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)

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)

In this two-part paper we present paranormal modal logic: a modal logic which is both paraconsistent and paracomplete. Besides using a general framework in which a wide range of logics – including normal modal logics, paranormal modal logics and classical logic – can be defined and proving some key theorems about paranormal modal logic (including that it is inferentially equivalent to classical normal modal logic), we also provide a philosophical justification for the view that paranormal modal logic is a formalization (...) of the notions of skeptical and credulous plausibility. (shrink)

En este ensayo me propongo dos cosas: a) indicar las razones por las cuales la interpretación predicativa de la teoría de la forma de Platón no es la más adecuada. b) proponer una interpretación alternaiva ¿también predicativa¿ pero más completa, agregando el concepto de modalidad. Creo que la última interpretación se encuentra más cerca del espíritu del texto original, en el sentido que estoy convencido de que algunas de las principales intuiciones que subdeterminan la teoría de las formas de Platón (...) están más desarrolladas y fijas en el lenguaje (por supuesto en un lenguaje diferente) por tal comentario explicativo. Más aún, en esta manera están asociadas ¿sugiriendo una relación histórica¿ a consideraciones actuales en relación al objetivo del conocimiento científico ya que están formuladas en términos modales (es decir, nomotéticos). (shrink)

Modal Meinongianism—the version of Meinongianism invented by Graham Priest—presupposes that we can think about absolute impossibilities. I defend the view that we can, by tidying up a couple of loose ends in Priest’s arguments to this effect from his book Towards Non-Being.

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.

Persuasive and perceptive, Rhetoric, Modality, Modernity is a novel rewriting of the history of rhetoric and a heady examination of the motives, issues, and ...

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

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.

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)

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)

If we accept the idea that the value of a “logic” depends on its ability to fit the usual meaning of the “logical constants” which it formalises and the inferences we draw on their basis, we may ask if the meaning of “possible” is well captured by normal modal logic. We are faced with the following puzzle: if is meaningful and non contradictory is it not a logical truth that ? First, it is shown why there is no logical law (...) of the form , being a neutral wff, and then some philosophical conclusions are drawn: “possible” relative to truth must be distinguished from possible “relative” to meaning, and the former only is formalised in modal logic. (shrink)

According to Amie Thomasson’s modal normativism, the function of modal discourse is to convey semantic rules. But what is a "semantic rule"? I raise three worries according to which there is no conception of a semantic rule that can serve the needs of a modal normativist. The first worry focuses on de re and a posteriori necessities. The second worry concerns Thomasson's inferential specification of the meaning of modal terms. The third worry asks about the normative status of semantic rules.

The paper defends the view that that a significant part of metaphysics should be understood as conceptual engineering, and explores its epistemological advantages and metaphysical implications. It discusses the challenge raised by moderate modal skepticism, which points out the lack of reliable methods for verifying modal statements through thought experiments. As I argue, a normative stance on metaphysical methodology, understanding it as engaging in conceptual engineering project, justifies the use of this method. By adopting an approach where the method of (...) cases offers reasons for adopting specific normative constraints on concept usage, the method becomes justifiable. Consequently, it can be employed to justify the revision of conceptual schemes and, in turn, validate certain modal claims about entities falling under the scrutinized concepts. The paper explores how this approach can methodologically enrich conceptual engineering-focused perspectives in metaphysics and examines its metaphysical consequences. In particular, it demonstrates that despite the mind-dependency of the method of cases results, it still leaves room for a metaphysically realistic viewpoint. (shrink)

In this paper, we consider recent attempts to metaphysically explain agentive modality in terms of conditionals. We suggest that the best recent accounts face counterexamples, and more worryingly, they take some agentive modality for granted. In particular, the ability to perform basic actions features as a primitive in these theories. While it is perfectly acceptable for a semantics of agentive modal claims to take some modality for granted in getting the extension of action claims correct, a metaphysical (...) explanation of agentive modality cannot, at least not in the way that conditional approaches to agentive modality do. We argue that this problem was present even in the classical conditional analysis. By a pessimistic induction, we suggest that, probably, no conditional approach to agentive modality will succeed. (shrink)

It is my aim in this paper to show that the contemporary assimilation of essence to modality is fundamentally misguided and that, as a consequence, the corresponding conception of metaphysics should be given up. It is not my view that the modal account fails to capture anything which might reasonably be called a concept of essence. My point, rather, is that the notion of essence which is of central importance to the metaphysics of identity is not to be understood (...) in modal terms or even to be regarded as extensionally equivalent to a modal notion. The one notion is, if I am right, a highly refined version of the other; it is like a sieve which performs a similar function but with a much finer mesh. (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 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)

We introduce quantificational modal operators as dynamic modalities with (extensions of) Henkin quantifiers as indices. The adoption of matrices of indices (with action identifiers, variables and/or quantified variables as entries) gives an expressive formalism which is here motivated with examples from the area of multi-agent systems. We study the formal properties of the resulting logic which, formally speaking, does not satisfy the normality condition. However, the logic admits a semantics in terms of (an extension of) Kripke structures. As a consequence, (...) standard techniques for normal modal logic become available. We apply these to prove completeness and decidability, and to extend some standard frame results to this logic. (shrink)

The practice of scientific modelling often resorts to hypothetical, false, idealised, targetless, partial, generalised, and other types of modelling that appear to have at least partially non-actual targets. In this paper, I will argue that we can avoid a commitment to non-actual targets by sketching a framework where models are understood as having networks of possibilities as their targets. This raises a further question: what are the truthmakers for the modal claims that we can derive from models? I propose that (...) we can find truthmakers for the modal claims derived from models in actuality, even in the case of supposedly non-actual targets. I then put this framework to use by examining a case study concerning the modelling of superheavy elements. (shrink)

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)

Originally published in 1993, Modalities in Medieval Philosophy looks at the idea of modality as multiplicity of reference with respect to alternative domains. The book examines how this emerged in early medieval discussions and addresses how it was originally influenced by the theological conception of God acting by choice. After a discussion of ancient modal paradigms, the author traces the interplay of old and new modal views in medieval logic and semantics, philosophy and theology. A detailed account is given (...) of late medieval discussions of the new modal logic, epistemic logic, and the logic norms. These theories show striking similarities to some basic tenets of contemporary approaches to modal matters. This work will be of considerable interest to historians of philosophy and ideas and philosophers of logic and metaphysics. (shrink)

A consequence relation is strongly classical if it has all the theorems and entailments of classical logic as well as the usual meta-rules (such as Conditional Proof). A consequence relation is weakly classical if it has all the theorems and entailments of classical logic but lacks the usual meta-rules. The most familiar example of a weakly classical consequence relation comes from a simple supervaluational approach to modelling vague language. This approach is formally equivalent to an account of logical consequence according (...) to which α1, ..., αn entails β just in case □α1, ..., □αn entails □β in the modal logic S5. This raises a natural question: If we start with a different underlying modal logic, can we generate a strongly classical logic? This paper explores this question. In particular, it discusses four related technical issues: (1) Which base modal logics generate strongly classical logics and which generate weakly classical logics? (2) Which base logics generate themselves? (3) How can we directly characterize the logic generated from a given base logic? (4) Given a logic that can be generated, which base logics generate it? The answers to these questions have philosophical interest. They can help us to determine whether there is a plausible supervaluational approach to modelling vague language that yields the usual meta-rules. They can also help us to determine the feasibility of other philosophical projects that rely on an analogous formalism, such as the project of defining logical consequence in terms of the preservation of an epistemic status. (shrink)

(2012). Modal logics for reasoning about infinite unions and intersections of binary relations. Journal of Applied Non-Classical Logics: Vol. 22, No. 4, pp. 275-294. doi: 10.1080/11663081.2012.705960.

It is widely agreed that the intelligibility of modal metaphysics has been vindicated. Quine's arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.2 But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest real notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every real sense. If there were nothing otherwise “uniquely metaphysically significant” about (...) metaphysical necessity, then paradigmatic metaphysical necessities would be necessary in one sense of “necessary”, not necessary in another, and that would be it. The question of whether they were necessary simpliciter would be like the question of whether the Parallel Postulate is true simpliciter – understood as a pure mathematical conjecture, rather than as a hypothesis about physical spacetime. In a sense, the latter question has no objective answer. In this article, I argue that paradigmatic questions of modal metaphysics are like the Parallel Postulate question. I then discuss the deflationary ramifications of this argument. I conclude with an alternative conception of the space of possibility. According to this conception, there is no objective boundary between possibility and impossibility. Along the way, I sketch an analogy between modal metaphysics and set theory. (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.

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)

Philosophers distinguish between having a property essentially and having it accidentally. The way the distinction has been drawn suggests that it is modal in character, and so that it can be captured in terms of necessity, or cognate notions. The present chapter takes the suggestion at face value by considering a number of modal characterizations of the essential/accidental distinction that have been articulated and discussed since the early 20th century, as well as some of the challenges that they face.

It is widely held that metaphysical modality is the broadest non-epistemic, alethic modality, and that /a posteriori/ modal essentialist truths, like that gold has atomic number 79, enjoy the necessity of the broadest alethic modality. One prominent argument for these conclusions--given by Cian Dorr, John Hawthorne, and Juhani Yli-Vakkuri--rests upon an extremely dubious premise: that certain pairs of properties—e.g., being gold and being made of atoms containing 79 protons—are one and the very same property. The two properties (...) are seen to be distinct on independent philosophical grounds. Metaphysical modality is in fact a restricted alethic modality. In particular, mathematical modality is broader than metaphysical modality. Arguably, the broadest alethic modality is logical modality, which is distinct from metaphysical modality. Even if it is metaphysically necessary that gold have atomic number 79, there is no logical/analytical inconsistency in the supposition that it does not. (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)

This book explores noteworthy approaches to modal syllogistic adopted by medieval logicians including Abélard, Albert the Great, Avicenna, Averröes, Jean Buridan, Richard Campsall, Robert Kilwardby, and William of Ockham. The book situates these approaches in relation to Aristotle's discussion in the Prior and Posterior Analytics, and other parts of the Organon, but also in relation to the thought of Alexander of Aphrodisias and Boethius on the one hand, and to modern interpretations of the modal syllogistic on the other. Problems explored (...) include: Aristotle's doctrine of modal conversion, the pure and mixed necessity-moods, modal ecthesis, the pure and mixed contingency-moods, and Aristotle's use of counter-examples. Medieval logicians brought various concepts to bear on these problems, including the distinction between per se and per accidens terms, the notion of essential predication, the distinction between ut nunc and simpliciter propositions, the distinction between de dicto and de re modals, and the notion of ampliation. All these are examined in this book. (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)

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)

Modals in St’át’imcets (Lillooet Salish) show two differences from their counterparts in English. First, they have variable quantificational force, systematically allowing both possibility and necessity interpretations; and second, they lexically restrict the conversational background, distinguishing for example between deontic and (several kinds of) epistemic modality. We provide an analysis of the St’át’imcets modals according to which they are akin to specific indefinites in the nominal domain. They introduce choice function variables which select a subset of the accessible worlds. Following (...) Klinedinst, we assume distributivity over the resulting set of worlds. St’át’imcets modals thus receive a uniform interpretation as (distributive) pluralities. The appearance of variability in modal force arises because the choice function can select a larger or smaller subset of accessible worlds. Finally, we discuss the implications of our analysis for the investigation of modal systems in other languages. (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)

I present an internal problem for David Lewis’s genuine modal realism. My aim is to show that his analysis of modality is inconsistent with his metaphysics. I consider several ways of modifying the Lewisian analysis of modality, but argue that none are successful. I argue that the problem also affects theories related to genuine modal realism, including the stage theory of persistence and modal fictionalism.

This collection highlights the new trend away from rationalism and toward empiricism in the epistemology of modality. Accordingly, the book represents a wide range of positions on the empirical sources of modal knowledge. Readers will find an introduction that surveys the field and provides a brief overview of the work, which progresses from empirically-sensitive rationalist accounts to fully empiricist accounts of modal knowledge. Early chapters focus on challenges to rationalist theories, essence-based approaches to modal knowledge, and the prospects for (...) naturalizing modal epistemology. The middle chapters present positive accounts that reject rationalism, but which stop short of advocating exclusive appeal to empirical sources of modal knowledge. The final chapters mark a transition toward exclusive reliance on empirical sources of modal knowledge. They explore ways of making similarity-based, analogical, inductive, and abductive arguments for modal claims based on empirical information. Modal epistemology is coming into its own as a field, and this book has the potential to anchor a new research agenda. (shrink)