This special issue of the Canadian Journal of Philosophy is dedicated to Timothy Williamson's work on modality. It consists of a new paper by Williamson followed by papers on Williamson's work on modality, with each followed by a reply by Williamson. -/- Contributors: Andrew Bacon, Kit Fine, Peter Fritz, Jeremy Goodman, John Hawthorne, Øystein Linnebo, Ted Sider, Robert Stalnaker, Meghan Sullivan, Gabriel Uzquiano, Barbara Vetter, Timothy Williamson, Juhani Yli-Vakkuri.

In recent work, E. J. Lowe presents an essence-based account of our knowledge of metaphysical modality that he claims to be superior to its main competitors. I argue that knowledge of essences alone, without knowledge of a suitable bridge principle, is insufficient for knowing that something is metaphysically necessary or metaphysically possible. Yet given Lowe's other theoretical commitments, he cannot account for our knowledge of the needed bridge principle, and so his essence-based modal epistemology remains incomplete. In addition to (...) that, Lowe's account implies a psychologically unrealistic reconstruction of how we ordinarily acquire knowledge of metaphysical modalities. The discussion of Lowe's suggestive essence-based account is also intended as a case study that illustrates a more general problem in the epistemology of modality: the great difficulty of explaining our modal knowledge in terms of a single overtly nonmodal kind of knowledge. The failure of Lowe's account suggests that such a sweeping reductive explanation of our modal knowledge might simply not be available. This should be good news for those philosophers who champion less reductive or more pluralistic accounts of our modal knowledge. (shrink)

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

I am interested in extending modal calculi by adding propositional quantifiers, given by the rules for quantifier introduction: provided that p does not occur free in A.

A new modal logic is introduced. It describes properties of provability by interpreting modality as a deductive closure operator on sets of formulas. Logic is proven to be decidable and complete with respect to this semantics.

This is indeed a very nice draft that I have read with great pleasure, and that has helped me to better understand the completeness proof for LCC. Modal fixed point logic allows for an illuminating new version (and a further extension) of that proof. But still. My main comment is that I think the perspective on substitutions in the draft paper is flawed. The general drift of the paper is that relativization, (predicate) substitution and product update are general operations (...) on models, and that it is important to check whether given logical languages are closed under these operations. FO logic is closed under relativization, predicate substitution and product constructions (such as those involved in relative interpretation). The minimal modal logic is closed under relativization, which explains the reduction of epistemic logic (withhout common knowledge) + public announcement to epistemic logic simpliciter (as observed in Van Benthem, [2]). The reduction breaks down as soon as one adds common knowledge. The minimal modal logic is also closed under substitution, which explains the reduction of epistemic logic plus (publicly observable) factual change to epistemic logic simpliciter, via the following reduction axioms (I use !p := φ for the operation of publicly changing the truth value of p to φ): [!p := φ]p ↔ φ [!p := φ]q ↔ q (p and q syntactically different ) [!p := φ]¬ψ ↔ ¬[!p := φ]ψ [!p := φ](ψ1 ∧ ψ2) ↔ [!p := φ]ψ1 ∧ [!p := φ]ψ2 [!p := φ][i]ψ ↔ [i][!p := φ]ψ Unlike the case of relativisation, this can be extended to the case of epistemic logic with common knowledge, by means of: [!p := φ]CGψ ↔ CG[!p := φ]ψ We get the following.. (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)

A finitary characterization for non-well-founded sets with finite transitive closure is established in terms of a greatest fixpoint formula of the modal μ-calculus. This generalizes the standard result in the literature where a finitary modal characterization is provided only for wellfounded sets with finite transitive closure. The proof relies on the concept of automaton, leading then to new interlinks between automata theory and non-well-founded sets.

Obituary. Ruth Barcan Marcus' contributions to modal logic and to semantics are discussed.

The volume under review contains work dedicated to the memory of Leo Esakia, who died in 2010, after having worked for over 40 years towards developing duality theory for modal and intuitionistic logics. The collection comprises ten technical contributions that follow the first chapter, in which the reader can find information on Esakia’s studies and career, as well as a complete list of his research publications. In the sequel, we will refer briefly to each of these ten chapters, following (...) the order in the list of contents.B. Jónsson and A. Tarski, in two papers they published in the early 1950s in the American Journal of Mathematics, initiated the study of duality for Boolean algebras with additional operations, via the theory of canonical extensions. Esakia was among the first researchers who studied duality for lattices with additional operations [Topological Kripke models. Soviet Math.Dokl. 15 , 147–151], in particular for Heyting algebras and S4 modal algebras. M. Gehrke, a .. (shrink)

The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to partial recursive function type constructor under the above interpretation. The cases of deterministic and non-deterministic functions are considered and for both of them semantically complete modal logics are described and decidability of these logics is established.

Hume regards the ‘absolute’ necessity attending demonstrable truths as simply an expression of our imaginative blocks, and thereby avoids any commitment to a mind-independent and extra-empirical domain of absolute modal properties and facts. I develop this expressivist interpretation of Hume’s metaphysics of absolute modality, situate it against a wider understanding of Hume’s philosophy of language, and defend it against some recent objections.

A striking feature of the contemporary philosophical scene is the flourishing of a number of research programs aimed in one way or another at making intentional soup out of nonintentional bones—more carefully, specifying in a resolutely nonintentional, nonsemantic vocabulary, sufficient conditions for states of an organism or other system to qualify as contentful representations. This is a movement with a number of players, but for my purposes here, the work of Dretske, Fodor, and Millikan can serve as paradigms. The enterprise (...) in which they are jointly engaged is not so much one of conceptual analysis as it has been traditionally understood as one of conceptual engineering. That is, instead of thinking about what ordinary people or even sophisticated philosophers already mean by terms such as ‘representation’, they appeal to the tools of the special sciences to describe abstractly, but in criticizable detail, how one might craft a situation in which some state arguably deserves to be characterized as ‘representationally contentful’ in various important senses. Insofar as the theories are good ones, they may shed light on how human knowers actually work. But their immediate aim is a broader one: to say what would count as doing the trick, rather than how we manage to do it. (shrink)

L’objectif de cette introduction est double : elle présente les articles rassembles dans ce volume et offre une synthèse des développements récents de l’épistemologie des modalités.The role of this introduction is twofold: it presents the papers collected in this volume and offers a synthesis of recent developments of the epistemology of modality.

This chapter analyzes several key themes in Kant’s views about modality. We begin with the pre-critical Only Possible Argument in Support of a Demonstration of the Existence of God, in which Kant distinguishes between formal and material elements of possibility, claims that all possibility requires an actual ground, and argues for the existence of a single necessary being. We then briefly consider how Kant’s views change in his mature period, especially concerning the role of form and thought in defining modality. (...) Kant’s mature views, however, present two difficult interpretive puzzles. The first puzzle concerns whether Kant has a generally reductive view of modality. While Kant’s views on logical modality, the role of actuality in grounding possibility, and the relation of modality to cognition all suggest reduction, we argue that the categorial status of modal concepts and the difficulty in even identifying amodal grounds for modal facts all suggest a non-reductive view. The second puzzle concerns whether Kant accepts modal facts or properties at the noumenal level. While Kant’s appeal to noumenal necessary connections, the contingency of noumenal willing, and the idea of a necessary noumenal being suggest that he endorses noumenal modality, his claims that modal concepts express only relations to the faculty of cognition and his claim that modal concepts arise from our distinctive psychological structures, we argue, suggest that he rejects noumenal modality. We conclude by considering potential solutions to these puzzles. (shrink)

In The Consolation of Philosophy Boethius addresses two main problems posed by the problem of future contingents that shed important light on his conception of necessity and possibility: (1) a logical problem that alleges that if propositions about the future are true now then they are necessarily true, and (2) a theological problem that centers on a supposed incompatibility between divine foreknowledge and a contingent future. In contrast to established readings of the Consolation, I argue that a proper understanding of (...) Book V requires understanding the modal concepts employed there in atemporal terms. This interpretation requires revising our traditional understanding of the two problems present in the Consolation text, particularly in seeing how timeless knowledge or truth could be conceived as a threat to human freedom. It also stresses the importance of a strategy used by Boethius to disambiguate the scope of modal operators used in his opponent’s arguments and how that strategy unifies his discussion in Book V. (shrink)

BERTRAND RUSSELL ON MODALITY AND LOGICAL RELEVANCE - SECOND EDITION of 2015. Praise for the first edition of 1999: "In the twenty-nine years since Russell's death, much of the major scholarship has drawn heavily on his manuscripts and unpublished correspondence. The author shows that the published Russell is capable of new interpretations; in particular, that modal notions such as possibility have a greater place in various aspects of his logical and philosophical thought than has been previously imagined." -Ivor Grattan-Guinness, (...) Foreword to the first edition. EXCERPT FROM PUBLISHED REVIEW: "Dejnožka's book is the first full-length study of modality in Russell. It is useful for its very full survey of passages in which Russell makes use of or alludes to modal notions. Dejnožka's command of Russell's huge output is indeed impressive and his utilization of it thorough...." - Nicholas Griffin, Studia Logica. EXCERPT FROM PUBLISHED REVIEW: "Dejnožka's book raises a very important point in the history of formal logic. Until now the major studies on this topic have drawn heavily on the development of classical logic as standardized by Gottlob Frege and Bertrand Russell. Dejnožka challenges the reader to open his mind for a new interpretation of Russell's work, in particular that modal and relevance notions have a greater place in his philosophy of logic than has been stressed before.... "Dejnožka rightly observes that many of Russell's insights on modality are a result of his discussions with Hugh MacColl, who was indeed the first to seriously attempt to develop formal modal logic. This particularly applies to Russell's conception of a modal logic without modal operators....That is, classical logic can be used to simulate modal expressions. Thus, the notions of (logical) necessity and possibility are not 'fundamental notions'....On this basis, Dejnožka develops a higher level of modality, where the quantification scope extends to the predicates yielding what Russell calls 'fully general propositions'.... "The best studied translation method is known as the standard translation, and it is quite compatible with Dejnožka's suggestions.... "Dejnožka's book is full of material which stimulates [one] to rethink Russell's philosophy of logic and...it is greatly to the author's credit that he brings to light such a wealth of crucial issues in the history and philosophy of logic. - Shahid Rahman, History and Philosophy of Logic. BOOK DESCRIPTION: This book is the only exhaustive study of Russell on modality and logical relevance ever written. This is the second edition, revised over a period of over sixteen years, and over twice as long. Russell initially rejects the possibility of a modal logic in an unpublished paper written ca. 1903-05 and read to an audience in 1905. But the very next year, he adopts the theory of modality he had rejected, and he repeats that theory in published works for many years to come. That theory, together with other texts scattered among Russell's writings, implies eight modal logics which Russell himself never expressly accepted. And Russell's express acceptance of the early Wittgenstein's theory of entailment ("following from") as truth-ground containment implies a deductive relevance logic in Russell's writings which Russell himself never expressly accepted. The book ends with a look at John Maynard Keynes and Anglo-American evidence law as the origins of Russell's theory of probability as degree of logical relevance. Thus the book is written toward the reunion of modern classical logicians with modal logicians and relevantists. On the reunion of modern classical logicians with relevantists, please see also The Concept of Relevance and the Logic Diagram Tradition (2012). Thus I hope to have created two new fields of Russell studies. I may have created a new legal field as well: the history of logical relevance in evidence law: 132 pages (368-500) in chapter 10. (shrink)

This collection of new essays on sensory individuals in unimodal and multimodal perception features contributions by outstanding researchers in the fields of philosophy of perception, experimental psychology, and cognitive neuroscience. The topics investigated include conceptual, developmental, and methodological aspects of object perception, and especially how various sense modalities construct their objects from sensory features and feature bearers. The interdisciplinary approach offered has enabled new directions in research on this subject. As ordered in this volume, the topics of the contributions progress (...) from treating neural sensory processes as primarily unisensory towards approaches that take perceptual processing to be modality-independent, meta-modal, and multimodal. Even within these latter approaches, sensory stimuli, sensory properties, brain activations, and corresponding perceptual phenomenology have often been characterized in a modality-specific way. Thus, it is timely to explore the relation between those processes that are unisensory and those that are multisensory. One of the primary themes of this collection is examining whether the basic building blocks of human perception are best understood as modality-dependent units of different forms or in terms of multimodal perceptual objects. Another theme is the relation between low-level object processing (segmentation and perceptual grouping processes) and high-level object knowledge embracing object concept and object-related expectations. A final theme is the role that perceptual objects play as loci of unification in unimodal and multimodal perception, namely that they enable binding and integration of sensory properties to individual entities or events. (shrink)

This paper discusses the account of alethic modality as presented by Wilfrid Sellars in his earlier work from 1947 to 1958. Its aim is twofold. First, I discuss Sellars' analysis by exploring its historical relationship to Carnap's account of modality. I argue that Carnap's early syntactic treatment of modality profoundly influenced Sellars' own so-called ‘regulist' account of modality in terms of rules of inference. Furthermore, it is suggested that Sellars' lesser-known possible worlds analysis was influenced by Carnap's later semantic account (...) of modality. The second aim of the paper is a critical one. I raise a number of objections to Sellars’ account of modality and argue that his account confronts some serious limitations. I also argue that Sellars does not provide a satisfying explanation of the relationship between his regulist account and his possible worlds analysis. I offer such an explanation by arguing that his regulist account should be understood as a pragmatic account of what is conveyed by the use of modal sentences, whereas his possible worlds analysis is a semantic account of the asserted content of modal statements. That is, the regulist account and the possible worlds analysis have different explanatory targets. (shrink)

Name der Zeitschrift: Kant-Studien Jahrgang: 108 Heft: 3 Seiten: 315-337.

Given a class $$\mathcal {C}$$ of models, a binary relation $$\mathcal {R}$$ between models, and a model-theoretic language L, we consider the modal logic and the modal algebra of the theory of $$\mathcal {C}$$ in L where the modal operator is interpreted via $$\mathcal {R}$$. We discuss how modal theories of $$\mathcal {C}$$ and $$\mathcal {R}$$ depend on the model-theoretic language, their Kripke completeness, and expressibility of the modality inside L. We calculate such theories for the (...) submodel and the quotient relations. We prove a downward Löwenheim–Skolem theorem for first-order language expanded with the modal operator for the extension relation between models. (shrink)

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

This paper investigates the truth values of modal sentences within fictional discourse. I investigate the consequences of (im)possible worlds–based theories of truth in fiction for the truth, in fiction, of (explicit) modal sentences. I elaborate on the consequences of explicit reliable (modal) sentences within the truth-in-fiction operators if we embed the normal modal logics. I prove that the current main possible worlds theories of truth-in-fiction make explicit reliable sentences within fiction truth-value equivalent to their possibility. This (...) has non-intuitive consequences if we employ normal modal logics. These consequences are shown to be contradictory. The main argument of the paper thus concerns the inconsistency of embedding the systems of normal modal logics within the truth-in-fiction operators provided in the discussion. (shrink)

1. Professor Brandom’s paper is addressed to a methodological question: When we set out to account for the intentionality of thought and language, what resources may we exploit? Which notions may we use? Brandom is a famously ambitious theorist. Unlike his colleague, John McDowell, Brandom has long maintained that we should at least aspire to explain intentionality in non-intentional terms. This leaves it open, however, which non-intentional resources are legitimate.

In this article I present several challenges to the view that Shelly Kagan calls ‘modal personism’. First, there is a plausible account of our identity that, if true, greatly diminishes the scope of Kagan's view. But the scope of the view is already quite limited because the category of modal persons is restricted to those non-persons that had but have lost the potential to become persons. If the category were to include non-persons that retain the potential to become (...) persons, Kagan's view would have implausible implications about abortion and about the moral status of certain animals. (shrink)

We show that modal logics characterized by a class of frames satisfying the insertion property are suitable for Reiter's default logic. We refine the canonical fix point construction defined by Marek, Schwarz and Truszczyński for Reiter's default logic and thus we addrress a new paradigm for nonmonotonic logic. In fact, differently from the construction defined by these authors. we show that suitable modal logics for such a construction must indeed contain K D4. When reflexivity is added to the (...) modal logic used for the fix point construction then we come to the Marek Schwarz and Truszczyński framework for Reiter's default logic. Our framework, in fact, is appropriate also to the family of modal logics in between S4 and S4f. If, instead, reflexivity is dropped, then we show that a new family of modal logics is gained, namely the modal logics in between KD4 and KD4Z. The upper bound can be extended to the modal logic KD4LZ whenever the propositional language taken into account is finite. (shrink)

The paper has a two-fold objective; firstly, scrutinising neo-Meinongianism as recently championed by Francesco Berto. Secondly, trying and arguing that the dispute between Meinongianism and (various kinkds of) Actualism is hardly cutting some relevant ice.