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)

This article is about Avicenna’s account of syllogisms comprising opposite premises. We examine the applications and the truth conditions of these syllogisms. Finally, we discuss the relation between these syllogisms and the principle of non-contradiction.

O desenvolvimento da filosofia acadêmica no Brasil é direcionada, entre vários fatores, pelas investigações dos diversos Grupos de Trabalho (GTs) da Associação Nacional de Pós-Graduação em Filosofia (ANPOF). Esses GTs se dividem de acordo com a temática investigada. O GT de Metafísica Analítica é relativamente novo e ainda tem poucos membros, mas os temas nele trabalhados são variados e todos centrais no debate metafísico contemporâneo internacional. A sua investigação se caracteriza pelo rigor lógico e conceitual com o qual aborda esses (...) tradicionais tópicos da metafísica. Embora os assuntos tratados tenham sido, em sua grande maioria, tópicos abordados e discutidos em reuniões remotas do GT, nem todos os membros do nosso grupo estão aqui representados. Esperamos apresentar seus trabalhos em futuros livros. Por enquanto, queremos apenas divulgar ao público acadêmico algumas de nossas produções, trabalhadas e produzidas exclusivamente para este livro. Segundo a caracterização tradicional, com a qual plenamente concordamos, a metafísica se ocupa com a natureza mais íntima e geral da realidade. Essa metafísica é, por um lado, ambiciosa: não pretende apenas expor a realidade segundo o modo como ela se apresenta para nós, mas como ela é ‘em si mesma’. Por outro lado, ela é modesta: ela sabe da sua dívida para com as outras disciplinas, especialmente lógica, linguagem e epistemologia. Além disso, ela se entende como sempre tentativa, provisória, aberta a críticas e revisões. Neste livro, tratamos temas como as categorias ontológicas fundamentais e as suas relações de dependência e de fundamentalidade, a natureza da composição mereológica, da persistência temporal e do próprio tempo, a natureza dos objetos abstratos e dos mundos possíveis, as naturezas do mundo quântico, da causalidade nômica do mundo físico, e, finalmente, de um dos objetos mais característicos da presença humana no nosso mundo físico, que é o objeto de arte. É claro que essa coletânea está longe de apresentar exaustivamente todos os tópicos da metafísica. Tentamos selecionar e organizar os textos da forma mais fluida possível, de modo que eles possam levar tanto a uma reflexão específica quanto a uma reflexão geral sobre a natureza da realidade. Ainda que tenha uma inerente incompletude, o livro serve à finalidade de levar o/a estudante de graduação e pós-graduação a refletir sobre temas contemporâneos da Metafísica Analítica. Justamente por ter esse objetivo de formentar a pesquisa em metafísica analítica nacional, optamos por traduzir muitos termos do inglês que ainda não tem uma tradução canônica, a fim de evitar anglicismos e contribuir para uma leitura mais natural. Muito mais do que leitores complacentes, esse livro pede por leitores críticos, debatedores corajosos, que estejam dispostos a contribuir e a propor novas teorias e argumentos. Agradecemos a todos os membros do GT de Metafísica Analítica da ANPOF e a todos os autores deste livro, que decidiram apresentar publicamente suas pesquisas à academia; aos membros do Grupo de Pesquisa Investigação Filosófica, que decidiram pela publicação deste livro; à Pró-Reitoria de PósGraduação e Pesquisa da Universidade Federal do Amapá, que o financiou; e ao NEPFIL Online e à Editora da UFPel, que o editaram e publicaram. [Guido Imaguire e Rodrigo Reis Lastra Cid, Organizadores] . (shrink)

Presenting the first comprehensive, in-depth study of hyperintensionality, this book equips readers with the basic tools needed to appreciate some of current and future debates in the philosophy of language, semantics, and metaphysics. After introducing and explaining the major approaches to hyperintensionality found in the literature, the book tackles its systematic connections to normativity and offers some contributions to the current debates. The book offers undergraduate and graduate students an essential introduction to the topic, while also helping professionals in related (...) fields get up to speed on open research-level problems. (shrink)

This paper describes and compares the first step in modern semantic theory for deontic logic which appeared in works of Stig Kanger, Jaakko Hintikka, Richard Montague and Saul Kripke in late 50s and early 60s. Moreover, some further developments as well as systematizations are also noted.

On one influential view, metaphysical fundamentality can be understood in terms of joint‐carving. Ted Sider has recently argued that (i) some first order quantifier is joint‐carving, and (ii) modal notions are not joint‐carving. After vindicating the theoretical indispensability of quantification against recent criticism, I will defend a logical result due to Arnold Koslow which implies that (i) and (ii) are incompatible. I will therefore consider an alternative understanding of Sider's metaphysics to the effect that (i) some first order quantifier is (...) joint‐carving, and (iii) intensional notions are not joint‐carving. Another result due to Koslow entails that (i) and (iii) are also incompatible. I will argue that this second result is inconclusive. Nevertheless, (iii) is incompatible with another tenet of Sider's metaphysics, namely that (iv) ‘being joint‐carving’ is itself joint‐carving. In order to resolve the inconsistency, I will tentatively argue that condition (iv) should be renounced. (shrink)

This essay considers Kant’s theory of modality in light of a debate in contemporary modal metaphysics and modal logic concerning the Barcan formulas. The comparison provides a new and fruitful perspective on Kant’s complex and sometimes confusing claims about possibility and necessity. Two central Kantian principles provide the starting point for the comparison: that the possible must be grounded in the actual and that existence is not a real predicate. Both are shown to be intimately connected to the Barcan formulas, (...) and Kant’s views on what he distinguishes as three different kinds of modality are then considered in light of this connection. (shrink)

In this paper I offer a novel analysis of Quine's indeterminacy puzzle and an unorthodox approach to its resolution. It is argued that the ultimate roots of indeterminacy lie not in behaviorism per se, but rather in Quine's commitment to a fundamental assumption about the nature of perceptual input, namely, the assumption that sensory information is strictly extensional. Calling this assumption the 'principle of input extensionalism' (PIE) I first demonstrate the fundamental role that it plays in generating Quine's argument for (...) the indeterminacy of translation. It is then argued that a tacit acceptance of PIE is prevalent among contemporary theories of cognition and representation, making Quine's puzzle a living challenge for cognitive science and the philosophy of mind. A standard way of responding to the challenge consists of the idea that the indeterminacy generated at the perceptual level is canceled out courtesy of the contribution of higher cognitive processes. However, I argue that such a top-down solution leaves much to be desired. As an alternative, I offer a bottom-up solution, which consists of a systematic rejection of PIE in favor of an intensional view of perceptual input rooted in contemporary action-based theories of perception, and in particular in the notion of perceptual invariants. (shrink)

Are moral judgements objective? This is a question of great complexity, and in what follows I shall try to cast some light on what it means, and on how it might be answered.

Are moral judgements objective? This is a question of great complexity, and in what follows I shall try to cast some light on what it means, and on how it might be answered.

The paper develops a set of quantified temporal alethic boulesic doxastic systems. Every system in this set consists of five parts: a ‘quantified’ part, a temporal part, a modal (alethic) part, a boulesic part and a doxastic part. There are no systems in the literature that combine all of these branches of logic. Hence, all systems in this paper are new. Every system is defined both semantically and proof-theoretically. The semantic apparatus consists of a kind of$$T \times W$$T×Wmodels, and the (...) proof-theoretical apparatus of semantic tableaux. The ‘quantified part’ of the systems includes relational predicates and the identity symbol. The quantifiers are, in effect, a kind of possibilist quantifiers that vary over every object in the domain. The tableaux rules are classical. The alethic part contains two types of modal operators for absolute and historical necessity and possibility. According to ‘boulesic logic’ (the logic of the will), ‘willing’ (‘consenting’, ‘rejecting’, ‘indifference’ and ‘non-indifference’) is a kind of modal operator. Doxastic logic is the logic of beliefs; it treats ‘believing’ (and ‘conceiving’) as a kind of modal operator. I will explore some possible relationships between these different parts, and investigate some principles that include more than one type of logical expression. I will show that every tableau system in the paper is sound and complete with respect to its semantics. Finally, I consider an example of a valid argument and an example of an invalid sentence. I show how one can use semantic tableaux to establish validity and invalidity and read off countermodels. These examples illustrate the philosophical usefulness of the systems that are introduced in this paper. (shrink)

As anyone who is familiar with the literature knows, there is a great deal of controversy concerning which, if any, of the extant theories of propositional modal logic correctly formalizes the logic of certain logical concepts such as analyticity and logical necessity. Most of the controversy concerns certain principles that involve iterated modalities (where one modal operator occurs within the scope of another). For example, there is considerable disagreement about whether the principle(□p⊃□□p)should be considered valid. However, when philosophers and logiciansapplymodal (...) logic to concrete problems, they rarely need principles which involve iterated modalities. For most practical purposes, principles involving only one layer of modalities are all that are needed. This suggests that if we try to construct a theory of modal logic in which there are no iterated modalities, we can avoid most of the controversy and still have a theory that is strong enough for all of the normal uses to which modal logic is put. (shrink)

Formal semantics and pragmatics as they have developed since the late 1960's have been shaped by fruitful interdisciplinary collaboration among linguists, philosophers, and logicians, among others, and in turn have had noticeable effects on developments in syntax, philosophy of language, computational linguistics, and cognitive science.In this paper I describe the environment in which formal semantics was born and took root, highlighting the differences in ways of thinking about natural language semantics in linguistics and in philosophy and logic. With Montague as (...) a central but not solo player in the story, I reflect on crucial developments in the 1960's and 70's in linguistics and philosophy, and the growth of formal semantics and formal pragmatics from there. I discuss innovations, key players, and leading ideas that shaped the development of formal semantics and its relation to syntax, to pragmatics, and to the philosophy of language in its early years, and some central aspects of its early impact on those fields. (shrink)

The logic Kf of the modalities of finite, devised to capture the notion of 'there exists a finite number of accessible worlds such that . . . is true', was introduced and axiomatized by Fattorosi. In this paper we enrich the logical framework of Kf: we give consistency properties and a tableau system (which yields the decidability) explicitly designed for Kf, and we introduce a shorter and more natural axiomatization. Moreover, we show the strong and suggestive relationship between Kf and (...) the much older logic of the physical modalities of Burks. (shrink)

Penelope Maddy has defended a modified version of mathematical platonism that involves the perception of some sets. Frederick Suppe has developed a conclusive reasons account of empirical knowledge that, when applied to the sets of interest to Maddy, yields that we have knowledge of these sets. Thus, Benacerraf's challenge to the platonist to account for mathematical knowledge has been met, at least in part. Moreover, it is argued that the modalities involved in Suppe's conclusive reasons account of knowledge can be (...) handled without recourse to either laws of nature or possible worlds, and that this approach is preferable. (shrink)

Most relational theories assert both that spatial discourse is reducible to talk about physical objects and their spatial relations, and that the relation of congruence derives from a non-metrical relation which intervals bear or possibly bear to measuring instruments. We have shown that there are serious logical difficulties involved in maintaining both these positions and the thesis of the continuity of space. We have also shown that Grünbaum's motivating argument for the reduction of congruence is unsound, and, moreover, that the (...) prospects of formulating the kind of definition which this reduction requires seem to rest upon a wholly vague notion of physical possibility. Alternatively, if congruence is taken as primitive, it seems plausible that spatial discourse can be reconstructed so that there is no ontological commitment to spatial objects other than physical objects. Whether or not this relational thesis is ultimately defensible requires more elaboration of the relational theory, and investigation of its role in the formalizations of current physical theories. It is odd, considering the wide currency of relational theories, that this work has never been done. (shrink)

We shall try to defend two non-standard views that run counter to two well-entrenched familiar views. The standard views are the universal and existential quantifiers of first-order logic are not modal operators, and the quantifiers are extensional. If that is correct then the counterclaims create genuine problems for some traditional philosophical doctrines.

1. This paper addresses the development of mutual relations between two sets of ideas in scholastic logic. First, consider the following statements: (1) It is impossible to encounter a chimera.(2)...

This article traces the development of possible worlds semantics through the work of: Wittgenstein, 1913-1921; Feys, 1924; McKinsey, 1945; Carnap, 1945-1947; McKinsey, Tarski and Jónsson, 1947-1952; von Wright, 1951; Becker, 1952; Prior, 1953-1954; Montague, 1955; Meredith and Prior, 1956; Geach, 1960; Smiley, 1955-1957; Kanger, 1957; Hintikka, 1957; Guillaume, 1958; Binkley, 1958; Bayart, 1958-1959; Drake, 1959-1961; Kripke, 1958-1965.

This paper charts some early history of the possible worlds semantics for modal logic, starting with the pioneering work of Prior and Meredith. The contributions of Geach, Hintikka, Kanger, Kripke, Montague, and Smiley are also discussed.

Here, I offer a rapid overview of the theory of metaphor, in order to situate the contributions to this volume in relation to one another and within the field more generally.

In this paper I argue against the commonly received view that Kripke's formal Possible World Semantics (PWS) reflects the adoption of a metaphysical interpretation of the modal operators. I consider in detail Kripke's three main innovations vis-à-vis Carnap's PWS: a new view of the worlds, variable domains of quantification, and the adoption of a notion of universal validity. I argue that all these changes are driven by the natural technical development of the model theory and its related notion of validity: (...) they are dictated by merely formal considerations, not interpretive concerns. I conclude that Kripke's model theoretic semantics does not induce a metaphysical reading of necessity, and is formally adequate independently of the specific interpretation of the modal operators. (shrink)

In this paper I analyze David Kaplan’s essay “Opacity”. In “Opacity” Kaplan attempts to dismiss Quine’s concerns about quantification across intensional (modal and intentional) operators. I argue that Kaplan succeeds in showing that quantification across intensional operators is logically coherent and that quantified modal logic is strictly speaking not committed to essentialism. However, I also argue that this is not in and of itself sufficient to support Kaplan’s more ambitious attempt to move beyond purely logical results and provide unified, uncontroversial (...) interpretations of both “believes” and “necessarily”. In the paper I raise several questions about the subject matter of logic and the role of semantics, with special focus on singular propositions. (shrink)

We present a puzzle about deontic modals. An adequate resolution requires abandoning the standard theory. What to replace it with isn’t clear. We consider two possibilities.

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 comprise a materially adequate fragment of the language of thought, and endeavor to show how such algebras provide the resources necessary to resolve Russell's paradox of propositions. I demonstrate, then, how modal expressivism can be regimented by modal coalgebraic automata, to which the above epistemic modal algebras are dually isomorphic. I examine, in particular, 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 paper aims to provide a mathematically tractable background against which to model both modal cognitivism and modal expressivism. I argue that epistemic modal algebras 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 dual. I examine, in particular, 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)

Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the work going on in our field—a (...) book would be needed for that. Instead, we have tried to select material that is of interest in its own right or exemplifies noteworthy features in interesting ways. Here are some themes that have guided us throughout the writing: • The back-and-forth between philosophy and modal logic. There has been a good deal of give-and-take in the past. Carnap tried to use his modal logic to throw light on old philosophical questions, thereby inspiring others to continue his work and still others to criticise it. He certainly provoked Quine, who in his turn provided—and continues to provide—a healthy challenge to modal logicians. And Kripke’s and David Lewis’s philosophies are connected, in interesting ways, with their modal logic. Analytic philosophy would have been a lot different without modal logic! • The interpretation problem. The problem of providing a certain modal logic with an intuitive interpretation should not be conflated with the problem of providing a formal system with a model-theoretic semantics. An intuitively appealing model-theoretic semantics may be an important step towards solving the interpretation problem, but only a step. One may compare this situation with that in probability theory, where definitions of concepts like ‘outcome space’ and ‘random variable’ are orthogonal to questions about “interpretations” of the concept of probability. • The value of formalisation. Modal logic sets standards of precision, which are a challenge to—and sometimes a model for—philosophy. Classical philosophical questions can be sharpened and seen from a new perspective when formulated in a framework of modal logic. On the other hand, representing old questions in a formal garb has its dangers, such as simplification and distortion. • Why modal logic rather than classical (first or higher order) logic? The idioms of modal logic—today there are many!—seem better to correspond to human ways of thinking than ordinary extensional logic. (Cf. Chomsky’s conjecture that the NP + VP pattern is wired into the human brain.) In his An Essay in Modal Logic (1951) von Wright distinguished between four kinds of modalities: alethic (modes of truth: necessity, possibility and impossibility), epistemic (modes of being known: known to be true, known to be false, undecided), deontic (modes of obligation: obligatory, permitted, forbidden) and existential (modes of existence: universality, existence, emptiness). The existential modalities are not usually counted as modalities, but the other three categories are exemplified in three sections into which this chapter is divided. Section 1 is devoted to alethic modal logic and reviews some main themes at the heart of philosophical modal logic. Sections 2 and 3 deal with topics in epistemic logic and deontic logic, respectively, and are meant to illustrate two different uses that modal logic or indeed any logic can have: it may be applied to already existing (non-logical) theory, or it can be used to develop new theory. (shrink)

The ontological assumptions of the modal logic of Saul Kripke are analyzed. Answers to the questions are given: What are the modalities? What is thesemantic problem that Kripke faced? How was it resolved? How a substitution oflogic reforms the ontological analyzes? This paper is also intended to be anintroduction to the semantics of Kripke's propositional modal logic.

The possible worlds semantics is articulated as one of the most relevant logical and philosophical theories of our time. The famous possible worlds form and have been part of the philosophical jargon of authors of the so-called analytical tendency in the last decades. It has also been a theory suitable for the treatment and approach of many topics and problems that have afflicted philosophers of all time. In this paper, we will focus on the origin, preparation and consolidation of PWS (...) and its central notions by hand of some of its main representatives. (shrink)