Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations (...) arise from algebraic terms of the intuitionistic modal language which have not been previously considered. We shall for instance investigate the variety of _weak implicative semilattices_, whose members are (non-necessarily distributive) meet semilattices endowed with a nucleus and an implication operation which is not a relative pseudo-complement but satisfies the postulates of Celani and Jansana’s strict implication. For each of these new classes of algebras we establish a representation and a topological duality which generalize the known ones for Heyting algebras enriched with a nucleus. (shrink)

Viewing the language of modal logic as a language for describing directed graphs, a natural type of directed graph to study modally is one where the nodes are sets and the edge relation is the subset or superset relation. A well-known example from the literature on intuitionistic logic is the class of Medvedev frames $\langle W,R\rangle$ where $W$ is the set of nonempty subsets of some nonempty finite set $S$, and $xRy$ iff $x\supseteq y$, or more liberally, where $\langle W,R\rangle$ (...) is isomorphic as a directed graph to $\langle \wp(S)\setminus\{\emptyset\},\supseteq\rangle$. Prucnal [32] proved that the modal logic of Medvedev frames is not finitely axiomatizable. Here we continue the study of Medvedev frames with extended modal languages. Our results concern definability. We show that the class of Medvedev frames is definable by a formula in the language of tense logic, i.e., with a converse modality for quantifying over supersets in Medvedev frames, extended with any one of the following standard devices: nominals (for naming nodes), a difference modality (for quantifying over those $y$ such that $x\not= y$), or a complement modality (for quantifying over those $y$ such that $x\not\supseteq y$). It follows that either the logic of Medvedev frames in one of these tense languages is finitely axiomatizable---which would answer the open question of whether Medvedev's [31] "logic of finite problems'' is decidable---or else the minimal logics in these languages extended with our defining formulas are the beginnings of infinite sequences of frame-incomplete logics. (shrink)

The paper deals with polymodal languages combined with standard semantics defined by means of some conditions on the frames. So, a notion of "polymodal base" arises which provides various enrichments of the classical modal language. One of these enrichments, viz. the base £(R,-R), with modalities over a relation and over its complement, is the paper's main paradigm. The modal definability (in the spirit of van Benthem's correspondence theory) of arbitrary and ~-elementary classes of frames in this base and in (...) some of its extensions, e.g., £(R,-R,R-1 ,_R-1), £(R,-R,=I=) etc., is described, and numerous examples of conditions definable there, as well as undefinable ones, are adduced. (shrink)

The present paper provides novel results on the model theory of Independence friendly modal logic. We concentrate on its particularly well-behaved fragment that was introduced in Tulenheimo and Sevenster (Advances in Modal Logic, 2006). Here we refer to this fragment as ‘Simple IF modal logic’ (IFML s ). A model-theoretic criterion is presented which serves to tell when a formula of IFML s is not equivalent to any formula of basic modal logic (ML). We generalize the notion of bisimulation familiar (...) from ML; the resulting asymmetric simulation concept is used to prove that IFML s is not closed under complementation. In fact we obtain a much stronger result: the only IFML s formulas admitting their classical negation to be expressed in IFML s itself are those whose truth-condition is in fact expressible in ML. (shrink)

How do modal expressions determine which possibilities they range over? According to the Modal Anchor Hypothesis (Kratzer in _The language-cognition interface: Actes du 19_ _e_ _congrès international des linguistes_, Libraire Droz, Genève, 179–199, 2013 ), modal expressions determine their domain of quantification from particulars (events, situations, or individuals). This paper presents novel evidence for this hypothesis, focusing on a class of Spanish relative clauses that host verbs inflected in the subjunctive. Subjunctive in Romance is standardly taken to be licensed only (...) in a subset of intensional contexts. However, in our relative clauses, subjunctive is exceptionally licensed in extensional contexts. At the same time, the interpretation of these relative clauses still involves modality, a type of modality that targets the goals of the agent of the main event. We argue that the pattern displayed by these relative clauses follows straightforwardly if subjunctive is associated with a modal operator that, like modal indefinites (Alonso-Ovalle and Menéndez-Benito in _Journal of Semantics_ 35(1):1–41, 2017 ), can project its domain from a volitional event. Overall, our proposal supports the event-based analysis of mood (Kratzer in Evidential mood in attitude and speech reports. Talk delivered at the 1st Syncart Workshop, Siena, July 13, 2016 ; Portner and Rubinstein in _Natural Language Semantics_ 28:343–393, 2020 ) and extends its application beyond attitudinal and modal complements. (shrink)

The first section of the chapter will address the philosophy of modality among Spinoza’s medieval Jewish predecessors, and, primarily, in Hasdai Crescas (1340-1410/11), a bold and original, anti-Aristotelian philosopher. This section should both complement the discussion of modality in medieval Christian and Islamic philosophy in the previous chapters of this volume and provide some lesser-known historical background to Spinoza’s own engagement with modal philosophy. Following a section on Spinoza’s definitions of his main modal concepts and his understanding (...) of contingency, I will turn, in the third section, to discuss the extent of Spinoza’s commitment to necessitarianism. The recent debate about whether Spinoza was a strict necessitarian has resulted in quite a few insights about Spinoza’s modal philosophy, but it has also detracted attention from some basic questions about Spinoza’s modal philosophy, and in the fourth and last section of the chapter, I will attempt to chart the foundational questions that still have been barely explored. The primary aim of this chapter it to provide a survey and outline of the chief elements of Spinoza’s modal philosophy. Still, beyond the mere overview of Spinoza’s arguments (and some major scholarly debates), I will also advance two original theses. First, I will show that Spinoza makes a distinction between two notions of contingency, and that once this important distinction is observed, Spinoza’s various assertions about contingency turn out to be consistent. Secondly, I will discuss the text (E2a1) which is commonly taken to be the strongest and most stubborn proof against the reading of Spinoza as strict necessitarianism; I will show that the basic meaning of this text has been widely misunderstood, and that E2a1 is perfectly compatible with strict necessitarianism. (shrink)

“Counterfactual” readings of might/could have were previously analyzed using metaphysical modal bases. This paper presents examples and scenarios where the assumptions of such a branching-time semantics are not met, because there are facts at the base world that preclude the complement of the modal becoming true. Additional arguments show that counterfactual readings are context dependent. These data motivate a semantics using a circumstantial (or factual) modal base, which refers to context-dependent facts about a world and time. The analysis is (...) formulated in a version of premise semantics for modality. (shrink)

Modal Logic, originally conceived as the logic of necessity and possibility, has developed into a powerful mathematical and computational discipline. It is the main source of formal languages aimed at analyzing complex notions such as common knowledge and formal provability. Modal and modal-like languages also provide us with families of restricted description languages for relational and topological structures; they are being used in many disciplines, ranging from artificial intelligence, computer science and mathematics via natural language syntax and semantics to philosophy. (...) This volume presents a broad and up-to-date view of the field, with contributions covering both the foundations of modal logic itself and each of the aforementioned application areas. Complemented with an editorial introduction covering the roots of modal logic, this book is indispensable for any advanced student and researcher in non-classical logic and its applications. (shrink)

On the basis of arguments put forth by (Kripke, 1977a) and (Kripke, 1980), it is widely held that one can sometimes rationally accept propositions of the form "P and not-P" and also that there are necessary a posteriori truths. We will find that Kripke's arguments for these views appear probative only so long as one fails to distinguish between semantics and presemantics—between the literal meanings of sentences, on the one hand, and the information on the basis of which one identifies (...) those literal meanings, on the other. This same failure, it will be argued, underlies the popular thesis that intersubstituting co-referring terms sometimes turns true sentences into false ones and vice versa. Though seemingly plausible, this thesis has a number of counterintuitive consequences, among them that the occurrence of “snow” in “it is true that snow is white” doesn’t refer to snow. An understanding of the distinction between semantics and presemantics suggests a way to develop a semantic system that doesn’t have these consequences and that, moreover, reconciles our intuitions concerning cognitive content with some powerfully argued theses of contemporary philosophy of language. Some of this paper's main contentions are anticipated by Andrzej Boguslawski in his 1994 paper “Sentential Complementation and Truth.”. (shrink)

The thought experiment is a seemingly indispensable tool in the armchair philosopher’s toolbox. One wonders, for example, how philosophers could come to think that justified true belief isn’t knowledge, that reference isn’t determined by an expression’s associated description, or that moral responsibility doesn’t require the ability to do otherwise, without the use of thought experiments. But even if thought experiments play an integral role in philosophical methodology, their legitimacy is at least initially puzzling: one would think that significant knowledge of (...) the world requires extensive empirical investigation. But since thought experiments are done from the armchair, how can they tell us about the world? -/- A standard account of the nature and utility of thought experiments provides an answer to this question, and in a way that fits naturally with a standard picture of the nature of the facts philosophers investigate: Philosophers are about the business of investigating the essences of things and kinds. But a thing’s essential and accidental properties are modal properties. Thus, one can discern a thing’s essence by discovering its modal profile. But if so, then thought experiments are naturally suited as tools for the armchair philosopher. For thought experiments shed light on modal facts. Therefore, since philosophers investigate essences, facts about essence are modal facts, and the thought experiment is one of the few tools they have for discerning such facts, thought experiments play a legitimate and indispensable role in philosophical methodology. In my dissertation, I argue that the standard account of the nature and utility of thought experiments is inadequate, and sketch a more promising account. -/- First, I argue that our knowledge of possibility is restricted to the relatively humdrum. And if so, then since the standard account ties the utility of thought experiments to our knowledge of possibility, too many thought experiments will be ruled out as useless, which raises serious concerns about the significance, and perhaps even the legitimacy, of armchair philosophy. Thus, there is pressure for armchair philosophers to reject the standard account. -/- Second, I sketch an alternative picture of the nature of facts philosophers investigate – one that’s more fine-grained than the standard modal-profile picture. Relatedly, I sketch a correspondingly fine-grained semantics for claims about such facts. This alternative picture underwrites the legitimacy of a hitherto underappreciated sort of thought experiment, which I call the non-modal thought experiment. Such thought experiments shed light on facts about the world that are more fine-grained than what can be discerned by merely examining their modal profiles. I argue that non-modal thought experiments often succeed at just the points where the more familiar modal thought experiments fail, and thus that the two are naturally suited to complement one another in the philosopher’s practice. -/- Finally, I exploit the points mentioned above to sketch an account of the variety and utility of thought experiments that’s much more nuanced than that of the standard account. I then illustrate some of its virtues by indicating its ability to account for a wide range of epistemically forceful thought experiments – both humdrum and exotic –, and by demonstrating how it can be used to make progress in debates that have reached a stalemate due to conflicting modal intuitions. -/- . (shrink)

In this paper I argue that noun complement modality cannot be treated as dependent on the meanings of lexical embedding predicates or of abstract performatives. Using two types of complement modalities, I show that their meanings and restrictions remain distinct and invariable regardless of the meanings of their embedding predicates. Then, using embedding predicates that can take both types of modalities, I show that the embedding predicates retain their meanings, regardless of the different modalities of their complements, (...) and they can undergo deletions requiring their identity. (shrink)

Si Dios es la razón suficiente del mundo, entonces parece seguirse que todos los eventos son consecuencia necesaria de un ser necesario. Para evadir esta conclusión, Leibniz formula en la década de 1670 una concepción modal que funda la contingencia en un rasgo lógico e intrínseco de las ideas de las cosas: la posibilidad de concebir la idea contraria sin contradicción. Hacia 1686, Leibniz complementa esta primera concepción con lo que considera su solución definitiva al problema de la contingencia: la (...) teoría del análisis infinito. Sin embargo, en otros escritos de ese año, propone dos vías alternativas de fundamentación de la contingencia. Este trabajo sugiere que esa pluralidad de modelos explicativos converge en una concepción integral de las modalidades que subyace como trasfondo de la reflexión modal leibniziana. If God is the sufficient reason for this world, then it seems to follow that every event is a necessary consequence of a necessary being. in order to avoid this conclusion, Leibniz states, during the 1670's, a modal conception that grounds contingency on a logical feature which is intrinsic to the ideas of things: the possibility of conceiving the opposite idea without contradiction. Towards 1686, Leibniz complements this first conception with what he considered to be his definitive solution to the problem of contingency: the theory of infinite analysis. However, in other writings from the same year, he proposes two different ways to explain contingency. This paper suggests that this plurality of models converges in a global conception of modalities, which lies at the background of Leibniz's modal thought. (shrink)

Some points are made about substance properties in their role of introducing mass terms. In particular, two conditions of distributivity and cumulativity of mass predicates expressing these properties are not the independent pair they first appear to be. A classification of macroscopic substance concepts is developed. This needs to be complemented in some way by the introduction of a modal qualification reminiscent of Aristotle's distinction between actual and potential presence of substances in a mixture. Consideration of the latter feature has (...) prompted Joe Earley to raise the question of whether there is any salt in the sea. I try to argue that there is. (shrink)

Can language directly access what is true, or is the truth judgment affected by the subjective, perhaps even solipsistic, constructs of reality built by the speakers of that language? The construction of such subjective representations is known as veridicality, and in this book Anastasia Giannakidou and Alda Mari deftly address the interaction between truth and veridicality in the grammatical phenomena of mood choice: the indicative and subjunctive choice in the complements of modal expressions (words like must, may, can, and possible) (...) and propositional attitude verbs (such as know, believe, remember, dream, and persuade). Combining several strands of analysis-formal linguistic semantics, syntactic theory, modal logic, and philosophy of language- Giannakidou and Mari's theory not only enriches the analysis of linguistic modality, but also offers a unified perspective of modals and propositional attitudes. Their synthesis covers mood, modality, and attitude verbs in Greek and Romance languages including Italian and French, while also offering broader applications for languages lacking systematic mood distinction, such as English, and explaining interactions between modality, time, and evidentiality. (shrink)

In “Elementa Juris Naturalis” (1671) G.W. Leibniz formulated the genius intuition about the fundamental unity of juridical and Aristotelian modalities. Interpreting and explicating this intuition by virtue of the deontic logic G.W. Wright arrived to the conclusion that the unity of modalities in question is not an equivalence relation but an analogy one. However a complement for G.W. Wright’s explication of the intuition of G.W. Leibniz was submitted. This complement was a two-valued algebra of formal-natural-law philosophy of juridical (...) and Aristotelian modalities as moral-legal evaluation-functions determined by one variable. In thepresent paper I submit a binary generalization of the mentioned unary complement. By virtue of this generalization some significant shortcomings of the complement in question are eliminated. The generalization deals with the modalities as moral-legal evaluation-functions determined by two variables. (shrink)

These short notes are intended to supplement the lectures and text ntroduce some of the basic concepts of Modal Logic. The primary goal is to provide students in Philosophy 151 at Stanford University with a study guide that will complement the lectures on modal logic. There are many textbooks that you can consult for more information. The following is a list of some texts (this is not a complete list, but a pointer to books that I have found particularly (...) useful). (shrink)

This paper discusses the interaction of aspect and modality, and focuses on the puzzling implicative effect that arises when perfective aspect appears on certain modals: perfective somehow seems to force the proposition expressed by the complement of the modal to hold in the actual world, and not merely in some possible world. I show that this puzzling behavior, originally discussed in Bhatt (1999, Covert modality in non-finite contexts) for the ability modal, extends to all modal auxiliaries with (...) a circumstantial modal base (i.e., root modals ), while epistemic interpretations of the same modals are immune to the effect. I propose that implicative readings are contingent on the relative position of the modal w.r.t. aspect: when aspect scopes over the modal (as I argue is the case for root modals), it forces an actual event, thereby yielding an implicative reading. When a modal element scopes over aspect, no actual event is forced. This happens (i) with epistemics, which structurally appear above tense and aspect; (ii) with imperfective on a root modal: imperfective brings in an additional layer of modality, itself responsible for removing the necessity for an actual event. This proposal enables us to solve the puzzle while maintaining a standardized semantics for aspects and modals. (shrink)

This monograph explores the logical systems of early logicians in the Arabic tradition from a theoretical perspective, providing a complete panorama of early Arabic logic and centering it within an expansive historical context. By thoroughly examining the writings of the first Arabic logicians, al-Fārābī, Avicenna and Averroes, the author analyzes their respective theories, discusses their relationship to the syllogistics of Aristotle and his followers, and measures their influence on later logical systems. Beginning with an introduction to the writings of the (...) most prominent Arabic logicians, the author scrutinizes these works to determine their categorical logic, as well as their modal and hypothetical logics. Where most other studies written on this subject focus on the Arabic logicians’ epistemology, metaphysics, and theology, this volume takes a unique approach by focusing on the actual technical aspects and features of their logics. The author then moves on to examine the original texts as closely as possible and employs the symbolism of modern propositional, predicate, and modal logics, rendering the arguments of each logician clearly and precisely while clarifying the theories themselves in order to determine the differences between the Arabic logicians’ systems and those of Aristotle. By providing a detailed examination of theories that are still not very well-known in Western countries, the author is able to assess the improvements that can be found in the Arabic writings, and to situate Arabic logic within the breadth of the history of logic. This unique study will appeal mainly to historians of logic, logicians, and philosophers who seek a better understanding of the Arabic tradition. It also will be of interest to modern logicians who wish to delve into the historical aspects and progression of their discipline. Furthermore, this book will serve as a valuable resource for graduate students who wish to complement their general knowledge of Arabic culture, logic, and sciences. (shrink)

In the literature on the interpretation of quantum mechanics, not many works attempt to adopt a proactive perspective aimed at seeing how different interpretations can enrich each other through a productive dialogue. In particular, few proposals have been devised to show that different approaches can be clarified by comparing them, and can even complement each other, improving or leading to a more fertile overall approach. The purpose of this paper is framed within this perspective of complementation and mutual enrichment. (...) In particular, the Relational Quantum Mechanics and the Modal-Hamiltonian Interpretation are compared, highlighting their differences and points of contact. The final purpose is to show that, in spite of their disagreements, they are not contradictory but, on the contrary, they can be made compatible from an overarching perspective and can even complement each other in a fruitful way. (shrink)

In this paper we consider the class of truth-functional modal many-valued logics with the complete lattice of truth-values. The conjunction and disjunction logic operators correspond to the meet and join operators of the lattices, while the negation is independently introduced as a hierarchy of antitonic operators which invert bottom and top elements. The non-constructive logic implication will be defined for a subclass of modular lattices, while the constructive implication for distributive lattices (Heyting algebras) is based on relative pseudo-complements as in (...) intuitionistic logic. We show that the complete lattices are intrinsically modal, with banal identity modal operator. We define the autoreferential set-based representation for the class of modal algebras, and show that the autoreferential Kripke-style semantics for this class of modal algebras is based on the set of possible worlds equal to the complete lattice of algebraic truth-values. The philosophical assumption is based on the consideration that each possible world represents a level of credibility, so that only propositions with the right logic value (i.e., level of credibility) can be accepted by this world, then we connect it with paraconsistent properties and LFI logics. The bottom truth value in this complete lattice corresponds to the trivial world in which each formula is satisfied, that is, to the world with explosive inconsistency. The top truth value corresponds to the world with classical logics, while all intermediate possible worlds represent the different levels of paraconsistent logics. (shrink)

Although it is frequently said that logic is a purely formal discipline lacking any content for special philosophical subdisciplines, I argue in this essay that the concepts of predication, and of the properties of objects presupposed by standard first-order logic are sufficient to address many of the traditional problems of ontology. The concept of an object's having a property is extended to provide an intensional definition of the existence of an object as the object's possessing a maximally consistent property combination, (...) consisting, for any property or its complement. Nonexistent objects by the proposed definition are those that either lack both some property and its complement, or have both a property and its complement included in its corresponding property combination. The definition in turn makes it possible to offer solutions based on purely logical concepts of such longstanding metaphysical problems as why there is something rather than nothing, and why there exists exactly one logically contingent actual world, itself a maximally consistent combination of true predication instances or facts. Additionally, the ontology upholds an argument in support of modal actualism and against modal realism, treating all logically possible worlds other than the actual world as predicationally incomplete nonexistent objects or semantic fictions. (shrink)

A necessary part of David Armstrong's account of truthmakers for modal truths is his Possibility principle: any truthmaker for a contingent truth is also a truthmaker for the possibility of the complement of that contingent truth (if T makes _p_ true and _p_ is contingent, then T makes ⋄∼_p_ true). I criticize Armstrong's Possibility principle for two reasons. First, his argument for the Possibility principle both relies on an unwarranted generalization and vitiates his desire for relevant truthmakers. His argument (...) undercuts relevant truthmakers by entailing that each contingent being is a truthmaker for all modal truths. Second, even if the argument seems successful, the Possibility principle is subject to counterexamples. Armstrong's being composed of more than fifty atoms makes it true _that something composed of more than fifty atoms exists_ and that truth is contingent, but his being composed of more than fifty atoms does not make it true _that it is possible that it is not the case that something composed of more than fifty atoms exists_. (shrink)

Let α be an arbitrary infinite ordinal, and. In [26] we studied—using algebraic logic—interpolation and amalgamation for an extension of first order logic, call it, with α many variables, using a modal operator of a unimodal logic that contributes to the semantics. Our algebraic apparatus was the class of modal cylindric algebras. Modal cylindric algebras, briefly, are cylindric algebras of dimension α, expanded with unary modalities inheriting their semantics from a unimodal logic such as, or. When modal cylindric algebras based (...) on are just cylindric algebras, that is to say,. This paper is a sequel to [26], where we study algebraically other properties of. We study completeness and omitting types (s) for s by proving several representability results for so‐called dimension complemented and locally finite. Furthermore, we study the notion of atom‐canonicity for, the variety of n‐dimensional modal cylindric algebras. Atom canonicity, a well known persistence property in modal logic, is studied in connection to for, which is restricted to the first n variables. We further continue our study of interpolation in [26] for algebraizable extensions of by studying using both algebraic logic and category theory. Our main results on are Theorems 3.7, 4.4 & 4.6, while our main results on amalgamation are Theorems 5.7, 5.10, 5.13 & 5.16. (shrink)

Infinitives are known to encode covert modality in certain environments including infinitival relatives and questions. Beyond these environments, however, the precise distribution and interpretation of infinitival modality remains poorly understood. In that light, this paper investigates infinitive-embedding _enough_/_too_ sentences like _Pat is tall enough to be the thief_ or _Lee is too old to drive_. These sentences have a modal semantics whose compositional source is contested: on one approach, the infinitive encodes the modality, and on another approach, (...) the _enough_/_too_ morpheme itself is modal. To adjudicate this debate, I consider heretofore largely overlooked _finite_-clause-embedding _enough_ sentences like _Pat is tall enough that she might/must be the thief_ or _Lee was fast enough that she won the race_. They provide, I argue, novel support for the view that the modality is in the embedded clause (whether nonfinite or finite) and not in _enough_/_too_. I then compare the covert modality of nonfinite _enough_ clauses to the covert modality of infinitival relatives, questions, and complements to attitude predicates and content nouns. I generalize that covert modality in nonfinite clauses never encodes epistemic necessity, and I tentatively hypothesize that this constraint reflects the marked status of nonfiniteness in the finite/nonfinite opposition. (shrink)

The purpose of this study is to propose new similarity measures namely rough variational coefficient similarity measure under the rough neutrosophic environment. The weighted rough variational coefficient similarity measure has been also defined. The weighted rough variational coefficient similarity measures between the rough ideal alternative and each alternative are xxxxx calculated to find the best alternative. The ranking order of all the alternatives can be determined by using the numerical values of similarity measures. Finally, an illustrative example has been provided (...) to show the effectiveness and validity of the proposed approach. Comparisons of decision results of existing rough similarity measures have been provided. (shrink)

This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency. In this paper, a new approach for multi-attribute group decision making problems is proposed by extending the TOPSIS method under rough neutrosophic environment. Rough neutrosophic set is characterized by the upper and lower approximation operators and the (...) pair of neutrosophic sets that are characterized by truth-membership degree, indeterminacy membership degree, and falsity membership degree. In the decision situation, ratings of alternatives with respect to each attribute are characterized by rough neutrosophic sets that reflect the decision makers’ opinion. Rough neutrosophic weighted averaging operator has been used to aggregate the individual decision maker’s opinion into group opinion for rating the importance of attributes and alternatives. Finally, a numerical example has been provided to demonstrate the applicability and effectiveness of the proposed approach. (shrink)

The deontic modal must has two surprising properties: an assertion of must p does not permit a denial of p, and must does not take past tense complements. I first consider an explanation of these phenomena that stays within Angelika Kratzer’s semantic framework for modals, and then offer some reasons for rejecting that explanation. I then propose an alternative account, according to which simple must sentences have the force of an imperative.

From playing basketball to ordering at a food counter, we frequently and effortlessly coordinate our attention with others towards a common focus: we look at the ball, or point at a piece of cake. This non-verbal coordination of attention plays a fundamental role in our social lives: it ensures that we refer to the same object, develop a shared language, understand each other’s mental states, and coordinate our actions. Models of joint attention generally attribute this accomplishment to gaze coordination. But (...) are visual attentional mechanisms sufficient to achieve joint attention, in all cases? Besides cases where visual information is missing, we show how combining it with other senses can be helpful, and even necessary to certain uses of joint attention. We explain the two ways in which non-visual cues contribute to joint attention: either as enhancers, when they complement gaze and pointing gestures in order to coordinate joint attention on visible objects, or as modality pointers, when joint attention needs to be shifted away from the whole object to one of its properties, say weight or texture. This multisensory approach to joint attention has important implications for social robotics, clinical diagnostics, pedagogy and theoretical debates on the construction of a shared world. (shrink)

A thorny question surrounding the meaning of ought concerns a felt distinction between deontic uses of ought that seem to evaluate a state of affairs versus those that seem to describe a requirement or obligation to perform an action, as in and, respectively. There ought not be childhood death and disease. You ought to keep that promise. Various accounts have been offered to explain the contrast between “agentive” and “non-agentive” ought sentences. One such account is the Agency-in-the-Prejacent theory, which traces (...) the difference to a particular kind of ambiguity in the prejacent. This theory has been criticized as linguistically unviable. Indeed, I level a few novel complaints against AIP myself in the present paper. But AIP has a kernel of genuine insight which allows us to explain the contrast—that the distinction between agentive and non-agentive ought sentences owes in part to the way natural language encodes information about agency. I develop this idea into a novel account that, like AIP, traces the contrast to an ambiguity in the complement of the modal. However, according to the view I propose, the Coercion View, a linguistically-motivated coercion operation produces the necessary grammatical conditions for agentive ought, which in turn allow a kind of variadic function operator in the style of to produce the semantic effect we see on display in agentive readings of ought. Having explained the mechanism by which we get this structure, I show that it corroborates some of the central intuitions underwriting agentive ought. I submit that the Coercion View offers an explanation of agentive ought to take at least as seriously as any of its competitors. (shrink)

Herman Dooyeweerd ( 1985 ) argued that among the modalities making up the fabric of reality a specifically economic one is to be found. The aim of the present paper is to discuss the texture of such a modality and how it both differentiates and intertwines with others. For an updated brief, albeit cogent and analytically lucid presentation of the Law Framework ontology, see Clouser ( 2009 ). Dooyeweerd’s view entails that the proper object of economics is irreducible to (...) that of other disciplines, but a non-reductionist view of the object of economics presupposes that the nuclear meaning of that discipline has been clearly delimited: this is required in order to determine its nature and separate identity as a scientific discipline. By ‘the nuclear meaning of a discipline’ I understand a pre-theoretical delimitation of its field of research, such as that of the field of physics, characterized by the laws governing force and energy. Within one and the same field there may be many theories, theories competing to explain the same phenomena, or dealing with phenomena so different that it is nearly impossible to trace conceptual connections among them. This last situation calls for a unified-field theory. In the second section of this paper I will attempt to defend a rather commonly accepted definition of the field of economics that sees this discipline as a science of choice. In the third I will show how the analytical conception it involves can be naturally complemented with a classificatory one. According to a classificatory conception, the aggregated social-level phenomena, patterns and regularities economic theories usually deal with, are economic in that sense, even though they are not prima facie cases of individual behavior, or are unintended consequences of aggregated individual choices. In the fourth I will discuss the meaning of the most general, supra-arbitrary economic laws—the modal laws of economics. In the final section I will offer a non-reductionist view of economics that nevertheless takes into account its intertwining with other spheres. (shrink)

Soft X‐ray tomography (SXT) is an imaging technique capable of characterizing and quantifying the structural phenotype of cells. In particular, SXT is used to visualize the internal architecture of fully hydrated, intact eukaryotic and prokaryotic cells at high spatial resolution (50 nm or better). Image contrast in SXT is derived from the biochemical composition of the cell, and obtained without the need to use potentially damaging contrast‐enhancing agents, such as heavy metals. The cells are simply cryopreserved prior to imaging, and (...) are therefore imaged in a near‐native state. As a complement to structural imaging by SXT, the same specimen can now be imaged by correlated cryo‐light microscopy. By combining data from these two modalities specific molecules can be localized directly within the framework of a high‐resolution, three‐dimensional reconstruction of the cell. This combination of data types allows sophisticated analyses to be carried out on the impact of environmental and/or genetic factors on cell phenotypes. (shrink)

This paper generalises and complements the work on combining temporal logics started by Finger and Gabbay [11, 10]. We present proofs of transference of soundness, completeness and decidability for the temporalisation of logics T for any flow of time, eliminating the original restriction that required linear time for the transference of those properties through logic combination. We also generalise such results to the external application of a multi-modal system containing any number of connectives with arbitrary arity, that respect normality.This generalisation (...) over generic flows of time propagates to other combinations of logics that can be interpreted in terms of temporalisations. In this way, the independent combination of temporal logics is studied over generic flows of time. We show the transfer of soundness, completeness and decidability for independent combination of temporal logics. Finally, we also discuss the independent combination of any finite number of normal multi-modal logics. (shrink)