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)

Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.

Modal ontolojik argüman, Tanrı’nın varlığını sadece bilfiil gerçek olan bu dünyada değil, bütün mümkün dünyalarda göstermeye yönelik bir argümandır. Anselm’in (1033-1109) Proslogion adlı eserinin 3. bölümünde “kendisinden daha büyüğü düşünülemeyen” şeklinde tanımlanan; Tanrı’nın var olmamasının da düşünülemeyeceğini, bu yüzden de varolmamasının imkansızlığı üzerinde kurulu yeni bir argüman bulunduğunu öne süren bazı araştırmacılar, bu argümanı mümkün dünyalar semantiği yardımıyla formüle edip, “modal ontolojik argüman” şeklinde adlandırmışlardır. Çok farklı şekillerde formüle edilmiş bu argüman kabaca Tanrı’nın mümkünse zorunlu olması, dolayısıyla bilfiil gerçek olan (...) bu dünyada da var olması gerektiğini savunur. (shrink)

Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.

A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers an (...) up-to-date and reliable guide essential for the student. (shrink)

Epistemic modal operators give rise to something very like, but also very unlike, Moore's paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequence are investigated. The semantics is then extended to probability operators. Some problems and prospects for probabilistic representations of content and context are explored.

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)

I critically examine the claim that modal collapse arguments against the traditional doctrine of divine simplicity (DDS) are in general fallacious. In a recent paper, Christopher Tomaszewski alleges that modal collapse arguments against DDS are invalid, owing to illicit substitutions of nonrigid singular terms into intensional contexts. I show that this is not, in general, the case. I show, further, that where existing modal collapse arguments are vulnerable to this charge the arguments can be repaired without any apparent dialectical impropriety. (...) I conclude that the genuine debate over modal collapse and divine simplicity and modal collapse is substantially a controversy over the metaphysics of divine action, and that this constitutes a fruitful direction in which to take future discussions of the subject. (shrink)

There is a lot that we don't know. That means that there are a lot of possibilities that are, epistemically speaking, open. For instance, we don't know whether it rained in Seattle yesterday. So, for us at least, there is an epistemic possibility where it rained in Seattle yesterday, and one where it did not. What are these epistemic possibilities? They do not match up with metaphysical possibilities - there are various cases where something is epistemically possible but not metaphysically (...) possible, and vice versa. How do we understand the semantics of statements of epistemic modality? The ten new essays in this volume explore various answers to these questions, including those offered by contextualism, relativism, and expressivism. (shrink)

Boris Kment takes a new approach to the study of modality that emphasises the origin of modal notions in everyday thought. He argues that the concepts of necessity and possibility originate in counterfactual reasoning, which allows us to investigate explanatory connections. Contrary to accepted views, explanation is more fundamental than modality.

In the middle of the last century, it was common to explain the notion of necessity in linguistic terms. A necessary truth, it was said, is a sentence whose truth is guaranteed by linguistic rules. Quine famously argued that, on this view, de re modal claims do not make sense. “Porcupettes are porcupines” is necessarily true, but it would be a mistake to say of a particular porcupette that it is necessarily a porcupine, or that it is possibly purple. Linguistic (...) theories of necessity fell out of favour with the publication of Kripke’s Naming and Necessity, and Quine’s arguments were put aside. In her recent book, Norms and Necessity, Amie Thomasson presents her modal normativism, which is an updated version of the mid-century theories just described. Quine’s arguments are thus relevant once again. We recapitulate Quine’s central argument, in the context of modal normativism. We then criticise Amie Thomasson’s discussion of de re modality. We finish by briefly presenting an alternative account of de re modal statements, which is compatible with modal normativism. (shrink)

Most Probably: Epistemic Modality in Old Babylonian by Nathan Wasserman is the first attempt to provide a description of the domain of epistemic modality in Old Babylonian Akkadian. This attempt is not entirely successful, for several reasons. Methodological inconsistency often impairs the author’s ability to convince the reader of his solutions. Both primary data and existing secondary literature are used only selectively, which renders the proposed description problematic. Finally, the lack of cross-referencing between the chapters evokes the feeling that the (...) different particles do not quite constitute a system. (shrink)

For a novice this book is a mathematically-oriented introduction to modal logic, the discipline within mathematical logic studying mathematical models of reasoning which involve various kinds of modal operators. It starts with very fundamental concepts and gradually proceeds to the front line of current research, introducing in full details the modern semantic and algebraic apparatus and covering practically all classical results in the field. It contains both numerous exercises and open problems, and presupposes only minimal knowledge in mathematics. A specialist (...) can use the book as a source of references. Results and methods of many directions in propositional modal logic, from completeness and duality to algorithmic problems, are collected and systematically presented in one volume. (shrink)

A very simple contextualist treatment of a sentence containing an epistemic modal, e.g. a might be F, is that it is true iff for all the contextually salient community knows, a is F. It is widely agreed that the simple theory will not work in some cases, but the counterexamples produced so far seem amenable to a more complicated contextualist theory. We argue, however, that no contextualist theory can capture the evaluations speakers naturally make of sentences containing epistemic modals. If (...) we want to respect these evaluations, our best option is a relativist theory of epistemic modals. On a relativist theory, an utterance of a might be F can be true relative to one context of evaluation and false relative to another. We argue that such a theory does better than any rival approach at capturing all the behaviour of epistemic modals. (shrink)

What does 'might' mean? One hypothesis is that 'It might be raining' is essentially an avowal of ignorance like 'For all I know, it's raining'. But it turns out these two constructions embed in different ways, in particular as parts of larger constructions like Wittgenstein's 'It might be raining and it's not' and Moore's 'It's raining and I don't know it', respectively. A variety of approaches have been developed to account for those differences. All approaches agree that both Moore sentences (...) and Wittgenstein sentences are classically consistent. In this paper I argue against this consensus. I adduce a variety of new data which I argue can best be accounted for if we treat Wittgenstein sentences as being classically inconsistent. This creates a puzzle, since there is decisive reason to think that 'Might p' is classically consistent with 'Not p'. How can it also be that 'Might p and not p' and 'Not p and might p' are classically inconsistent? To make sense of this situation, I propose a new theory of epistemic modals and their interaction with embedding operators. This account makes sense of the subtle embedding behavior of epistemic modals, shedding new light on their meaning and, more broadly, the dynamics of information in natural language. -/- . (shrink)

This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.

This book is collection of the the author’s previously published papers on the philosophy of modality and tense and it also includes three unpublished papers. The author provides an exposition and defence of certain positions for which he is well-known: the intelligibility of modality de re; the primitiveness of the modal; and the primacy of the actual over the possible. He also argues for some less familiar positions: the existence of distinctive forms of natural and normative necessity, not reducible to (...) any form of metaphysical necessity; the need to make a distinction between the worldly and unworldly, analogous to the distinction between the tensed and the tenseless; and the viability of a nonstandard form of realism about tense, which recognizes the tensed character of reality without conceding there is any privileged standpoint from which it is to be viewed. (shrink)

According to the modal view, essence admits of reductive analysis in exclusively modal terms. Fine (1994) argues that modal view delivers an inadequate analysis of essence. This paper defends the modal view from Fine's challenge. This defense proceeds by examining the disagreement between Finean primitivists and Quinean eliminativists about essence. In order to model this disagreement, a distinction between essence and a separable concept, nature, is required. This distinction is then used to show that Fine's challenge is misdirected and therefore (...) unsuccessful. (shrink)

We argue that genuine modal realism can be extended, rather than modified, so as to allow for the possibility of nothing concrete, a possibility we term ‘metaphysical nihilism’. The issue should be important to the genuine modal realist because, not only is metaphysical nihilism itself intuitively plausible, but also it is supported by an argument with pre-theoretically credible premises, namely, the subtraction argument. Given the soundness of the subtraction argument, we show that there are two ways that the genuine modal (...) realist can accommodate metaphysical nihilism: (i) by allowing for worlds containing only spatiotemporal points and (ii) by allowing for a world containing nothing but the null individual. On methodological grounds, we argue that the genuine modal realist should reject the former way but embrace the latter way. (shrink)

This paper explains and defends the idea that metaphysical necessity is the strongest kind of objective necessity. Plausible closure conditions on the family of objective modalities are shown to entail that the logic of metaphysical necessity is S5. Evidence is provided that some objective modalities are studied in the natural sciences. In particular, the modal assumptions implicit in physical applications of dynamical systems theory are made explicit by using such systems to define models of a modal temporal logic. (...) Those assumptions arguably include some necessitist principles. -/- Too often, philosophers have discussed ‘metaphysical’ modality — possibility, contingency, necessity — in isolation. Yet metaphysical modality is just a special case of a broad range of modalities, which we may call ‘objective’ by contrast with epistemic and doxastic modalities, and indeed deontic and teleological ones (compare the distinction between objective probabilities and epistemic or subjective probabilities). Thus metaphysical possibility, physical possibility and immediate practical possibility are all types of objective possibility. We should study the metaphysics and epistemology of metaphysical modality as part of a broader study of the metaphysics and epistemology of the objective modalities, on pain of radical misunderstanding. Since objective modalities are in general open to, and receive, natural scientific investigation, we should not treat the metaphysics and epistemology of metaphysical modality in isolation from the metaphysics and epistemology of the natural sciences. -/- In what follows, Section 1 gives a preliminary sketch of metaphysical modality and its place in the general category of objective modality. Section 2 reviews some familiar forms of scepticism about metaphysical modality in that light. Later sections explore a few of the many ways in which natural science deals with questions of objective modality, including questions of quantified modal logic. (shrink)

The present monograph is a slightly revised version of my Habilitations schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997. It collects work on proof systems for modal and constructive logics I have done over the last few years. The main concern is display logic, a certain refinement of Gentzen's sequent calculus developed by Nuel D. Belnap. This book is far from offering a comprehensive presentation of generalized sequent systems for modal logics broadly conceived. (...) The proof-theory of non-classical logics is a rapidly developing field, and even the generalizations of the ordinary notion of sequent listed in Chapter 1 can hardly be presented in great detail within a single volume. In addition to further investigating the various approaches toward generalized Gentzen systems, it is important to compare them and to discuss their relative advantages and disadvantages. An initial attempt at bringing together work on different kinds of proof systems for modal logics has been made in [188]. Another step in the same direction is [196]. Since Chapter 1 contains introductory considerations and, moreover, every remaining chapter begins with some surveying or summarizing remarks, in this preface I shall only emphasize a relation to philosophy that is important to me, register the sources of papers that have entered this book in some form or another, and acknowledge advice and support. (shrink)

This essay proposes a new theory of agentive modals: ability modals and their duals, compulsion modals. After criticizing existing approaches—the existential quantificational analysis, the universal quantificational analysis, and the conditional analysis—it presents a new account that builds on both the existential and conditional analyses. On this account, the act conditional analysis, a sentence like ‘John can swim across the river’ says that there is some practically available action that is such that if John tries to do it, he swims across (...) the river. The essay argues that the act conditional analysis avoids the problems faced by existing accounts of agentive modality and shows how the act conditional analysis can be extended to an account of generic agentive modal claims. The upshot is a new vantage point on the role of agentive modal ascriptions in practical discourse: ability ascriptions serve as a kind of hypothetical guarantee, and compulsion ascriptions as a kind of nonhypothetical guarantee. (shrink)

This volume contains eighteen papers, three with new postscripts, that were written over the past 35 years. Five of the papers have not been previously published. Together they provide a comprehensive account of modal reality—the realm of possible worlds—from a Humean perspective, with excursions into neighboring topics in metaphysics. Part 1 sketches an account of reality as a whole, both the mathematical and the modal, defending a form of plenitudinous realism: every consistent proposition is true of some portion of reality. (...) Part 2 presents and defends a realist theory of concrete possible worlds with an absolute ontological distinction between the actual and the merely possible. Part 3 presents and defends a Humean account of modal plenitude, formulating and endorsing principles of recombination, of plenitude of possible structures, and of plenitude of alien contents. Part 4 applies the Humean account to truthmaking, mereology, spacetime, and quantities. I argue that holding fast to Humean strictures leads to views that differ in radical ways from those put forth by contemporary metaphysicians. (shrink)

Some arguments against David Lewis’s modal realism seek to exploit apparent inconsistencies between it and anthropic reasoning. A recent argument, in particular, seeks to exploit an inconsistency between modal realism and typicality anthropic premises, premises common in the literature on physical multiverses, to the effect that observers who are like human observers in certain respects must be typical in the relevant multiverse. Here I argue that typicality premises are not applicable to the description of Lewis’s metaphysical multiverse, where the proportions (...) of metaphysically possible observers possessing the pertinent properties can be independently established by metaphysical reasoning. However, other kinds of reasonable anthropic premises can be seen to be consistent with and usable within modal realism. (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)

The philosophy of modality investigates necessity and possibility, and related notions--are they objective features of mind-independent reality? If so, are they irreducible, or can modal facts be explained in other terms? This volume presents new work on modality by established leaders in the field and by up-and-coming philosophers. Between them, the papers address fundamental questions concerning realism and anti-realism about modality, the nature and basis of facts about what is possible and what is necessary, the nature of modal knowledge, modal (...) logic and its relations to necessary existence and to counterfactual reasoning. The general introduction locates the individual contributions in the wider context of the contemporary discussion of the metaphysics and epistemology of modality. (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)

It is often assumed that when one party felicitously rejects an assertion made by an- other party, the first party thinks that the proposition asserted by the second is false. This assumption underlies various disagreement arguments used to challenge contex- tualism about some class of expressions. As such, many contextualists have resisted these arguments on the grounds that the disagreements in question may not be over the proposition literally asserted. The result appears to be a dialectical stalemate, with no independent (...) method of determining whether any particular instance of disagreement is over the proposition literally asserted. In this paper, I propose an independent method for assessing whether a disagreement is about what’s literally asserted. Focusing on epistemic modals throughout, I argue that this method provides evidence that some epistemic modal disagreements are in fact not over the proposition literally asserted by the utterance of the epistemic modal sentence. This method provides a way to break the stalemate, and reveals a new data point for theories of epistemic modals to predict—that is, how there can be such modal disagreements. In the rest of the paper, I motivate a general theory of how to predict these kinds of disagreements, and then offer some brief remarks about how contextualist, relativist, and expressivist theories of epistemic modals might accommodate this new data point. (shrink)

Provisional draft, pre-production copy of my book “The Modal Future” (forthcoming with Cambridge University Press).

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)

Some claim that Composition as Identity (CI) entails Mereological Essentialism (ME). If this is right, then we have an effective modus tollens against CI: ME is clearly false, so CI is, too. Rather than deny the conditional, I will argue that a CI theorist should embrace ME. I endorse a theory of modal parts such that ordinary objects are spatially, temporally, and modally extended. Accepting modal parts is certainly beneficial to CI theorists, but it also provides elegant solutions to the (...) traditional puzzles of constitution, making it a competitive move in its own right. (shrink)

We analyze the precise modal commitments of several natural varieties of set-theoretic potentialism, using tools we develop for a general model-theoretic account of potentialism, building on those of Hamkins, Leibman and Löwe [14], including the use of buttons, switches, dials and ratchets. Among the potentialist conceptions we consider are: rank potentialism, Grothendieck–Zermelo potentialism, transitive-set potentialism, forcing potentialism, countable-transitive-model potentialism, countable-model potentialism, and others. In each case, we identify lower bounds for the modal validities, which are generally either S4.2 or S4.3, (...) and an upper bound of S5, proving in each case that these bounds are optimal. The validity of S5 in a world is a potentialist maximality principle, an interesting set-theoretic principle of its own. The results can be viewed as providing an analysis of the modal commitments of the various set-theoretic multiverse conceptions corresponding to each potentialist account. (shrink)

There are three primary aims of the book. The first, set out in the book's introduction, is to explain how two fairly recent developments in philosophy, externalism and modalism, provide the basis for a promising account of knowledge - an account that achieves anti-skeptical results and avoids Gettier-style counterexamples that are based on an agent having warranted beliefs that are merely luckily true. Epistemological externalism is the thesis that not all the factors that make a true belief a case of (...) knowledge need to be cognitively accessible or "internal" to the agent. Modalism, as the author construes it, is the use of possible worlds talk in clarifying what would or might be the case and what is necessarily so." "The second objective is to work through the different modalized epistemologies extant in the literature, assessing their strengths and weaknesses, with a view toward constructing a working theory. Finally, the author proposes the theory that knowledge is reliably formed, sensitive true belief, and defends the theory against objections."--Jacket. (shrink)

Designed for use by philosophy students, this book provides an accessible, yet technically sound treatment of modal logic and its philosophical applications. Every effort has been made to simplify the presentation by using diagrams in place of more complex mathematical apparatus. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, non-rigid designators, definite descriptions, and the de-re de-dictio distinction. Discussion of philosophical issues concerning (...) the development of modal logic is woven into the text. The book uses natural deduction systems and also includes a diagram technique that extends the method of truth trees to modal logic. This feature provides a foundation for a novel method for showing completeness, one that is easy to extend to systems that include quantifiers. (shrink)

This paper motivates and develops a novel semantic framework for deontic modals. The framework is designed to shed light on two things: the relationship between deontic modals and substantive theories of practical rationality and the interaction of deontic modals with conditionals, epistemic modals and probability operators. I argue that, in order to model inferential connections between deontic modals and probability operators, we need more structure than is provided by classical intensional theories. In particular, we need probabilistic structure that interacts directly (...) with the compositional semantics of deontic modals. However, I reject theories that provide this probabilistic structure by claiming that the semantics of deontic modals is linked to the Bayesian notion of expectation. I offer a probabilistic premise semantics that explains all the data that create trouble for the rival theories. (shrink)