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)

In lieu of an abstract, here is a brief excerpt of the content:LITERAL AND METAPHORICAL USES OF DISCOURSE IN THE REPRESENTATION OF GOD IN HIS SEMINAL work on the theory of signs, Charles Morris affirms that human beings are " the dominant sign-using animals" and that" the human mind is inseparable from the functioning of signs-if indeed mentality is not to be identified with such functioning." 1 By means of acculturation we learn to use and interpret signs, both linguistic and (...) non-linguistic; and by virtue of these capacities we can appropriately designate the human animal as homo symbolicus, homo loquens, and homo sapiens. Indeed, all forms of human culture presuppose the ability to use and interpret signs, including that form of human culture which leads us to speak of ourselves as homo religious. Over the years I have come to understand and speak of religion as a community with its cultus. There is the community, be it triba1, national, or universal with its polity or structure and ongoing history; and there is the cultus with its organic system of linguistic and nonlinguistic signs, encompassing ·such elements as stories, creeds, scriptures, doctrines, theologies, confessions, prayers, chants, songs, rites, rituals, sacraments, artifacts, etc. Like any other cultural system, scheme or network of signs one can characterize a religious cultus as an inter -subjective set of signs whose usage is determined by the implicit or explicit rules that govern the relations of signs to each other; the relations of the signs to the objects which the signs designate or denote, or stand for in some way; and the relations of signs to the users or interpreters of these signs and to those who are affected by these signs in some way. 1 Charles W. Morris, FoundatioJi of the Theory of Signs, in International Encyclopedia of Unified Science, Vol. I, No. 2 (Chicago: University of Chicago Press, 1939), p. L 6~7 628 WILLIAM L. POWER: Given this understanding of community and cultus, one can describe a religion as an organized group of socially interdependent human beings which uses or employs ·a system of linguistic and nonlinguistic signs to represent reality in its various modalities and mixtures of good and evil and to affect human ways of life on the basis of that representation. Altering the terminology somewhat, one could say that a religious community uses its cultus to proclaim, enact, and display a comprehensive worldview.and to form and tr:msform the ethospathos of human beings in their solidarity and solitude. Expressed semiotically, there is the system of signs of a particular community, the intended signification of these signs, and the significance of these signs for those who use and are affected by them. What distinguishes a religion from other forms of human culture is that a rel·igious cultuml sy•stem or a religious community with its cultus is primarily concerned with ultimate or supreme reality or with that which is divine, holy, or sacred and that reality's bearing on and relevance for human life and well-being. In short, a religion is a cultural system which functions to map the whole of re.ality and to acculturate in desirable ways or to civilize. If a religion is a cultural system, then one can identify three distinct yet inseparably related dimensions of every religion. There is 1) the cultural dimension consisting of the interrelruted signs, symbols and expressions of a cultus; 2) the reality and value dimension consisting of the ontological and axiological purport of the cultus; and 3) the experiential dimension consisting of the existential import of the cultus. It is this thioo dimension which has led many in the past and in the present to speak of religion as piety, consciousness of things divine, ultimate concern, religiousness, etc. In the tradition of Peircian semiotics, one can speak of these three dimensions as the syntactic, semantic, and praigmatic dimensions of a religion; and they can be analyzed and studied with the aid of syntactics or syntax, semantics, and pr:agmatics, which as a unity LITERAL AND METAPHORICAL USES OF DISCOURSE 629 constitute the discipline of semiotics. As Peirce recognized, modem semiotics is continuous with the Medieval trivium of grammar, logic, and rhetoric-the semiotics of almost a millennium a;go... (shrink)

Possible worlds, concrete or abstract as you like, are irrelevant to the truthmakers for modality—or so I shall argue in this paper. First, I present the neo-Humean picture of modality, and explain why those who accept it deny a common sense view of modality. Second, I present what I take to be the most pressing objection to the neo-Humean account, one that, I argue, applies equally well to any theory that grounds modality in possible worlds. Third, I present an alternative, (...) properties-based theory of modality and explore several specific ways to flesh the general proposal out, including my favored version, the powers theory. And, fourth, I offer a powers semantics for counterfactuals that each version of the properties-based theory of modality can accept, mutatis mutandis. Together with a definition of possibility and necessity in terms of counterfactuals, the powers semantics of counterfactuals generates a semantics for modality that appeals to causal powers and not possible worlds. (shrink)

A complex theory concerning powers, natures, and causal necessity has emerged from the writings of P. H. Hare, E. H. Madden, and R. Harré. In the course of rebutting objections that other critics have raised to the power account of causation, I correct three of its genuine difficulties: its attempt to analyze power attributions in terms of conditional statements; its characterization of the relation between something's powers and its nature; and its doctrines concerning conceptual necessity. The resulting interpretation (...) of causal modalities is then subsumed under a more general power account of modality, related at a number of points to considerations concerning powers, and further illustrating their philosophical importance. (shrink)

In this article I critically assess Deleuze’s interpretation of Spinoza’s metaphysics of modes. I argue that the conception of modal essence that Deleuze attributes to Spinoza is untenable in terms of Spinoza’s metaphysics. I further show that the idea that modal essences are eternally static degrees of power is incompatible with Spinoza’s ethics, wherein modes strive to increase their power by means of positive interactions with others. I suggest that Deleuze’s interpretation of this crucial aspect of (...) Spinozism runs the risk of reinstating Platonic idealist and moralistic themes, of the kind that both Spinoza and Deleuze are committed to overcoming. (shrink)

Many authors have noted that there are types of English modal sentences cannot be formalized in the language of basic first-order modal logic. Some widely discussed examples include “There could have been things other than there actually are” and “Everyone who is actually rich could have been poor.” In response to this lack of expressive power, many authors have discussed extensions of first-order modal logic with two-dimensional operators. But claims about the relative expressive power of (...) these extensions are often justified only by example rather than by rigorous proof. In this paper, we provide proofs of many of these claims and present a more complete picture of the expressive landscape for such languages. (shrink)

In _Modal Logic for Open Minds,_ Johan van Benthem provides an up-to-date introduction to the field of modal logic, outlining its major ideas and exploring the numerous ways in which various academic fields have adopted it. Van Benthem begins with the basic theories of modal logic, semantics, bisimulation, and axiomatics, and also covers more advanced topics, such as expressive power and computational complexity. The book then moves to a wide range of applications, including new developments in information (...) flow, intelligent agency, and games. Taken together, the chapters show modal logic at the crossroads of philosophy, mathematics, linguistics, computer science, and economics. Most of the chapters are followed by exercises, making this volume ideal for undergraduate and graduate students in philosophy, computer science, symbolic systems, cognitive science, and linguistics. (shrink)

We illustrate, with three examples, the interaction between boolean and modal connectives by looking at the role of truth-functional reasoning in the provision of completeness proofs for normal modal logics. The first example (§ 1) is of a logic (more accurately: range of logics) which is incomplete in the sense of being determined by no class of Kripke frames, where the incompleteness is entirely due to the lack of boolean negation amongst the underlying non-modal connectives. The second (...) example (§ 2) focusses on the breakdown, in the absence of boolean disjunction, of the usual canonical model argument for the logic of dense Kripke frames, though a proof of incompleteness with respect to the Kripke semantics is not offered. An alternative semantic account is developed, in terms of which a completeness proof can be given, and this is used (§ 3) in the discussion of the third example, a bimodal logic which is, as with the first example, provably incomplete in terms of the Kripke semantics, the incompleteness being due to the lack of disjunction (as a primitive or defined boolean connective). (shrink)

It is shown that the expressive power of second-order propositional modal logic whose modalities are S4.2 or weaker is the same as that of second-order predicate logic.

Any successful account of the metaphysics of mechanistic causation must satisfy at least five key desiderata. In this article, I lay out these five desiderata and explain why existing accounts of the metaphysics of mechanistic causation fail to satisfy them. I then present an alternative account that does satisfy the five desiderata. According to this alternative account, we must resort to a type of ontological entity that is new to metaphysics, but not to science: constraints. In this article, I explain (...) how a constraints-based metaphysics fits best with the emerging consensus on the nature of mechanistic explanation. 1Introduction2Renormalizability2.1The first two desiderata: Intrinsicness and productivity2.2The third desideratum: Scientific validity or non-mysteriousness2.3The fourth desideratum: Directionality2.4The fifth desideratum: Perspectival nature of mechanisms3Constraints and Causation3.1Multi-perspectival realism and causal structure3.2Causal structure as laws3.3Causal structures in analytical mechanics: Constraints3.4A metaphysics inspired by analytical mechanics: Constraints as ontologically primitive modal structures4Constraints and Mechanistic Causal Powers 4.1Inter- versus intra-perspectival categories4.2Mechanistic causal powers are grounded by constraints4.3Intrinsicness and constraints4.4Constraints and productiveness4.5Constraints and directionality5Conclusion. (shrink)

Dispositionality is a modal notion of a certain sort. When an object is said to have a disposition, we typically understand this to mean that under certain circumstances, the object would behave in a certain way. For instance, a fragile object is disposed to break when dropped onto a concrete surface. It need not actually break - its being fragile has implications that, so to speak, point beyond the actual world. According to dispositionalism, all modal features of the (...) world may be accounted for in terms of its dispositional features. My aim in this paper is to assess the prospects for dispositionalism by examining the most promising theories. Sections 1 and 2 clarify the assumptions and desiderata of a successful dispositionalist theory of modality. Section 3 introduces the principles governing the dispositionalist theories that apparently meet the desiderata. Sections 4 through 6 show that dispositionalism nonetheless faces three problems: while dispositions help account for modal features of the world that are local, diachronic, or gradable, they cannot account for certain modal features of the world that are global, synchronic, or absolute. I end by discussing the costs of preserving dispositionalism. (shrink)

We develop a method for showing that various modal logics that are valid in their countably generated canonical Kripke frames must also be valid in their uncountably generated ones. This is applied to many systems, including the logics of finite width, and a broader class of multimodal logics of ‘finite achronal width’ that are introduced here.

In this paper I examine Grace A. de Laguna’s theory of universals in its historical context and in relation to contemporary debates in analytic metaphysics. I explain the central features of her theory, arguing that her theory should be classified as a form of immanent realism and as a powers ontology. I then show in what ways her theory affords a theory of modality in terms of potentialities and discuss some of its consequences along the way.

In _Modal Logic for Open Minds,_ Johan van Benthem provides an up-to-date introduction to the field of modal logic, outlining its major ideas and exploring the numerous ways in which various academic fields have adopted it. Van Benthem begins with the basic theories of modal logic, semantics, bisimulation, and axiomatics, and also covers more advanced topics, such as expressive power and computational complexity. The book then moves to a wide range of applications, including new developments in information (...) flow, intelligent agency, and games. Taken together, the chapters show modal logic at the crossroads of philosophy, mathematics, linguistics, computer science, and economics. Most of the chapters are followed by exercises, making this volume ideal for undergraduate and graduate students in philosophy, computer science, symbolic systems, cognitive science, and linguistics. (shrink)

Dispositionalism is the theory of modality that grounds all modal truths in powers: all metaphysically possible and necessary truths are to be explained by pointing to some actual power, or absence thereof. One of the main reasons to endorse dispositionalism is that it promises to deliver an especially desirable epistemology of modality. However, so far this issue has not be fully investigated with the care it is due. The aim of this paper is to fill this gap. We (...) will cast some doubts on whether the dispositionalist really is in a better position to explain our modal knowledge. In fact, we argue that there is a tension between some core tenets of a powers metaphysics and the very features that make dispositionalism the ideal backdrop for a desirable epistemology of modality. We conclude that this leaves dispositionalists who want to deliver the promised epistemology with a hard, currently unfulfilled, task. (shrink)

Actualists of a certain stripe—dispositionalists—hold that metaphysical modality is grounded in the powers of actual things. Roughly: p is possible iff something has, or some things have, the power to bring it about that p. Extant critiques of dispositionalism focus on its material adequacy, and question whether there are enough powers to account for all the possibilities we intuitively want to countenance. For instance, it seems possible that none of the actual contingent particulars ever existed, but it is impossible (...) to explain this by appealing to the powers of some actual thing or things to bring it about. I argue instead that dispositionalism, in the simple form championed by its proponents, is formally inadequate. Dispositionalists interpret the modal operators as simple existential claims about powers, but if we interpret the operators that way, the resulting system of modal logic is too weak to capture metaphysical modality. I argue that we can modify the standard dispositionalist interpretations of the operators to secure formal adequacy, but at the cost of accepting that not all modality is grounded in powers. This, I shall suggest, is not a bad thing—the resulting theory still has powers at its core and has certain attractive features, in addition to formal adequacy, that the standard theory lacks. (shrink)

Individual objects have potentials: paper has the potential to burn, an acorn has the potential to turn into a tree, some people have the potential to run a mile in less than four minutes. Barbara Vetter provides a systematic investigation into the metaphysics of such potentials, and an account of metaphysical modality based on them. -/- In contemporary philosophy, potentials have been recognized mostly in the form of so-called dispositions: solubility, fragility, and so on. Vetter takes dispositions as her starting (...) point, but argues for and develops a more comprehensive conception of potentiality. She shows how, with this more comprehensive conception, an account of metaphysical modality can be given that meets three crucial requirements: Extensional correctness: providing the right truth-values for statements of possibility and necessity; formal adequacy: providing the right logic for metaphysical modality; and semantic utility: providing a semantics that links ordinary modal language to the metaphysics of modality. -/- The resulting view of modality is a version of dispositionalism about modality: it takes modality to be a matter of the dispositions of individual objects. This approach has a long philosophical tradition going back to Aristotle, but has been largely neglected in contemporary philosophy. In recent years, it has become a live option again due to the rise of anti-Humean, powers-based metaphysics. The aim of Potentiality is to develop the dispositionalist view in a way that takes account of contemporary developments in metaphysics, logic, and semantics. (shrink)

According to dispositionalism about modality, a proposition <p> is possible just in case something has, or some things have, a power or disposition for its truth; and <p> is necessary just in case nothing has a power for its falsity. But are there enough powers to go around? In Yates (2015) I argued that in the case of mathematical truths such as <2+2=4>, nothing has the power to bring about their falsity or their truth, which means they (...) come out both necessary and not possible. Combining this with axiom (T), it is easy to derive a contradiction. I suggested that dispositionalists ought to retreat a little and say that <p> is possible just in case either p, or there is a power to bring it about that p, grounding the possibility of mathematical propositions in their truth rather than in powers. Vetter’s (2015) has the resources to provide a response to my argument, and in her (2018) she explicitly addresses it by arguing for a plenitude of powers, based on the idea that dispositions come in degrees, with necessary properties a limiting case of dispositionality. On this view there is a power for <2+2=4>, without there being a power to bring about its truth. In this paper I argue that Vetter’s case for plenitude does not work. However, I suggest, if we are prepared to accept metaphysical causation, a case can be made that there is indeed a power for <2+2=4>. (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)

This dissertation is about flexibility as a dimension of reality, an objective—independent of mind and language—phenomenon typically referred to as ‘metaphysical modality’. It develops a novel modal account of why reality could be different: that is, why claims like “Possibly, there are talking donkeys,” or “Humphrey could have won the election” are true or false. I contend that primitive dispositional properties called ‘powers’ explain such claims, and do so better than possible-world accounts of modality. The problem with possible-world accounts (...) is that they fail to capture what we mean by modal terms like ‘possibly’, ‘can’, or ‘necessarily’. The phenomenon they capture with possible worlds cannot adequately explain, for instance, that Humphrey regrets not winning the election because: he could have made a difference. Humphrey is told that he could have won the election because some entity represents him as such. But what does some entity’s representing Humphrey have to do with whether Humphrey could have won the election? Simply calling that entity a ‘possible world’ is no help. Powers do better in this regard, preserving a common-sense notion of modality where, because of what a power can do it acts as a cross-roads in history, marking places where reality could have unfolded differently. As such, powers are more clearly modally significant than possible worlds. The conclusion shows how to use powers to underwrite possible-world semantics without possible worlds. (shrink)

Several philosophers have recently suggested that truths about unactualized metaphysical possibilities are true in virtue of the existence of actual objects and their dispositional properties. For example, on this view, it is true that unicorns are metaphysically possible only if some actual object has (or had) the disposition to bring it about that there are unicorns. This view, a dispositionalist version of what has recently been dubbed “The New Actualism,” is a proposal about the nature of modal truthmakers. But, (...) I will argue, this proposal entails much more than that. Here, I will demonstrate that, if the modal truthmakers are the dispositional properties of actual objects, then either (i) there exists one or more causally potent necessary beings, or (ii) necessarily, there exists an actually infinite number of contingent beings. (shrink)

Over the last half century, possible worlds have bled into almost every area of philosophy. In the metaphysics of modality, for example, philosophers have used possible worlds almost exclusively to illuminate discourse about metaphysical necessity and possibility. But recently, some have grown dissatisfied with possible worlds. Why are horses necessarily mammals? Because the property of being a horse bears a special relationship to the property of being a mammal, they say. Not because every horse is a mammal in every possible (...) world. Some have recently begun to use properties to develop rivals to possible worlds semantics which may someday compare in formal power and capture the different systems of modal logic. In this paper, I do two things. I first offer a quick primer on possible worlds semantics. Then I discuss three rivals and the work they have left to do. (shrink)

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

The modal object calculus is the system of logic which houses the (proper) axiomatic theory of abstract objects. The calculus has some rather interesting features in and of itself, independent of the proper theory. The most sophisticated, type-theoretic incarnation of the calculus can be used to analyze the intensional contexts of natural language and so constitutes an intensional logic. However, the simpler second-order version of the calculus couches a theory of fine-grained properties, relations and propositions and serves as a (...) framework for defining situations, possible worlds, stories, and fictional characters, among other things. In the present paper, we focus on the second-order calculus. The second-order modal object calculus is so-called to distinguish it from the second-order modal predicate calculus. Though the differences are slight, the extra expressive power of the object calculus significantly enhances its ability to resolve logical and philosophical concepts and problems. (shrink)

I propose that we approach the epistemology of modality by putting modal metaphysics first and, specifically, by investigating the metaphysics of essence. Following a prominent Neo-Aristotelian view, I hold that metaphysical necessity depends on the nature of things, namely their essences. I further clarify that essences are core properties having distinctive superexplanatory powers. In the case of natural kinds, which is my focus in the paper, superexplanatoriness is due to the fact that the essence of a kind is what (...) causes all the many properties and behaviors that are typically shared by all the instances of the kind. Accordingly, we know what is necessarily true of kinds by knowing what is essential to them in the sense of actually playing such causal-explanatory roles. Modal reasoning aimed at discovering metaphysical necessity thus proceeds via essentialist deduction: we move from essentialist truths to reach necessary truths. (shrink)

Power is clearly a crucial concept for feminist theory. Insofar as feminists are interested in analyzing power, it is because they have an interest in understanding, critiquing, and ultimately challenging the multiple array of unjust power relations affecting women in contemporary Western societies, including sexism, racism, heterosexism, and class oppression. In "The Power of Feminist Theory," Amy Allen diagnoses the inadequacies of previous feminist conceptions of power, and draws on the work of a diverse group (...) of theorists of power, including Michel Foucault, Judith Butler, and Hannah Arendt, in order to construct a new feminist conception of power. The conception of power developed in this book enables readers to theorize domination, resistance, and solidarity, and, perhaps more importantly, to do so in a way that illuminates the interrelatedness of these three modalities of power. (shrink)

"Powers and Capacities in Philosophy" is designed to stake out an emerging, discipline-spanning neo-Aristotelian framework grounded in realism about causal powers. The volume brings together for the first time original essays by leading philosophers working on powers in relation to metaphysics, philosophy of natural and social science, philosophy of mind and action, epistemology, ethics and social and political philosophy. In each area, the concern is to show how a commitment to real causal powers affects discussion at the level in question. (...) In metaphysics, for example, realism about powers is now recognized as providing an alternative to orthodox accounts of causation, modality, properties and laws. Dispositional realist philosophers of science, meanwhile, argue that a powers ontology allows for a proper account of the nature of scientific explanation. In the philosophy of mind there is the suggestion that agency is best understood in terms of the distinctive powers of human beings. Those who take virtue theoretic approaches in epistemology and ethics have long been interested in the powers that allow for knowledge and/or moral excellence. In social and political philosophy, finally, powers theorists are interested in the powers of sociological phenomena such as collectivities, institutions, roles and/or social relations, but also in the conditions of possibility for the cultivation of the powers of individuals. The book will be of interest to philosophers working in any of these areas, as well as to historians of philosophy, political theorists and critical realists. (shrink)

In this paper, I distinguish between two varieties of actualism—hardcore actualism and softcore actualism—and I critically discuss Ross Cameron’s recent arguments for preferring a softcore actualist account of the truthmakers for modal truths over hardcore actualist ones. In the process, I offer some arguments for preferring the hardcore actualist account of modal truthmakers over the softcore actualist one.

The volume brings together for the first time original essays by leading philosophers working on powers in relation to metaphysics, philosophy of natural and social science, philosophy of mind and action, epistemology, ethics and social and political philosophy. In each area, the concern is to show how a commitment to real causal powers affects discussion at the level in question. In metaphysics, for example, realism about powers is now recognized as providing an alternative to orthodox accounts of causation, modality, properties (...) and laws. Dispositional realist philosophers of science, meanwhile, argue that a powers ontology allows for a proper account of the nature of scientific explanation. In the philosophy of mind there is the suggestion that agency is best understood in terms of the distinctive powers of human beings. Those who take virtue theoretic approaches in epistemology and ethics have long been interested in the powers that allow for knowledge and/or moral excellence. In social and political philosophy, finally, powers theorists are interested in the powers of sociological phenomena such as collectivities, institutions, roles and/or social relations, but also in the conditions of possibility for the cultivation of the powers of individuals. The book will be of interest to philosophers working in any of these areas, as well as to historians of philosophy, political theorists and critical realists. (shrink)

We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics (...) x ⊧ ⍯φ iff Vy(y ≠ x → y ⊧ φ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in ℒ $_{c}$ . Strong completeness of the normal ℒ $_{c}$ logics is proved with respect to models in which all worlds are named. Every ℒ $_{c}$ -logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from ℒ to ℒ $_{c}$ are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched. (shrink)

Neil E. Williams develops a systematic metaphysics centred on the idea of powers, as a rival to neo-Humeanism, the dominant systematic metaphysics in philosophy today. Williams takes powers to be inherently causal properties and uses them as the foundation of his explanations of causation, persistence, laws, and modality.

We study several modal languages in which some (sets of) generalized quantifiers can be represented; the main language we consider is suitable for defining any first order definable quantifier, but we also consider a sublanguage thereof, as well as a language for dealing with the modal counterparts of some higher order quantifiers. These languages are studied both from a modal logic perspective and from a quantifier perspective. Thus the issues addressed include normal forms, expressive power, completeness (...) both of modal systems and of systems in the quantifier tradition, complexity as well as syntactic characterizations of special semantic constraints. Throughout the paper several techniques current in the theory of generalized quantifiers are used to obtain results in modal logic, and conversely. (shrink)

The aim of Modality and Explanatory Reasoning (MER) is to shed light on metaphysical necessity and the broader class of modal properties to which it belongs. This topic is approached with two goals: to develop a new and reductive analysis of modality, and to understand the purpose and origin of modal thought. I argue that a proper understanding of modality requires us to reconceptualize its relationship to causation and other forms of explanation such as grounding, a relation that (...) connects metaphysically fundamental facts to non-fundamental ones. While many philosophers have tried to give modal analyses of causation and explanation, often in counterfactual terms, I argue that we obtain a more plausible, explanatorily powerful and unified theory if we regard explanation as more fundamental than modality. The function of modal thought is to facilitate a common type of thought experiment – counterfactual reasoning – that allows us to investigate explanatory connections and which is closely related to the controlled experiments of empirical science. Necessity is defined in terms of explanation, and modal facts often reflect underlying facts about explanatory relationships. The study of modal facts is important for philosophy not because these facts are of much metaphysical interest in their own right, but largely because they provide evidence about explanatory connections. (shrink)

A powerful challenge to some highly influential theories, this book offers a thorough critical exposition of modal realism, the philosophical doctrine that many possible worlds exist of which our own universe is just one. Chihara challenges this claim and offers a new argument for modality without worlds.

We propose and investigate a uniform modal logic framework for reasoning about topology and relative distance in metric and more general distance spaces, thus enabling the comparison and combination of logics from distinct research traditions such as Tarski’s for topological closure and interior, conditional logics, and logics of comparative similarity. This framework is obtained by decomposing the underlying modal-like operators into first-order quantifier patterns. We then show that quite a powerful and natural fragment of the resulting first-order logic (...) can be captured by one binary operator comparing distances between sets and one unary operator distinguishing between realised and limit distances . Due to its greater expressive power, this logic turns out to behave quite differently from both and conditional logics. We provide finite axiomatisations and ExpTime-completeness proofs for the logics of various classes of distance spaces, in particular metric spaces. But we also show that the logic of the real line is not recursively enumerable. This result is proved by an encoding of Diophantine equations. (shrink)

There has been much discussion of powers or real dispositions in the past decade, but there remains an issue that has been inadequately treated. This concerns the precise modal value that comes with dispositionality. We contend in this paper that dispositionality involves a non-alethic, sui generis, irreducible modality. Dispositions only tend towards their manifestations; they do not necessitate them. Tendency is, of course, a dispositional term itself, so this last statement offers little by way of illumination. But given our (...) thesis on the irreducible nature of dispositionality, we maintain that it cannot be explicated correctly in non-dispositional terms. Nevertheless, we all have experience of dispositionality at work, through the exercise or our own powers and the action of other powers upon us. The notion of dispositionality that we acquire is one that involves a modality stronger than pure contingency but weaker than necessity. The recognition of this distinct modal value for dispositionality is one of the biggest oversights in the growing literature in the area. Yet it is there for all to see in even the most mundane example. (shrink)

I analyse Kripke’s modal argument against the mind-brain identity theories. Specifically, he argues against the identity between pain and C-fibres simulation by pointing out the difference between this identity claim and the theoretical identifications, such as ‘Water is H2O’ and ‘Lightning is a motion of electric charges’. Kripke’s argument relies on the assumption that the experience of pains is a simple and homogenous phenomenon, but scientific research shows that it is in fact a quite complex one. We can distinguish (...) at least three components: sensory-discriminative, motivational-affective and cognitive. This discovery makes it possible to reject Kripke’s argument, but it also uncovers a major flaw that is common to all modal arguments against physicalism. They proclaim to answer the fundamental question about the nature of our world by relying on our powers of imagination and without having the relevant factual knowledge. (shrink)

Imperialism seems to be deeply antithetical to democracy. Yet, at least one form of imperialism – what I call “hands-off imperialism" – seems to be perfectly compatible with the kind of self-governance commonly thought to be the hallmark of democracy. The solution to this puzzle is to recognize that democracy involves more than self-governance. Rather, it involves what I call self-rule. Self-rule is an example of what Philip Pettit has called a modally demanding value. Modally demanding values are, roughly, values (...) the instantiation of which depends not only on what actually happens, but on what would happen in certain non-actual circumstances. Self-rule is the modally demanding counterpart of self-governance, since it requires, not merely that the members of a state actually govern themselves, but that they would continue to do so across a range of non-actual situations. Moreover, the value of self-rule (and hence democracy) is not reducible to the value of self-governance. Understanding the modally demanding character of democracy allows us to appreciate what is democratically objectionable about occupation by a foreign power, even if there is no prospect of the foreign power intervening in the governance of the occupied state by its members. (shrink)

Modal collapse arguments are all the rage in certain philosophical circles as of late. The arguments purport to show that classical theism entails the absurdly fatalistic conclusion that everything exists necessarily. My first aim in this paper is bold: to put an end to action-based modal collapse arguments against classical theism. To accomplish this, I first articulate the ‘Simple Modal Collapse Argument’ and then characterize and defend Tomaszewski’s criticism thereof. Second, I critically examine Mullins’ new modal (...) collapse argument formulated in response to the aforementioned criticism. I argue that Mullins’ new argument does not succeed. Third, I critically examine a powers-based modal collapse argument against classical theism that has received much less attention in the literature. Fourth, I show why God’s being purely actual, as well God’s being identical to each of God’s acts, simply cannot entail modal collapse given indeterministic causation. This, I take it, signals the death of modal collapse arguments. But not all hope is lost for proponents of modal collapse arguments—for the death is a fruitful one insofar as it paves the way for new inquiry into at least two new potential problems for classical theism. Showing this is my paper’s second aim. (shrink)

We introduce the subject of modal model theory, where one studies a mathematical structure within a class of similar structures under an extension concept that gives rise to mathematically natural notions of possibility and necessity. A statement φ is possible in a structure (written φ) if φ is true in some extension of that structure, and φ is necessary (written φ) if it is true in all extensions of the structure. A principal case for us will be the class (...) Mod(T) of all models of a given theory T—all graphs, all groups, all fields, or what have you—considered under the substructure relation. In this article, we aim to develop the resulting modal model theory. The class of all graphs is a particularly insightful case illustrating the remarkable power of the modal vocabulary, for the modal language of graph theory can express connectedness, k-colorability, finiteness, countability, size continuum, size ℵ1, ℵ2, ℵω, ℶω, first ℶ-fixed point, first ℶ-hyper-fixed point, and much more. A graph obeys the maximality principle φ(a)→φ(a) with parameters if and only if it satisfies the theory of the countable random graph, and it satisfies the maximality principle for sentences if and only if it is universal for finite graphs. (shrink)

In this paper we study the expressive power and definability for modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the Goldblatt–Thomason definability theorem in terms of the well-established first-order topological language.