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)

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.

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)

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)

Philosophers struggle to explain why human beings with deep cognitive impairments have a higher moral status than certain non-human animals. Modal personism promises to solve this problem. It claims that humans who lack the capacities of “personhood” and the potential to develop them nonetheless could have been persons. I argue that modal personism has poor prospects because it's hard to see how we could offer a plausible account of modal personhood. I search for an adequate understanding of modal personhood by (...) considering existing accounts and sketching new ones. But each account fails, either because it objectionably excludes some deeply cognitively impaired humans from the class of modal persons or because it makes modal personhood doubtfully relevant to moral status. And the modal personist cannot solve this problem by appealing to the misfortune suffered by modal persons. (shrink)

In this paper we reply to arguments of Kroon (“Characterization and Existence in Modal Meinongianism”. Grazer Philosophische Studien 86, 23–34) to the effect that Modal Meinongianism cannot do justice to Meinongian claims such as that the golden mountain is golden, and that it does not exist.

Fragmentalism allows incompatible facts to constitute reality in an absolute manner, provided that they fail to obtain together. In recent years, the view has been extensively discussed, with a focus on its formalisation in model-theoretic terms. This paper focuses on three formalisations: Lipman’s approach, the subvaluationist interpretation, and a novel view that has been so far overlooked. The aim of the paper is to explore the application of these formalisations to the alethic modal case. This logical exploration will allow us (...) to study (i) cases of metaphysical incompatibility between modal facts and (ii) cases of modal dialetheias. In turn, this will enrich our understanding of the role of impossibility in the fragmentalist framework. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of (...) large cardinal axioms, undecidable propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter 2 argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter 3 provides an abstraction principle for epistemic (hyper-)intensions. Chapter 4 advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal μ-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal μ-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal μ-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter 6 advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter 7 provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters 2 and 4 are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters 8-12 provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter 8 examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of Ω-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter 9 examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter 10 examines the philosophical significance of hyperintensional Ω-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter 11 provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter 12 avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (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.

In this paper, I support a hybrid view regarding the metaphysics of worlds. I endorse Lewisian Modal Realism for possible worlds (LMR). My aim is to come up with a hybrid account of impossible worlds that provides all the plenitude of impossibilities for all fine-grained intentional contents. I raise several challenges for such a plenitudinous hybrid theory. My version of hybrid modal realism builds impossible worlds as set-theoretic constructions out of genuine individuals and sets of them, that is, as set-theoretic (...) constructions from parts and sets of parts of genuine Lewisian worlds. _Structured worlds_ are defined as sets of tuples: structured entities built out of Lewisian ‘raw material’. These structured worlds are ersatz worlds, some of which are impossible. I claim that propositions must be sets of worlds rather than members of sets. Once the construction is in place, I evaluate the proposal and show that my hybrid account is able to supply a plenitude of impossibilities and thus giving the resources to make all the hyperintensional distinctions we are looking for, whilst remaining Lewisian-conservative. (shrink)

In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This constitutes a new proof of (...) S4 as being "the logic of topological spaces", but now under the perspective of paraconsistency. (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)

Considerations involving disagreement, as well as related considerations involving correction and retraction, have played an important role in recent debates about epistemic modals. For instance, it has been argued that contextualist views about epistemic modals have problems when it comes to explaining cases of disagreement. In response to these challenges, I explore the idea that the relevant cases of disagreement may involve credal disagreement. In a case of credal disagreement, the parties have different degrees of belief or credences. There does (...) not have to be a difference in outright beliefs in order for the parties to disagree. I argue that the idea of credal disagreement allows us to make sense of otherwise problematic cases of disagreement involving epistemic modals. I also discuss how these ideas can be extended to cases of correction and retraction. (shrink)

This chapter provides a selective survey of prominent theories of the semantics of deontic modals in logic and natural language. We focus on Kratzer’s (1977; 1981; 1991) semantics and extensions to this analysis. Kratzer’s semantics has been far and away the most influential theory of deontic modals, which provide a base case for the interpretation of normative language in general. Understanding the logic and truth-conditions of normative language is one of the core areas of metaethics. It informs our understanding of (...) normative arguments and normative reasoning. As this chapter will emphasize, some forms of normative language don’t allow for the inferences that classical logic trains philosophers to expect. Understanding what inferences are valid for normative language should impact our under-standing of how we reason, and should reason, about the normative. We will first look at how deontic modals are understood in the context of modal logic and natural language. Then we’ll survey some recent debates and discoveries in the literature on deontic modals in natural language. We close with some considerations about the relevance of natural language to metaethics. (shrink)

Recent work on the imagination has stressed the epistemic significance of imaginative experiences, notably in justifying modal beliefs. An immediate problem with this is that modal beliefs appear to admit of justification through the mere exercise of rational capacities. For instance, mastery of the concepts of square, circle, and possibility should suffice to form the justified belief that a square circle is not possible, and mastery of the concepts of pig, flying, and possibility should suffice to form a justified belief (...) that a flying pig is possible. It is thus unnecessary to try to imagine a square circle or a flying pig to justify these beliefs. In this paper, I consider three ways to defend the epistemic role of imagination in modal epistemology against this challenge. One claims that modal beliefs simply admit of justification by two separate sources: rational capacities and imaginative experience. Another holds that while beliefs about logical or conceptual modality can be justified entirely by rational capacities, beliefs about metaphysical modality require imaginative experiences. The third, which I defend, is the idea that imagination is relevant in the first instance not to modal knowledge but to modal understanding: even where imaginative experience is unnecessary for the justification of modal beliefs, it is indispensable for directly grasping certain modal propositions. (shrink)

Modality: A History provides readers a sweeping study of the history of philosophical work on modal concepts. Everyday discourse is saturated with appeals to what might be the case or to what must be true or to what cannot happen. Possibility, necessity, and impossibility are modal terms, and philosophers have long wondered how to best understand them. This volume traces the history of some of the most prominent and important contributions to our understanding of possibility and necessity over the (...) past two and half millennia of western philosophy, from ancient Greek philosophers through current debates in the 21st century. Over the course of nine chapters from prominent scholars, this volume traces a history of modal theorizing that begins with extended discussions of Aristotle and the Stoics. Several chapters discuss insights and disagreements among Latin, Arabic, and Jewish medieval scholastics, such as Al-Ghazâlî, Scotus, and Crescas. Three chapters center on early modern philosophers, whose modal views were deeply shaped by this conceptual inheritance but also departed from it in significant ways: Descartes, Malebranche, Locke, Spinoza, Leibniz, and Hume. Kant and Hegel's modal contributions are presented in their own chapter, and another chapter traces the legacy of Kant's account on early-to-mid 20th century modal views, including Husserl, Heidegger, Russell, and Quine. The revival of modal metaphysics in the more recent work of Kripke, Marcus, and Lewis has led to a new flourishing of modal theories, including in recent debates among neo-Aristotelians, as the final chapter illustrates. Although modal concepts are interesting and important on their own, theories of modality often intersect with other significant philosophical topics, such as time, freedom, and God. Modal concepts also extend beyond metaphysics. To illustrate the role of modality in other domains, several small-scale studies, or Reflections, are dispersed among these main chapters on modality in cosmology, religion, music, literature, and logic. Readers will learn how a seemingly timeless and changeless cluster of modal concepts have undergone significant revisions and enjoy a rich developmental history. (shrink)

My essay, “Multi-modal argumentation” was published in the journal, _Philosophy of the Social Sciences,_ in 1994. This information appeared again in my book, _Coalescent argumentation_ in 1997. In the ensuing twenty years, there have been many changes in argumentation theory, and I would like to take this opportunity to examine my now middle-aged theory in light of the developments in our discipline. I will begin by relating how a once keen intended lawyer and then formal logician ended up in argumentation (...) theory. (If you do not care to read this bit of autobiography, skip to Section 2). (shrink)

In this paper, we present a modality-free pre-rough algebra. Łukasiewicz Moisil algebra and Wajsberg algebra are equivalent under a transformation. A similar type of equivalence exists in our proposed definition and standard definition of pre-rough algebra. We obtain a few modality-free algebras weaker than pre-rough algebra. Furthermore, it is also established that modality-free versions for other analogous structures weaker than pre-rough algebra do not exist. Both Hilbert-type axiomatization and sequent calculi for all proposed algebras are presented.

This paper discusses two versions of reliabilism: modal and probabilistic reliabilism. Modal reliabilism faces the problem of the missing closeness metric for possible worlds while probalistic reliabilism faces the problem of the relevant reference class. Despite the severity of these problems, reliabilism is still very plausible (also for independent reasons). I propose to stick with reliabilism, propose a contextualist (or, alternatively, harmlessly relativist) solution to the above problems and suggest that probabilistic reliabilism has the advantage over modal reliabilism.

This book concerns the philosophical analysis of modal sentences. David Lewis' Modal Translation Scheme 'translates' sentences of quantified modal logic into sentences of predicate logic supplemented by counterpart theory. A number of theoretical advantages are thereby secured. One component of the translation scheme makes reference to non-actual but possible worlds i.e. the primitive predicate "at a world(s), w". The author addresses the problem of advanced modal sentences which threaten this predicate and so the ability of genuine realism to secure the (...) aforementioned theoretical benefits. The problem of advanced modal sentences is a relatively new field of philosophical research. This ground-breaking book will primarily be of interest to researchers in modality, particularly those working in this field. (shrink)

Discrimination is a central epistemic capacity but typically, theories of discrimination only use discrimination as a vehicle for analyzing knowledge. This paper aims at developing a self-contained theory of discrimination. Internalist theories of discrimination fail since there is no compelling correlation between discriminatory capacities and experiences. Moreover, statistical reliabilist theories are also flawed. Only a modal theory of discrimination is promising. Versions of sensitivity and adherence that take particular alternatives into account provide necessary and sufficient conditions on discrimination. Safety in (...) contrast is not sufficient for discrimination as there are cases of safety that are clearly instances of discrimination failure. The developed account of discrimination between objects will be extended to discrimination between kinds and between types. (shrink)

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

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)

Graph-based frames have been introduced as a logical framework which internalises an inherent boundary to knowability (referred to as ‘informational entropy’), due, e.g. to perceptual, evidential or linguistic limits. They also support the interpretation of lattice-based (modal) logics as hyper-constructive logics of evidential reasoning. Conceptually, the present paper proposes graph-based frames as a formal framework suitable for generalising Pawlak's rough set theory to a setting in which inherent limits to knowability exist and need to be considered. Technically, the present paper (...) establishes systematic connections between the first-order correspondents of Sahlqvist modal reduction principles on Kripke frames, and on the more general relational environments of graph-based and polarity-based frames. This work is part of a research line aiming at: (a) comparing and inter-relating the various (first-order) conditions corresponding to a given (modal) axiom in different relational semantics; (b) recognising when first-order sentences in the frame-correspondence languages of different relational structures encode the same ‘modal content’; (c) meaningfully transferring relational properties across different semantic contexts. The present paper develops these results for the graph-based semantics, polarity-based semantics, and all Sahlqvist modal reduction principles. As an application, we study well known modal axioms in rough set theory (such as those corresponding to seriality, reflexivity, and transitivity) on graph-based frames and show that, although these axioms correspond to different first-order conditions on graph-based frames, their intuitive meaning is retained. This allows us to introduce the notion of hyperconstructivist approximation spaces as the subclass of graph-based frames defined by the first-order conditions corresponding to the same modal axioms defining classical generalised approximation spaces, and to transfer the properties and the intuitive understanding of different approximation spaces to the more general framework of graph-based frames. The approach presented in this paper provides a base for systematically comparing and connecting various formal frameworks in rough set theory, and for the transfer of insights across different frameworks. (shrink)

This essay defends two theses regarding the explanation, or ground, of modality in the early modern period. First, for philosophers in the period, essences ground a range of important modal facts. Second, as the period progresses, we witness increased skepticism about certain modal facts, due to a growing skepticism about the scope or existence of essences. These theses are supported by examination of three case studies: Descartes’ treatment of substance and mode (which forms the core of his ontology); Malebranche’s (...) treatment of causation (which bears on his defense of occasionalism); and Locke’s treatment of necessary connections among properties (which is related to his accounts of individuals and kinds). It is shown that in each case, claims about necessity and possibility take center stage, and that in each case, the status of these claims hinges on the status of claims about essences. (shrink)

It is commonly believed that intrinsically bad possible worlds are inconsistent with the perfect goodness of God. A perfectly good being could not exist in possible worlds that are intrinsically bad. Indeed it is widely believed that possible worlds that are insufficiently good are inconsistent with a perfectly good God. Modal atheological arguments aim to show that, since the pluriverse includes intrinsically bad worlds and insufficiently good worlds, there necessarily does not exist a perfectly good God. I show that modal (...) atheological arguments are in general invalid. Modal atheological arguments fail to show that there exists no perfectly good God even on the assumption that there are extremely bad worlds in the pluriverse. Modal atheological arguments depend entirely on the logic of modality in S5. But the logic of S5 ensures that a perfectly good God is consistent with extremely bad possible worlds and so guarantees that a perfectly good God is consistent with a plenitudinous pluriverse. (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.

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)

Modal intuitions are not only the primary source of modal knowledge but also the primary source of modal error. An explanation of how modal error arises — and, in particular, how erroneous modal intuitions arise — is an essential part of a comprehensive theory of knowledge and evidence. This chapter begins with a summary of certain preliminaries: the phenomenology of intuitions, their fallibility, the nature of concept-understanding and its relationship to the reliability of intuitions, and so forth. It then identifies (...) two sources of modal error: the first has to do with the failure to distinguish between metaphysical possibility and various kinds of epistemic possibility; the second, with the local misunderstanding of one's concepts. The first source of error is widely misunderstood; the second source has not been discussed in philosophical literature. This source of modal error, and the potential to overcome it, has wide-ranging implications for philosophical method. The failure to understand these sources of modal error has recently led to sceptical accounts of intuition and modal error, which are, ultimately self-defeating. (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.

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)

This paper aims to provide a mathematically tractable background against which to model both modal cognitivism and modal expressivism. I argue that epistemic modal algebras, endowed with a hyperintensional, topic-sensitive epistemic two-dimensional truthmaker semantics, comprise a materially adequate fragment of the language of thought. I demonstrate, then, how modal expressivism can be regimented by modal coalgebraic automata, to which the above epistemic modal algebras are categorically dual. I examine five methods for modeling the dynamics of conceptual engineering for intensions and (...) hyperintensions. I develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. I examine then the virtues unique to the modal expressivist approach here proffered in the setting of the foundations of mathematics, by contrast to competing approaches based upon both the inferentialist approach to concept-individuation and the codification of speech acts via intensional semantics. (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)