Neste estudo, dá-se continuidade à exposição do scotismo do mestre franciscano chileno Alfonso Briceño (1587-1668), pondo a ênfase em um de seus cinco Apêndices Metafísicos, que constam em suas Controversiae (Madri, 1639-1642). No terceiro Apêndice Metafísico, após expor o conceito metafísico de “distinção”, após apresentar a sua doutrina da “distinção de razão” e após uma digressão sobre a “distinção precisiva”, Briceño dá início à sua apresentação da “distinção real”, da qual a “distinção formal” será um (...) tipo especial e particularmente controverso. Passo intermediário para a compreensão da distinção formal é uma breve exposição dos tipos de distinção real e uma discussão articulada sobre um tipo especial de “distinção modal” na escola scotista. O significado e a importância dessa distinção na metafísica scotista de Alfonso Briceño são o enfoque deste estudo. (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 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)

O texto visa apresentar e explicar o papel desempenhado pelas noções de telos e arché na compreensão tanto do movimento dos animais quanto da ação humana realizada no âmbito ético-político. Além disso, pretende evidenciar a importância de estabelecer a distinção modal do tempo em passado, presente e futuro elaborada na Ética a Nicômacos, em oposiçãoà abordagem quantitativa do mesmo empreendida na Física, a fim de poder explicar o silogismo prático.

O artigo procura reexaminar o seguinte problema clássico: qual é, no atributo pensamento, o modo infinito mediato? Contrariamente à posição de Gueroult segundo a qual “nada na Ética nos informa a esse respeito e é preciso decidir-se a interpretar”, o artigo procura mostrar que é possível encontrar em Ética V, 36 e seu corolário, ou seja, no amor infinito que Deus possui para consigo mesmo, a resposta buscada. Uma vez que este amor preenche todas as condições requeridas para ocupar o (...) lugar deste suposto “membro ausente”, não é necessário formular uma hipótese interpretativa forte, isto é, “fabricar uma prótese” para substitui-lo. (shrink)

Luiz Henrique Lopes dos Santos, em seu texto sobre "Leibniz e a questão dos futuros contingentes”, argumenta em favor de seu diagnóstico segundo o qual, no fundo, a principal diferença entre as doutrinas de Espinosa e Leibniz reside no fato de que o primeiro, diferentemente do segundo, não sabia lógica. Este texto procura objetar à sua posição, respondendo às críticas do autor à posição de Espinosa quanto à liberdade divina. Procurarei mostrar que, sob o aspecto preciso da articulação aí estabelecida (...) entre a distinção vontade/entendimento e a questão dos possíveis jamais realizados, ela não poderia estar disponível para a metafísica de Espinosa, não por ele ter ignorado um princípio básico da lógica modal, como alega o autor, mas porque ele compreende diferentemente o estatuto ontológico da unidade das coisas individuais e, portanto, dos agentes humanos. (shrink)

Not all categorization is conceptual. Many of the experimental findings concerning infant and animal categorization invite the hypothesis that the subjects form abstract perceptual representations, mental models or cognitive maps that are not composed of concepts. The paper is a reflection upon the idea that conceptual categorization involves the ability to make categorical judgements under the guidance of norms of rationality. These include a norm of truth-seeking and a norm of good evidence. Acceptance of these norms implies willingness to defer (...) to cognitive authorities, unwillingness to commit oneself to contradictions, and knowledge of how to reorganize one's representational system upon discovering that one has made a mistake. It is proposed that the cognitive architecture required for basic rationality is similar to that which underlies pretend-play. The representational system must be able to make room for separate 'mental spaces' in which alternatives to the actual world are entertained. The same feature underlies the ability to understand modalities, time, the appearance-reality distinction, other minds, and ethics. Each area of understanding admits of degrees, and mastery takes years. But rational concept-management, at least in its most rudimentary form, does not require a capacity to form second-order representations. It requires knowledge of how to operate upon, and compare, the contents of different mental spaces.Nem toda categorização é conceitual. Muitas das descobertas experimentais sobre o processo de categorização nas crianças e animais sugerem a hipótese segundo a qual os sujeitos formam representações perceptuais abstratas, modelos mentais ou mapas cognitivos que não são compostos de conceitos. Este artigo é uma reflexão acerca da ideia de que categorização conceitual envolve a habilidade de fazer julgamentos categoriais, tender como guia as normas de racionalidade. Estas incluem uma norma de busca da verdade e uma norma de evidência adequada. A aceitação dessas normas implica boa vontade em respeitar as autoridades cognitivas, o desejo de evitar as contradições e o conhecimento de como reorganizar seu sistema representacional após descobrir que se cometeu um erro. Sugere-se que a arquitetura cognitiva requerida pela racionalidade básica é semelhante àquela subjacente ao jogo do "faz de conta". O sistema representacional deve ser capaz de arrumar lugar para "espaços mentais", nos quais alternativas para o mundo real são consideradas. A mesma característica subjaz à habilidade de compreender modalidades, tempo, a distinção entre aparência e realidade, outras mentes e éticas. Cada área de compreensão admite graus, e o seu domínio leva anos. Contudo a manipulação racional de conceitos, pelo menos na sua forma mais rudimentar, não requer a capacidade de formar representações de segunda ordem. Ela requer conhecimento do procedimento de como operar e comparar os conteúdos dos diferentes espaços mentais. (shrink)

Primeiramente, oferecemos uma apresentação teórica da representação do pensamento prático, começando pela distinção entre silogismo dialético e silogismo demonstrativo. Fazemos referência à crítica de Toulmin contra o dedutivismo dominante de seu tempo. Em seguida, fornecemos argumentos para apoiar a relevância heurística do modelo de Toulmin para entender a discussão sobre a inclusão da lógica padrão na representação do pensamento comum. Afirmamos que o projeto analítico toulmaniano permite entender, com clareza metódica, a derrotabilidade dos argumentos do senso comum por meio (...) da investigação da noção modal de probabilidade na linguagem comum. First, we offer theoretical resemblance of the representation of practical reasoning, beginning with the distinction between demonstrative and dialectical syllogism. We make reference to the Toulmin’s critique against to the dominant deductivism in his time. Then we give arguments to sustain the heuristic relevance of Toulmin’s model to understand the discussion about the inclusion of default logics in the representation of ordinary reasoning. We assert that the Toulminian analytic design allows to understand, with methodical clarity, the defeasibility of common sense arguments by means of the investigation of the modal notion of probability in ordinary language. (shrink)

RESUMO Neste ensaio analiso as diferentes modalidades de pensamento que ocorrem entre a filosofia e as imagens em movimento partindo da distinção metafilosófica elaborada por Gilles Deleuze entre “pensar” e “filosofar”. Esta é uma distinção fundamental para a possível elaboração de uma filosofia do cinema, ou, pelo menos, para afirmar que “o cinema filosofa”, uma tese atualmente imersa num certo equívoco. Neste sentido, como possível resolução para tal mal-entendido, sugiro uma adequada designação deleuziana de “pensar com conceitos” e (...) “pensar com imagens”, num processo recíproco fundamental entre o campo filosófico e o não filosófico das artes. Começando com uma introdução à noologia em Deleuze e uma descrição dessas ideias e do seu valor estético, prossigo com uma análise mais detalhada sobre imagens em movimento, metáforas e adaptação cinematográfica de modo a, dentro de uma abordagem pós-continental e pós-analítica, questionar se o cinema filosofa. ABSTRACT In this essay I analyse the different modalities of thought that occur between philosophy and moving images, beginning with Gilles Deleuze’s metaphilosophical distinction between “thinking” and “philosophizing”. This is an essential distinction for the possible elaboration of a film philosophy, or at least one which claims that “film philosophizes,” a thesis that is nowadays immerged in a certain misconstruction. In this sense, I suggest, as a conceivable resolution to this misunderstanding, a more proper Deleuzian designation of “thinking with concepts” and “thinking with images,” in a fundamental reciprocal process between the philosophical and non-philosophical fields of the arts. Starting with an introduction to Deleuze’s noology and a description of these ideas and their aesthetic value, I proceed with a closer analysis of moving images, metaphors, and film adaptation in order to question, within a post-continental-analytic approach, whether film philosophizes. (shrink)

ResumoTomando como referência o campo dos estudos sobre deficiência (disability studies) e a conceitualização de capacitismo – forma particular de marginalização das pessoas com deficiência –, o artigo investiga a ligação entre as ideias eugenistas e o surgimento de uma modalidade de educação destinada a essas pessoas, a educação especial. Nesse sentido, as ciências biomédicas, ao operarem uma separação entre normalidade e anormalidade ofereceram as bases necessárias para a distinção entre capazes e incapazes, tornando estes inferiores àqueles. Por sua (...) vez, isso leva a pôr em questão as matrizes epistemológicas que subjazem tais distinções, considerando-as como participantes nos fundamentos do pensamento ocidental e, portanto, implicadas nos projetos políticos que desembocaram em segregação racial, social e desumanização de diferentes grupos.Palavras-chave: Estudos sobre Deficiência. Capacitismo. Educação. Educação Especial. AbstractTaking as reference the field of disability studies and the conceptualization of ableism - a particular form of marginalization of people with disabilities - this article investigates the connection between eugenic ideas and the emergence of a modality of education aimed at these people: special education. In this sense, the biomedical sciences offered, by operating a separation between normality and abnormality, the necessary basis for the distinction between capable and incapable, making these inferior to those. In turn, this leads us to question the epistemological matrices that underlie such distinctions, considering them as participants in the foundations of Western thought and, therefore, implicated in the political projects that led to racial, social segregation and dehumanization of different groups.Keywords: Disability Studies. Ableism. Education. Special Education. (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.

Abstract Timothy Williamson has recently proposed to undermine modal skepticism by appealing to the reducibility of modal to counterfactual logic ( Reducibility ). Central to Williamson’s strategy is the claim that use of the same non-deductive mode of inference ( counterfactual development , or CD ) whereby we typically arrive at knowledge of counterfactuals suffices for arriving at knowledge of metaphysical necessity via Reducibility. Granting Reducibility, I ask whether the use of CD plays any essential role in a (...) Reducibility-based reply to two kinds of modal skepticism. I argue that its use is entirely dispensable, and that Reducibility makes available replies to modal skeptics which show certain propositions to be metaphysically necessary by deductive arguments from premises the modal skeptic accepts can be known. Content Type Journal Article Pages 1-19 DOI 10.1007/s11098-011-9784-4 Authors Juhani Yli-Vakkuri, Wolfson College, Oxford University, Oxford, OX2 6UD UK Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116. (shrink)

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

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

Moti Mizrahi (2013) presents some novel counterexamples to Hypothetical Syllogism (HS) for indicative conditionals. I show that they are not compelling as they neglect the complicated ways in which conditionals and modals interact. I then briefly outline why HS should nevertheless be rejected.

Neste artigo, traremos a distinção entre vontade própria e liberdade, para designar como a relação do homem não é a de domínio com as coisas, tampouco de si mesmo, e sim um desprendimento que une a alma com a dimensão plena e livre de Deus em si mesmo. As noções de sujeição e obediência se mostram aí em sentido ontológico, nas quais o homem mantém uma ligação de dependência no ser com o transbordamento de tal dimensão maior. Ao se (...) retirar da posição de apego consigo próprio e com um entendimento de ser enquanto materialidade definitiva, o homem muda a relação com o mundo e passa a ver e a ter Deus em todas as coisas, na sua soltura e desprendimento de categorização e pré-determinação. (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. (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 critically examine the claim that modal collapse arguments against the traditional doctrine of divine simplicity (DDS) are in general fallacious. In a recent paper, Christopher Tomaszewski alleges that modal collapse arguments against DDS are invalid, owing to illicit substitutions of nonrigid singular terms into intensional contexts. I show that this is not, in general, the case. I show, further, that where existing modal collapse arguments are vulnerable to this charge the arguments can be repaired without any (...) apparent dialectical impropriety. I conclude that the genuine debate over modal collapse and divine simplicity and modal collapse is substantially a controversy over the metaphysics of divine action, and that this constitutes a fruitful direction in which to take future discussions of the subject. (shrink)

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)

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

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.

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)

Este artigo tem como objetivo tratar da crítica de Hegel a Kant a partir da distinção entre legalidade e moralidade. Enquanto Kant permanece preso ao formalismo, Hegel aponta princípios conteudísticos, pois considera que somente a partir deles é possível estabelecer deveres particulares. Kant define o certo, o bem e o justo a partir de um procedimento que visa à universalidade. A distinção entre legalidade e moralidade é realizada a partir de seus móbeis. A razão, em Kant, não é (...) legisladora, pois não está preocupada com “o que deve ser feito”, mas “como deve ser feito”. O imperativo categórico é regulador e orientador. Já Hegel critica o formalismo da teoria kantiana. A eticidade tem como grande objetivo a libertação da indeterminação, da imediatez e do natural. Isso ocorre instaurando-se a mediação e produzindo, consequentemente, a determinação. (shrink)

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

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

The function of a trait token is usually defined in terms of some properties of other (past, present, future) tokens of the same trait type. I argue that this strategy is problematic, as trait types are (at least partly) individuated by their functional properties, which would lead to circularity. In order to avoid this problem, I suggest a way to define the function of a trait token in terms of the properties of the very same trait token. To able to (...) allow for the possibility of malfunctioning, some of these properties need to be modal ones: a function of a trait is to do F just in case its doing F would contribute to the inclusive fitness of the organism whose trait it is. Function attributions have modal force. Finally, I explore whether and how this theory of biological function could be modified to cover artifact function. (shrink)

Recently, Kit Fine's (1994) view that modal truths aretrue in virtue of,grounded in, orexplained byessentialist truths has been under attack. In what follows we offer two responses to the wave of criticism against his view. While the first response is pretty straightforward, the second is based on the distinction between, what we call,Reductive Finean EssentialismandNon-Reductive Finean Essentialism. Engaging the work of Bob Hale onNon-Reductive Finean Essentialism, we aim to show that the arguments against Fine's view are unconvincing, while we (...) acknowledge the presence of a deep standoff between the two views. (shrink)

Em sua Crítica da Razão Pura, Kant diferencia criteriosamente aparecimento [Erscheinug] de fenômeno [Phaenomenon]. Esta distinção está presente tanto na primeira edição quanto na segunda. Não seguir com rigor este critério, ou o fazê-lo de maneira inadequada, oculta importantes informações e pode ofuscar elementos fundamentais à compreensão da sua argumentação em etapas decisivas. O presente trabalho busca determinar o que Kant entende por cada um destes termos. In his Critic of Pure Reason, Kant judiciously differentiates appearance [Erscheinug] from phenomenon[Phaenomenon]. (...) This distinction is present in first edition as much as in the second. Don’t follow this criterion, ormake it in inadequate way, occult important information and may obfuscating fundamental elements for the understanding of his argumentation in decisive stages. The present work searches to determine what Kant understands foreach one of these terms. (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)

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)

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

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)

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