (first-person method), literature of phenomenological and semiotic descriptions (second-person perspective) and experimental findings (third-person perspective). The results of this analysis show that (a) 71 of the 118 sensory and emotional signs are cross-modally indexical, (b) only 10 of the 71 signs can be regarded as cross-modally iconic, (c) cross-modal iconicity is highly diagrammatic, (d) iconicity and indexicality are highly integrated, and (e) articulatory feedback matters in the formation of semiotic patterns. This study contributes to our understanding of cross-modal iconicity in signed languages, as well as studies in semiotic systems more generally. (shrink)

Relativized Metaphysical Modality (RMM: Murray and Wilson, 'Relativized metaphysical modality', Oxford Studies in Metaphysics, 2012; Murray, Perspectives on Modal Metaphysics, 2017) exploits 'two-dimensionalist' resources to metaphysical, rather than epistemological, ends: the second dimension offers perspective-dependence without contingency, diverting attacks on 'Classical' analyses of modals (in effect, analyses validating S5 and the Barcan Formulae). Here, we extend the RMM program in two directions. First, we harvest resources for RMM from Lewis's 1980 'Context--Index' (CI) framework: (a) the ban in CI on binding (...) into context-arguments (akin to Kaplan's 'monstrosity' ban) projects a bright line between perspective-dependence and contingency; and (b) CI-postulated connections among meaning, content, truth, argument-structure, context, and modality collectively generate a 'Generalized Humphrey Problem' for any non-Classical analysis (examples covered include appeals to accessibility, contingent domains, and counterpart relations). Second, we sharpen the tools of RMM-based metaphysical analysis, and extend their domain of coverage across familiar anomalies for Classical modals: we revisit earlier RMM-based bulwarks for S5 (against 'Chisholm's Paradox' for moderate flexibility of essence, and nomological necessitarianism); and we now similarly shore up the Barcan Formulae (against the apparent contingency of existence and nonexistence). (shrink)

We assume a central thesis about modal auxiliaries due to Angelika Kratzer, the modal base presupposition: natural language expressions that contain a modal component in their meaning, including all English modal auxiliaries and epistemic modal auxiliaries (EMA)s in particular, presuppose a modal base, a function that draws from context a relevant set of propositions which contribute to a premise-semantics for the modal. Accepting this thesis for EMAs leaves open (at least) the following two questions about the meaning of English EMAs (...) like _must_ and _might_: (i) What constraints, if any, are there on the character of the premise set for an EMA? And (ii) what is the nature of the relationship between premises and conclusion that is required for truth of the EMA statement? I argue for at least a partial answer to (i), with a hypothesis about constraints on the modal base for an EMA: EMAs, unlike some other types of modals, are indexical: They are anchored to an agent-in-a-situation whose doxastic state is currently under discussion in the context of utterance. Realized in a Kratzerian semantics, indexicality sheds new light on a number of outstanding puzzles, including the widely observed variability of anchoring of EMAs, the ways in which EMAs differ from so-called root modals, Yalcin’s (Mind 116:983–1026, 2007) puzzle (a version of Moore’s paradox for epistemic modals embedded under attitudes), how to explain the apparent weakness of necessity EMAs, and problems with second order belief and disagreement. (shrink)

Journal Name: Semiotica Issue: Ahead of print.

In Kripke-semantics for modal logic, the truth value of a sentence depends on the choice of a semantic index. It means that application of such semantics to natural language analysis requires indication of an index relevant for semantic analysis. It is commonly accepted that the relevant index is initialised by the context of an utterance. The idea has been rejected by the semanticists investigating tempo-modal languages in the framework of indeterminism, which generated the problem of initialization of the semantic index. (...) I present the main argument of those semanticists and describe several responses to the initialisation problem. I finally argue that under certain metaphysical and semantic assumptions, one can respond to the initialisation failure in the classical way, even in indeterministic contexts. (shrink)

Consider two standard quantified modal languages A and P whose vocabularies comprise the identity predicate and the existence predicate, each endowed with a standard S5 Kripke semantics where the models have a distinguished actual world, which differ only in that the quantifiers of A are actualist while those of P are possibilist. Is it possible to enrich these languages in the same manner, in a non-trivial way, so that the two resulting languages are equally expressive-i.e., so that for each sentence (...) of one language there is a sentence of the other language such that given any model, the former sentence is true at the actual world of the model iff the latter is? Forbes (1989) shows that this can be done by adding to both languages a pair of sentential operators called Vlach-operators, and imposing a syntactic restriction on their occurrences in formulas. As Forbes himself recognizes, this restriction is somewhat artificial. The first result I establish in this paper is that one gets sameness of expressivity by introducing infinitely many distinct pairs of indexed Vlach-operators. I then study the effect of adding to our enriched modal languages a rigid actuality operator. Finally, I discuss another means of enriching both languages which makes them expressively equivalent, one that exploits devices introduced in Peacocke (1978). Forbes himself mentions that option but does not prove that the resulting languages are equally expressive. I do, and I also compare the Peacockian and the Vlachian methods. In due course, I introduce an alternative notion of expressivity and I compare the Peacockian and the Vlachian languages in terms of that other notion. (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”.

Modal Platonism utilizes "weak" logical possibility, such that it is logically possible there are abstract entities, and logically possible there are none. Modal Platonism also utilizes a non-indexical actuality operator. Modal Platonism is the EASY WAY, neither reductionist nor eliminativist, but embracing the Platonistic language of abstract entities while eliminating ontological commitment to them. Statement of Modal Platonism. Any consistent statement B ontologically committed to abstract entities may be replaced by an empirically equivalent modalization, MOD(B), not so ontologically committed. This (...) equivalence is provable using Modal/Actuality Logic S5@. Let MAX be a strong set theory with individuals. Then the following Schematic Bombshell Result (SBR) can be shown: MAX logically yields [T is true if and only if MOD(T) is true], for scientific theories T. The proof utilizes Stephen Neale's clever model-theoretic interpretation of Quantified Lewis S5, which I extend to S5@. (shrink)

This paper argues in favor of a treatment of discourse about fiction in terms of operators on character, that is, Kaplanesque ‘monsters’. The first three sections criticize the traditional analysis of ‘according to the fiction’ as an intensional operator, and the approach to fictional discourse grounded on the notion of contextual shifts. The final sections explain how an analysis in terms of monsters yields the correct readings for a variety of examples involving modal and temporal indexicals.

It is a commonsense thesis that unactualized possibilities are not parts of actuality. To keep his modal realism in line with this thesis, David Lewis employed his indexical account of the term “actual.” I argue that the addition of counterpart theory to Lewis’s modal realism undermines his strategy for respecting the commonsense thesis. The case made here also reveals a problem for Lewis’s attempt to avoid haecceitism.

Cut reductions are defined for a Kripke-style formulation of modal logic in terms of indexed systems of sequents. A detailed proof of the normalization (cutelimination) theorem is given. The proof is uniform for the propositional modal systems with all combinations of reflexivity, symmetry and transitivity for the accessibility relation. Some new transformations of derivations (compared to standard sequent formulations) are needed, and some additional properties are to be checked. The display formulations [1] of the systems considered can be presented (...) as encodings of Kripke-style formulations. (shrink)

This paper provides a semantic analysis of the particles afinal (European Portuguese) and alla fine (Italian) in terms of the notion of truth unpersistence, which can be situated at the intersection of epistemic modality and discourse structure. In the analysis proposed, the particles are propositional operators and require that the truth of a proposition p* fail to persist through a temporal succession of epistemic states, this proposition being incompatible with the prejacent, and that the interlocutors share knowledge of a previous (...) epistemic attitude toward p*. We analyze two main cases (plan-related and non plan-related propositions) and also show that these particles are indexical to one (or more) epistemic agent(s) and allow for shifts in perspective. (shrink)

We need modal imagination in order to extend our conception of reality - and, in particular, of human beings - beyond our immediate experience in the indexical present; and we need to do this in order to preserve the significance of human interaction. To make this leap of imagination successfully is to achieve not only insight but also an impartial perspective on our own and others' inner states. This perspective is a necessary condition of experiencing compassion for others. This is (...) the primary thesis I will try to defend in this discussion. (shrink)

This thesis consists of four essays and an introduction dedicated to two main topics: indexicality and presupposition. The first essay is concerned with an alleged problem for the standard treatment of indexicals on which their linguistic meanings are functions from context to content. Since most indexicals have their content settled, on an occasion of use, by the speaker’s intentions, some authors have argued that this standard picture is inadequate. By demonstrating that intentions can be seen as a parameter of the (...) kind of context that characters operate on, these arguments are rejected. In addition, it is argued that a more recent, variable-based framework is naturally interpreted as an intention-sensitive semantics. The second essay is devoted to the phenomenon of descriptive uses of indexicals on which such an expression seems to contribute, not its standard reference as determined by its character, but a property to the interpretation. An argument that singular readings of the cases in question are incoherent is shown to be incorrect, and an approach to descriptive readings is developed on which they arise from e-type uses akin to other well known cases. Further, descriptive readings of the relevant kind are seen to arise only in the presence of adverbs of quantification, and all sentences in which such an adverb takes scope over an indexical are claimed to be ambiguous between a referential and an e-type reading. The third essay discusses a version of the variable analysis of pronouns on which their descriptive meanings are relegated to the so-called phi-features – person, gender and number. In turn, the phi-features are here seen as triggering semantic presuppositions that place constraints on the definedness of pronouns, and ultimately of sentences in which they appear. It is argued that the descriptive information contributed by the phi-features diverges radically from presuppositional information of both semantic and pragmatic varieties on several dimensions of comparison, and instead the main role of the phi-features is seen to be that of guiding hearers’ attempts to ascertain the speaker’s intentions. The fourth essay addresses an issue concerning the treatment of presuppositions in dynamic semantics. Representing a semantic treatment of pragmatic presuppositions, the dynamic framework is shown to incorrectly regard conversational infelicity as sufficient for semantic undefinedness, given the standard way of defining truth in terms of context change. Further, it is shown that a proposal for a solution fail to make correct predictions for epistemic modals. A novel framework is developed on which context change potentials act on contexts that have more structure than the contexts usually countenanced by dynamic semantics, and it is shown that this framework derives truth from context change while making correct predictions for both presuppositions and modals. (shrink)

This paper looks at what David Kaplan's work on indexicals can teach us about logic and the philosophy of logic, and also what Kaplan's logic (i.e. the Logic of Demonstratives) can teach us about indexicals. The lessons are i) that logical consequence is not necessary truth-preservation, ii) that that the linguistic doctrine of necessary truth (also called conventionalism about modality) fails, and iii) that there is a kind of barrier to entailment between non-context-sensitive and context-sensitive claims.

John Perry's book Knowledge, Possibility, and Consciousness is a lucid and engaging defense of a physicalist view of consciousness against various anti-physicalist arguments. In what follows, I will address Perry's responses to the three main anti-physicalist arguments he discusses: the zombie argument , the knowledge argument , and the modal argument.

This article brings two outstanding figures into conversation about the problem of fictional entities and their indeterminacies: Roman Ingarden and David Lewis. Lewis’s account of fiction lacks an adequate ontology of ficta-qua-objects. Relying on his modal realism does not help, for it would make ficta “concrete” entities that merely indexically differ from our world’s entities. In this regard, I refer to Ingarden’s “purely intentional entities”. I read Lewis’s possible worlds in terms of Ingarden’s ontology; hence establishing what I term a (...) “Purely Intentional Modal Fictionalism”. In so doing, the demarcation between fiction and actuality is preserved. In return, Lewis’s Analyses adequately account for Ingarden’s “spots of indeterminacy”. Therefore, my proposal reconciles Ingarden’s ficta with Lewis’s possibilist approach to truth in fiction. This approach grounds Lewis’s account in a less problematic ontology with a distinct sui generis status for ficta and provides Ingarden’s ficta with better determination principles. (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)

Many powerful logics exist today for reasoning about multi-agent systems, but in most of these it is hard to reason about an infinite or indeterminate number of agents. Also the naming schemes used in the logics often lack expressiveness to name agents in an intuitive way.To obtain a more expressive language for multi-agent reasoning and a better naming scheme for agents, we introduce a family of logics called term-modal logics. A main feature of our logics is the use of modal (...) operators indexed by the terms of the logics. Thus, one can quantify over variables occurring in modal operators. In term-modal logics agents can be represented by terms, and knowledge of agents is expressed with formulas within the scope of modal operators. (shrink)

Sider offers a new take on a linguistic account of necessity. In this paper, I assess his view’s vulnerability to objections made against more traditional linguistic accounts, especially an argument I call the “indexical problem.” I conclude that the indexical problem has no force against Sider’s approach because the view is able to attribute modal properties directly to propositions, rather than indirectly via analytic sentences that express them. However, Sider also argues that traditional linguistic accounts fail because of two well-known (...) problems, and I argue that the same two problems undermine his own account. (shrink)

David Lewis has shocked the philosophical community with his original version of extreme modal realism according to which “every way that a world could possibly be is a way that some world is”. Logical Space is a plenitude of isolated physical worlds, each being the actualization of some way in which a world could be, that bear neither spatiotemporal nor causal relations to each other. Lewis has given independent, converging arguments for this. One is the argument from the indexicality of (...) actuality, the other an elaborate cost-benefit argument of the inference-to-the-best explanation sort to the effect that a systematic analysis of a number of concepts, including modality, causality, propositions and properties, fares better under his theory than under any rival one that takes a possible world to be either a linguistic entity or an ersatz abstract entity such as a maximal compossible set of properties, propositions or states of affairs. Lewis' legion of critics have confined themselves mostly to attempts at a reductio ad absurdum of his theory or to objections to his various analyses. The indexical argument, on the other hand, has not been subject to careful critical scrutiny. It is the purpose of this paper to show that this argument cannot withstand such scrutiny. Its demise, however, leaves untouched his argument from the explanatory superiority for his extreme modal realism. (shrink)

We define and study the notion of an indexed frame. This is a bi-dimensional structure consisting of a Cartesian product equipped with relations which only relate pairs if they coincide in one of their components. We show that these structures are quite ubiquitous in modal logic, showing up in the literature as products of Kripke frames, subset spaces, or temporal frames for STIT logics. We show that indexed frames are completely characterised by their ‘orthogonal’ relations, and we provide (...) their sound and complete logic. Using these ‘orthogonality’ results, we provide necessary and sufficient conditions for an arbitrary Kripke frame to be isomorphic to certain well-known bi-dimensional structures. (shrink)

Theorists with otherwise radically different commitments agree that epistemic modals mark the necessity or possibility of a prejacent proposition relative to a body of evidence or knowledge. However, there is vast disagreement about the semantics of epistemic modals, which stems in part from the fact that statements of epistemic possibility or necessity make no explicit reference to a speaker or group, an audience, or an evidence set. This volume introduces new philosophical papers that mark a significant contribution to the debate (...) about epistemic modals. (shrink)

The Kuznetsov-Index of a modal logic is the least cardinal such that any consistent formula has a Kripke-model of size if it has a Kripke-model at all. The Kuznetsov-Spectrum is the set of all Kuznetsov-Indices of modal logics with countably many operators. It has been shown by Thomason that there are tense logics with Kuznetsov-Index . Futhermore, Chagrov has constructed an extension of K4 with Kuznetsov-Index . We will show here that for each countable ordinal there are logics with Kuznetsov-Index (...) . Furthermore, we show that the Kuznetsov-Spectrum is identical to the spectrum of indices for -theories which is likewise defined. A particular consequence is the following. If inaccessible (weakly compact, measurable) cardinals exist, then the least inaccessible (weakly compact, measurable) cardinal is also a Kuznetsov-Index. (shrink)

In this paper, I attempt to throw some light on modal realism. Since it is David Lewis who has put forward the best arguments for thar position, I focus on his work. In the first, I point out that his approach does not provide an adequate account for the intuitive lack of symmetry between the actual and the possible. To begin with, I try to show that the strategy of appealing to both the spatio-temporal network and causality is not at (...) all satisfactory. Secondly, I criticize the argument for modal realism that is based on theoretical benefits. Then, I defend the view that Lewis' indexical analysis of the concept of actuality does not satisfy his own criterion of acceptability: an analysis of actuality should account for the intuitions about our actual word. I claim thet Lewis' objections to other positions can be raised against his own position. Finally, I conclude that, even though Lewis is right in claiming that actualist conceptions do not explain why the possible is not part of the actual, the realist conception fail to account for the special ontological status that we intuitively grant to our own world. (shrink)

Modal Meinongianism provides the semantics of sentences involving intentional verbs Priest. To that end, Modal Meinongianism employs a pointed non-normal quantified modal logic model. Like earlier Meinongian views Modal Meinongianism has a characterisation principle, that claims that any condition whatsoever is satisfied by some object in some world. Recently, Everett has proposed an argument against QCP that, if successful, gives rise to problems identical to those Russell raised for Naïve Meinongianism, namely that it allows for true contradictions, and allows us (...) to define anything into existence. Everett claims that the ordinary meanings of “actual” license an inference pattern, such that if an object satisfies Actual A at some world, then that object satisfies A in the actual world. Given that actual world is the designated point of evaluation for truth simpliciter, QCP would fall prey to Russell’s criticisms. As opposed to Everett, I argue that, even if we grant Everett the assumption that “actual” is a modal indexical that rigidly refers to the actual world, it does not conform to the inference pattern above. This is because when an object satisfies Actual A at some world, this alters the assertoric force of “actual”, because “actual” is interpreted in the scope of some modal or intentional operator. I also explain that Everett’s proposed example carries existential commitment because the problematic noun-phrase occurs outside the scope of a modal or intentional operator. (shrink)

We present a general approach to quantified modal logics that can simulate most other approaches. The language is based on operators indexed by terms which allow to express de re modalities and to control the interaction of modalities with the first-order machinery and with non-rigid designators. The semantics is based on a primitive counterpart relation holding between n-tuples of objects inhabiting possible worlds. This allows an object to be represented by one, many, or no object in an (...) accessible world. Moreover by taking as primitive a relation between n-tuples we avoid some shortcoming of standard individual counterparts. Finally, we use cut-free labelled sequent calculi to give a proof-theoretic characterisation of the quantified extensions of each first-order definable propositional modal logic. In this way we show how to complete many axiomatically incomplete quantified modal logics. (shrink)

The word 'actually' often refers to what is in fact the case, but it also often points to what would have been the case in a possible situation that is being envisaged. To capture such nuances, the formal languages discussed in the paper add subscripts to modal operators; in the model theory the subscripts allow an actuality operator to turn the evaluation of a formula to a world introduced by a preceding possibility or necessity operator having the same subscript. The (...) paper covers both propositional and predicate logic and proves the completeness of axiomatizations that extend standard modal systems beginning with K. (shrink)

Some logical properties of modal languages in which actuality is expressible are investigated. It is argued that, if a sentence like 'Actually, Quine is a distinguished philosopher' is understood as a special case of world-indexed sentences (the index being the actual world), then actuality can be expressed only under strong modal assumptions. Some rival rigid and indexical approaches to actuality are discussed.

In this paper, I attempt to explain one of the most controversial views attributed to the Stoic Chrysippus: that the impossible can follow from the possible. My solution finds in Chrysippus a distinction later made by the medieval logician John Buridan: that between being possible (there being a state of affairs that may occur) and being possibly-true (there being some proposition whose truth-conditions are that state of affairs). Buridan and Chrysippus have radically opposing views on the nature of propositions. What (...) their conceptions share is the conclusion that at least some propositions must be contingent beings. They argue for this while maintaining a rigorous commitment to the view that propositions are strictly bivalent. In 2. I explain the Chrysippean passage in terms of a distinction Buridan makes explicitly. In 3. I show how the distinction follows implicitly from the Stoic theory of quantification. In 4. I compare the modality with other aspects of Stoic logic. In 5. I discuss how the distinction behaves in the future tense. (shrink)

This work is divided in two papers (Part I and Part II). In Part I, we study a class of polymodal logics (herein called the class of "Rare-logics") for which the set of terms indexing the modal operators are hierarchized in two levels: the set of Boolean terms and the set of terms built upon the set of Boolean terms. By investigating different algebraic properties satisfied by the models of the Rare-logics, reductions for decidability are established by faithfully translating the (...) Rare-logics into more standard modal logics. The main idea of the translation consists in eliminating the Boolean terms by taking advantage of the components construction and in using various properties of the classes of semilattices involved in the semantics. The novelty of our approach allows us to prove new decidability results (presented in Part II), in particular for information logics derived from rough set theory and we open new perspectives to define proof systems for such logics (presented also in Part II). (shrink)

This work is divided in two papers (Part I and Part II). In Part I, we introduced the class of Rare-logics for which the set of terms indexing the modal operators are hierarchized in two levels: the set of Boolean terms and the set of terms built upon the set of Boolean terms. By investigating different algebraic properties satisfied by the models of the Rare-logics, reductions for decidability were established by faithfully translating the Rare-logics into more standard modal logics (some (...) of them contain the universal modal operator).In Part II, we push forward the results from Part I. For Rare-logics with nominals (present at the level of formulae and at the level of modal expressions), we show that the constructions from Part I can be extended although it is technically more involved. We also characterize a class of standard modal logics for which the universal modal operator can be eliminated as far as satifiability is concerned. Although the previous results have a semantic flavour, we are also able to define proof systems for Rare-logics from existing proof systems for the corresponding standard modal logics. Last, but not least, decidability results for Rare-logics are established uniformly, in particular for information logics derived from rough set theory. (shrink)

What kind of semantics should someone who accepts the epistemicist theory of vagueness defended in Timothy Williamson’s Vagueness (1994) give a definiteness operator? To impose some interesting constraints on acceptable answers to this question, I will assume that the object language also contains a metaphysical necessity operator and a metaphysical actuality operator. I will suggest that the answer is to be found by working within a three-dimensional model theory. I will provide sketches of two ways of extracting an epistemicist semantics (...) from that model theory, one of which I will find to be more plausible than the other. (shrink)

We consider a simple modal logic whose nonmodal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of _T_, _S4_, and _S5_, such logics are useful, as shown in previous work by Baltag, Coecke, and the first author, for encoding and reasoning about information and misinformation in multiagent systems. For the propositional-only fragment of (...) such a dynamic epistemic logic, we present an algebraic semantics, using lattices with agent-indexed families of adjoint pairs of operators, and a cut-free sequent calculus. The calculus exploits operators on sequents, in the style of “nested” or “tree-sequent” calculi; cut-admissibility is shown by constructive syntactic methods. The applicability of the logic is illustrated by reasoning about the muddy children puzzle, for which the calculus is augmented with extra rules to express the facts of the muddy children scenario. (shrink)

In celebrating Arthur Prior we celebrate what he gave to the world. Much of this is measured by what others have made of his ideas after his death. The focus of this paper is a little different. It looks at what Prior himself thought he was accomplishing. In particular it considers Prior’s attitude to the semantic metatheory of the logics that he was interested in. The paper sets out some characteristics of the metalogical study of intensional languages in terms of (...) an indexical theory of truth conditions stated in the language of set theory. In examining Prior’s work using these characteristics, it emerges that Prior had serious reservations about this way of studying modal and tense logics. (shrink)

This paper concerns the applications of two-dimensional modal semantics to the explanation of the contents of speech and thought. Different interpretations and applications of the apparatus are contrasted. First, it is argued that David Kaplan's two-dimensional semantics for indexical expressions is different from the use that I made of a formally similar framework to represent the role of contingent information in the determination of what is said. But the two applications are complementary rather than conflicting. Second, my interpretation of the (...) apparatus is contrasted with that of David Chalmers, Frank Jackson, and David Lewis. It is argued that this difference reflects a contrast between internalist and externalist approaches to the problem of intentionality. (shrink)

If the contemporary rebirth of the ontological argument had its conception in Norman Malcolm's discovery of a second Anselmian argument it had its full-term delivery as a healthy philosophical progeny with Alvin Plantinga's sophisticated modal version presented in the tenth chapter of The Nature of Necessity. This latter argument has been the centre of a huge body of literature over the last fifteen years, and deservedly so. One is impressed that this version of Anselm's jewel is valid and sound if (...) any is. (shrink)

In this paper we present tableau methods for two-dimensional modal logics. Although models for such logics are well known, proof systems remain rather unexplored as most of their developments have been purely axiomatic. The logics herein considered contain first-order quantifiers with identity, and all the formulas in the language are doubly-indexed in the proof systems, with the upper indices intuitively representing the actual or reference worlds, and the lower indices representing worlds of evaluation—first and second dimensions, respectively. The tableaux (...) modulate over different notions of validity such as local, general, and diagonal, besides being general enough for several two-dimensional logics proposed in the literature. We also motivate the introduction of a new operator into two-dimensional languages and explore some of the philosophical questions raised by it concerning the relations there are between actuality, necessity, and the a priori, that seem to undermine traditional intuitive interpretations of two-dimensional operators. (shrink)

This paper exhibits a general and uniform method to prove axiomatic completeness for certain modal fixpoint logics. Given a set Γ of modal formulas of the form γ, where x occurs only positively in γ, we obtain the flat modal fixpoint language by adding to the language of polymodal logic a connective γ for each γΓ. The term γ is meant to be interpreted as the least fixed point of the functional interpretation of the term γ. We consider the following (...) problem: given Γ, construct an axiom system which is sound and complete with respect to the concrete interpretation of the language on Kripke structures. We prove two results that solve this problem.First, let be the logic obtained from the basic polymodal by adding a Kozen–Park style fixpoint axiom and a least fixpoint rule, for each fixpoint connective γ. Provided that each indexing formula γ satisfies a certain syntactic criterion, we prove this axiom system to be complete.Second, addressing the general case, we prove the soundness and completeness of an extension of . This extension is obtained via an effective procedure that, given an indexing formula γ as input, returns a finite set of axioms and derivation rules for γ, of size bounded by the length of γ. Thus the axiom system is finite whenever Γ is finite. (shrink)

Recent studies have provided evidence of associations between neurochemistry and reading (dis)ability (Pugh et al., 2014). Based on a long history of studies indicating that fluent reading entails the automatic convergence of the written and spoken forms of language and our recently proposed Neural Noise Hypothesis (Hancock et al., 2017), we hypothesized that individual differences in cross-modal integration would mediate, at least partially, the relationship between neurochemical concentrations and reading. Cross-modal integration was measured in 231 children using a two-alternative forced (...) choice cross-modal matching task with three language conditions (letters, words, and pseudowords) and two levels of difficulty within each language condition. Neurometabolite concentrations of Choline (Cho), Glutamate (Glu), gamma-Aminobutyric (GABA), and N- acetyl-aspartate (NAA) were then measured in a subset of this sample (n = 70) with Magnetic Resonance Spectroscopy (MRS). A structural equation mediation model revealed that the effect of cross-modal word matching mediated the relationship between increased Glu (which has been proposed to be an index of neural noise) and poorer reading ability. In addition, the effect of cross-modal word matching fully mediated a relationship between increased Cho and poorer reading ability. Multilevel mixed effects models confirmed that lower Cho predicted faster cross-modal matching reaction time, specifically in the hard word condition. These Cho... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 62.1 (2001) 121-140 [Access article in PDF] The Rhetoric of Modal Equivocacy in Cartesian Transubstantiation Julian Bourg Everyday language, in which words are not defined, is a medium in which nobody can express himself unequivocally. Robert Musil 1René Descartes's attempt to explain Eucharistic transubstantiation has long been understood as a dramatically significant moment in his tightrope walk across the medieval-to-modern divide. 2 Modeled (...) on the Last Supper in the New Testament, the Eucharistic rite had been explained in the Catholic tradition after the twelfth century in the scholastic philosophical language of substance and accident. 3 As the Council of Trent reaffirmed in 1551, this transubstantiation was a conversion "of the whole substance of the bread into the substance of the Body and of the whole substance of the wine into the substance of His blood... the appearances [speciebus] only of the bread and wine remaining." 4 Christ was [End Page 121] held to be "truly, really, and substantially contained under the species of those sensible things," under what still appeared to be bread and wine. 5Descartes's dilemma was that on one hand he was dead set against the hylomorphic theory of substance and accident, and on the other hand he found himself obliged by some of his interlocutors to comment on transubstantiation. It was a balancing act that pleased no one for very long, since despite his sometimes eager discussions of the Eucharist, he was not, as he admitted, "a theologian by profession." 6 The putative heterodoxy of Cartesian transubstantiation was principally responsible for his works being placed on the Index of Prohibited Books in 1663 and for his thought being banned from schools under Louis XIV in 1671. 7 His treatment of the Eucharistic question also distressed others in the seventeenth and early eighteenth centuries, such as Thomas Hobbes and Isaac Newton, who were unhappy that Descartes had bothered with such a theological non-issue. 8 For the many post-seventeenth-century advocates of a proto-secular Descartes as the godfather of modern philosophy, Cartesian transubstantiation has proved similarly inconvenient.The indisputable connections between Descartes and his scholastic forerunners, exemplified by the Eucharistic question, service a basic question of contemporary Cartesian scholarship. As Émile Boutroux put it, how was new wine poured from old bottles? 9 Accepting as axiomatic that there was something both radical and original in the Cartesian project but without falling back on pieties about his turn toward the modern subject, we must ask how Descartes put forth novel claims in conceptual language regarded by his contemporaries as resonant, if not consonant, with the scholastic intellectual culture of Catholic Reform France. More precisely, setting aside the not-very-defensible position that such language was merely incidental to Cartesian thought (a position that dehistoricizes Descartes as a precocious Enlightener), the dilemma then becomes explaining how original positions were elaborated within scholastic language. One important task is accounting for what Descartes did with that vocabulary--how he pointed words and concepts in new and surprising directions. The Eucharist becomes crucial in this perspective. [End Page 122]Though the question of Cartesian transubstantiation has been discussed for some time, the topic is worth revisiting again in light of two themes, rhetoric and the Cartesian theory of modes. My argument is that Descartes used one particular scholastic term, "mode," in equivocal ways and that this equivocation was in multiple senses rhetorical. This rhetoric coalesced and came to the fore around the Eucharist because, given the intellectual-political climate of the Catholic Reformation, the stakes of transubstantiation were so high. That Descartes used certain scholastic terms in equivocal or ambiguous ways should come as no surprise. Of interest, though, is the fact that by definition "mode" meant many things. This ambiguous term facilitated ambiguous intellectual positions about the Eucharist that allowed Descartes more generally (no matter what he "really" intended) to skirt between an orthodoxy that represented the past and an originality, not without dangers in his time, that seem to gesture toward our day. Foregrounded with regard to... (shrink)

ObjectiveThe objective of this study was to validate the computerized Symbol Digit Modalities Test in a Swiss pediatric cohort, in comparing the Swiss sample to the Canadian norms. Secondly, we evaluated sex effects, age-effects, and test–retest reliability of the c-SDMT in comparison to values obtained for the paper and pencil version of the Symbol Digit Modalities Test.MethodsThis longitudinal observational study was conducted in a single-center setting at the University Children’s Hospital of Bern. Our cohort consisted of 86 children (...) aged from 8 to 16 years. The cohort included both healthy participants and patients hospitalized for a non-neurological disease. Forty eight participants were assessed during two testing sessions with the SDMT and the c-SDMT.ResultsTest–retest reliability was high in both tests. A reliable change index was calculated for the SDMT and the c-SDMT corrected for practice effects. While a significant age effect on information processing speed was observed, no such effect was found for sex. When data on the c-SDMT performance of the Swiss cohort was compared with that from a Canadian cohort, no significant difference was found for the mean time per trial in any age group. Norm values for age groups between 8 and 16 years in the Swiss cohort were established.ConclusionNorms for the c-SDMT between the Swiss and the Canadian cohort were comparable. The c-SDMT is a valid alternative to the SDMT. It is a feasible and easy to administer bedside tool due to high reliability and the lack of motor demands. (shrink)

The tableaux-constructions have a number of properties which advantageously distinguish them from equivalent axiomatic systems . The proofs in the form of tableaux-constructions have a full accordance with semantic interpretation and subformula property in the sense of Gentzen’s Hauptsatz. Method of tatleaux-construction gives a good substitute of Gentzen’s methods and thus opens a good perspective for the investigations of theoretical as well as applied aspects of logical calculi. It should be noted that application of tableau method in modal, tense, relevant (...) and other non-classical logics is connected with serious difficulties. Tableaux variants are constructed only for a few normal modal systems. As to relevant and paraconsistent logic, the absence of its tableau variants may be considered as a question of special interest. We shall formulate the tableaux for propositional modal system S4.1, S4.2, S4.3, S4.4 and relevant R∗ and E ∗ using Beth’s tableaux construction with indexed formulas. (shrink)