Although we are enthusiastic about a Darwinian approach to culture, we argue that the overview presented in the target article does not sufficiently emphasize the crucial explanatory role that psychology plays in the study of culture. We use a number of examples to illustrate the variety of ways by which appeal to psychological factors can help explain cultural phenomena. (Published Online November 9 2006).

In this defense of Reliabilism, I argue that there has been 'selection for' accurate indexical beliefs. I offer empirical evidence and examples to suggest that Steve Stich's defense of the opposite claim in The Fragmentation of Reason is misguided.

Humans interpret others. We are able to anticipate both the actions and intentional states of other agents. We do not do so perfectly, but since we are complex and flexible creatures even limited success needs explanation. For some years now Steve Stich (frequently in collaboration with Shaun Nichols) has been both participant in, and observer of, debates about the foundation of these capacities (Stich and Nichols 1992; Stich and Nichols 1995). As a commentator on this debate, (...) Stich (with Nichols) gave explicit and fair-minded sketches of the cognitive architectures presupposed by the various theories of mindreading. As a participant, Stich has mostly been a defender of the theory-theory, the view that normal human agents have an internally represented theory of other agents and they use that theory in interpreting other agents. The main recent rival to this position, simulationism, claims that agents use their own decision-making mechanisms as a model of those of other agents, and derive their predictions by modelling others in something like the way aeronautical engineers derive predictions from the use of scale models in wind-tunnels. Stich has been sceptical about this alternative, for on his view simulation theory makes mistaken predictions about both the development of interpretive competence and about the pattern of interpretive success and failure. (shrink)

Steve Stich used to be an eliminativist. As far as I can tell, he renounced eliminativism about the time that he moved from the west to the east pole.1 Stich was right to reject eliminativism, though I am not convinced that he rejected it for the right reasons. Stich 1983 contains a comprehensive attack on representational content, a central feature of both folk psychology and the Representational Theory of Mind, the leading philosophical construal of scientific psychology. (...) Stich’s current position on the role of content in psychological explanation is not entirely clear. One of my aims in this chapter is simply to invite Stich to clarify his views on representational content; the question that forms the title of this chapter is therefore addressed directly to Stich. I begin by sketching his original anti-content argument. I then trace some later developments in his thinking about content. I argue that content does play an important role in scientific psychology, for precisely the reasons that Stich identified in his original argument against content. I conclude with some general remarks on eliminativism. (shrink)

Many philosophical naturalists eschew analysis in favor of discovering metaphysical truths from the a posteriori, contending that analysis does not lead to philosophical insight. A countercurrent to this approach seeks to reconcile a certain account of conceptual analysis with philosophical naturalism; prominent and influential proponents of this methodology include the late David Lewis, Frank Jackson, Michael Smith, Philip Pettit, and David Armstrong. Naturalistic analysis is a tool for locating in the scientifically given world objects and properties we quantify over in (...) everyday discourse. This collection gathers work from a range of prominent philosophers who are working within this tradition, offering important new work as well as critical evaluations of the methodology. Its centerpiece is an important posthumous paper by David Lewis, "Ramseyan Humility," published here for the first time. The contributors first address issues of philosophy of mind, semantics, and the new methodology's a priori character, then turn to matters of metaphysics, and finally consider problems regarding normativity. Conceptual Analysis and Philosophical Naturalism is one of the first efforts to apply this approach to such a wide range of philosophical issues. _Contributors: _David Braddon-Mitchell, Mark Colyvan, Frank Jackson, Justine Kingsbury, Fred Kroon, David Lewis, Dustin Locke, Kelby Mason, Jonathan McKeown-Green, Peter Menzies, Robert Nola, Daniel Nolan, Philip Pettit, Huw Price, Denis Robinson, Steve Stich, Daniel Stoljar The hardcover edition does not include a dust jacket. (shrink)

Chapter One: James is often accused of claiming that a belief is true just in case it is useful. The objections to this view are obvious. I offer a more sophisticated interpretation of James's theory of truth, and defend it from the standard objections. Chapter Two: I discuss Steve Stich's notorious claim that `once we have a clear view of the matter, most of us will not find any value, either intrinsic or instrumental, in having true beliefs.' I (...) argue that Stich reaches this conclusion only because he makes some false assumptions about content-determination. I show that using an interpretationist account of content-determination we can explain the value of true beliefs. Chapters Three and Four: `Definitionalism' is my name for the thesis that the theorems of mathematics are a priori because they are entailed by definitions. I discuss two objections to this view: the `Kantian' objection and the Quinean objection. According to the `Kantian' objection, definitionalism must be false because existential generalisations can't be true by definition. According to the Quinean objection, the definitionalist's distinction between definitions and other statements is illicit, because it is not discernible in mathematical practice. I argue that the Kantian objection is misguided, but the Quinean objection is correct. Chapter Five: Elitists draw a distinction between two sorts of word: the elite and the plebeian. They claim that only by using the elite words can we describe the world as it is `anyway'; using the plebeian words, we can at best describe the world as it seems to us, with our own particular physiology, tastes and history. For the sake of argument I grant these claims, but then contend that we have no way of identifying the elite expressions. (shrink)

Considerable debate in philosophy of psychology has recently focussed upon two central themes. One concerns the ontological status of propositional attitudes like beliefs and desires, the other on the proper computational account of cognitive architecture. In the ontological debate, the two most prominent positions are eliminativism, which claims that commonsense psychology is false because there are no such things as beliefs and desires; and versions of intentional realism, which counters that beliefs and desires actually do exist in the mind/brain. In (...) the cognitive architecture debate, there are again two outstanding views: classical cognitivism, which holds that cognition is something closely akin to symbol manipulation; and parallel distributed processing, which roughly maintains that cognition is the distributed activation of several simple, non-symbolic processing units. Furthermore, in spite of their different topics, the two debates have been linked by a number of authors who suggest that where you stand in the cognitive architecture debate should help determine where you stand in the debate over prepositional attitudes. So, for example, writers like Jerry Fodor have used the plausibility of classical cognitivism to defend a realist interpretation of propositional attitudes, while writers like Steve Stich and myself have argued that certain forms of connectionism support eliminativism. (shrink)

From Descartes to Popper, philosophers have criticized and tried to improve the strategies of reasoning invoked in science and in everyday life. In recent years leading cognitive psychologists have painted a detailed, controversial, and highly critical portrait of common sense reasoning. Stephen Stich begins with a spirited defense of this work and a critique of those writers who argue that widespread irrationality is a biological or conceptual impossibility.Stich then explores the nature of rationality and irrationality: What is it (...) that distinguishes good reasoning from bad? He rejects the most widely accepted approaches to this question approaches which unpack rationality by appeal to truth, to reflective equilibrium or conceptual analysis. The alternative he defends grows out of the pragmatic tradition in which reasoning is viewed as a cognitive tool. Stich's version of pragmatism leads to a radical epistemic relativism and he argues that the widespread abhorrence of relativism is ill founded. (shrink)

In this article, we posit that a cross-scale perspective is valuable for studies of organizational resilience. Existing research in our field primarily focuses on the resilience of organizations, that is, the factors that enhance or detract from an organization’s viability in the face of threat. While this organization level focus makes important contributions to theory, organizational resilience is also intrinsically dependent upon the resilience of broader social-ecological systems in which the firm is embedded. Moreover, long-term organizational resilience cannot be well (...) managed without an understanding of the feedback effects across nested systems. For instance, a narrow focus on optimizing organizational resilience from one firm’s perspective may come at the expense of social-ecological functioning and ultimately undermine managers’ efforts at long-term organizational survival. We suggest that insights from natural science may help organizational scholars to examine cross-scale resilience and conceptualize organizational actions within and across temporal and spatial dynamics. We develop propositions taking a complex adaptive systems perspective to identify issues related to focal scale, slow variables and feedback, and diversity and redundancy. We illustrate our theoretical argument using an example of Unilever and palm oil production in Borneo. (shrink)

Over the last two decades, debates over the viability of commonsense psychology have been center stage in both cognitive science and the philosophy of mind. Eliminativists have argued that advances in cognitive science and neuroscience will ultimately justify a rejection of our "folk" theory of the mind, and of its ontology. In the first half of this book Stich, who was at one time a leading advocate of eliminativism, maintains that even if the sciences develop in the ways that (...) eliminativists foresee, none of the arguments for ontological elimination are tenable. Rather than being resolved by science, he contends, these ontological disputes will be settled by a pragmatic process in which social and political considerations have a major role to play. In later chapters, Stich argues that the widespread worry about "naturalizing" psychological properties is deeply confused, since there is no plausible account of what naturalizing requires on which the failure of the naturalization project would lead to eliminativism. He also offers a detailed analysis of the many different notions of folk psychology to be found in philosophy and psychology, and argues that simulation theory, which purports to be an alternative to folk psychology, is not supported by recent experimental findings. (shrink)

The recent discovery of an interpretation of constructive type theory into abstract homotopy theory suggests a new approach to the foundations of mathematics with intrinsic geometric content and a computational implementation. Voevodsky has proposed such a program, including a new axiom with both geometric and logical significance: the Univalence Axiom. It captures the familiar aspect of informal mathematical practice according to which one can identify isomorphic objects. While it is incompatible with conventional foundations, it is a powerful addition to homotopy (...) type theory. It also gives the new system of foundations a distinctly structural character. (shrink)

An affirmative answer is given to the question quoted in the title.

A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems, as well as numerous examples and exercises.

The primary goal of this paper is not to argue for the “influence” of Cassirer, but rather to make known the reception of Cassirer in Japanese philosophy, illustrate the interconnection between Cassirer’s critique of culture and that of Japanese philosophy, and hopefully spark interest in what might be a fruitful dialog between Cassirer scholars and those working in Japanese philosophy. Historically, the paper defines Japanese philosophy and makes known its engagement with Western philosophy and the Marburg school of neo-Kantianism and (...) its project of a critique of culture during its own self-development. Systematically, the paper points to the possible interconnection between Cassirer’s critique of culture and that of Japanese philosophy and makes the case for a mutually productive dialog between Cassirer scholars and those working in Japanese philosophy. Implicitly, the paper attempted to show that an engagement with Japanese philosophy from the perspective of a critique of culture forces us to question the Western dichotomy between philosophy and religion and the importance of this for the further development of a non-Eurocentric critique of culture. And by extension, that a critique of culture must be cognitive of the historicity of the culture from which it speaks. (shrink)

Quillen [17] introduced model categories as an abstract framework for homotopy theory which would apply to a wide range of mathematical settings. By all accounts this program has been a success and—as, e.g., the work of Voevodsky on the homotopy theory of schemes [15] or the work of Joyal [11, 12] and Lurie [13] on quasicategories seem to indicate—it will likely continue to facilitate mathematical advances. In this paper we present a novel connection between model categories and mathematical logic, inspired (...) by the groupoid model of (intensional) Martin–Löf type theory [14] due to Hofmann and Streicher [9]. In particular, we show that a form of Martin–Löf type theory can be soundly modelled in any model category. This result indicates moreover that any model category has an associated “internal language” which is itself a form of Martin-Löf type theory. This suggests applications both to type theory and to homotopy theory. Because Martin–Löf type theory is, in one form or another, the theoretical basis for many of the computer proof assistants currently in use, such as Coq and Agda (cf. [3] and [5]), this promise of applications is of a practical, as well as theoretical, nature. This paper provides a precise indication of this connection between homotopy theory and logic; a more detailed discussion of these and further results will be given in [20]. (shrink)

From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models can be topologized in such a way that the theory can be recovered from its space of models. The situation can be cast as a formal duality relating two categories of syntax and semantics, mediated by homming into a common dualizing object, in this (...) case 2.In the present work, we generalize the entire arrangement from propositional to first-order logic, using a representation result of Butz and Moerdijk. Boolean algebras are replaced by Boolean categories presented by theories in first-order logic, and spaces of models are replaced by topological groupoids of models and their isomorphisms. A duality between the resulting categories of syntax and semantics, expressed primarily in the form of a contravariant adjunction, is established by homming into a common dualizing object, now Sets, regarded once as a boolean category, and once as a groupoid equipped with an intrinsic topology.The overall framework of our investigation is provided by topos theory. Direct proofs of the main results are given, but the specialist will recognize toposophical ideas in the background. Indeed, the duality between syntax and semantics is really a manifestation of that between algebra and geometry in the two directions of the geometric morphisms that lurk behind our formal theory. Along the way, we give an elementary proof of Butz and Moerdijkʼs result in logical terms. (shrink)

ABSTRACT The influence of Cassirer's work on Bakhtin's writings from the 1930s has been studied in some detail but scholars have not examined Bakhtin's early work, Toward a Philosophy of the Act (K filosofii postupka), in connection with Cassirer's philosophy. The article first reveals how attuned Bakhtin was with the intellectual Zeitgeist not only of his own times, but also that of the 20th century. The uncanny intellectual harmony between the ideas of Bakhtin and Cassirer can be seen at the (...) very beginning of Bakhtin's career. The two thinkers are united in their reception, transformation, and attempt to reconcile two antithetical philosophical positions dominant at the beginning of the 20th century: the transcendental philosophy of Kant, Neo-Kantianism, and the Lebensphilosophie of Simmel, Bergson, and Heidegger. Bakhtin and Cassirer were alarmed by the cultural pessimism and potential nihilism inherent in the position of Lebensphilosophie. Next, the author shows ways in which Bakhtin's and Cassirer's ideas resonate with those of the later 20th century Jacques Derrida. (shrink)

This paper is the second in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...) so as to shed new light on the relevant strengths and limits of higher-order logic. (shrink)

The purpose of this informal survey article is to introduce the reader to a new and surprising connection between Logic, Geometry, and Algebra which has recently come to light in the form of an interpretation of the constructive type theory of Per Martin-Löf into homotopy theory and higher-dimensional category theory.

This paper provides a reading of Nishitani’s philosophy of culture. It argues that the advent of nihilism is the logical conclusion of what will be called the “fracturing of culture” in which philosophy and religion lose their creative force to revitalize a cultural tradition as the sense of being-in-time that forms the historical life of a historical world. Section two sets out the paradoxical nature of Nishitani’s philosophy of culture as both a transcendental and existential project. Section three draws attention (...) to the fact that a concept of culture always belongs to a concrete culture as part of its own understanding of itself. Section four interprets the advent of nihilism in terms of a crisis of culture that ensues from the loss of the existential understanding of history that grounds a cultural world, that forms the standpoint of a historical event of worlding, the historical life that we are. Section five examines Nishitani’s project in terms of the reappropriation of a lost tradition through an existential receptive reinterpretation of Buddhism. Section six argues that for Nishitani the advent of nihilism comes about as a result of the negation of myth by science and thus the overcoming of nihilism comes about through the recollection of myth. Section seven determines the nature of myth for Nishitani through a comparison with Cassirer’s and Heidegger’s understanding of myth. Three elements of myth are focused on: 1) myth as an existential confrontation with being-in-the-world; 2) this existential being-in-the-world forms an existential being-in-time; and 3) myth is the position of the imagination, a thinking by means of form-images [keizō 形像] (Bild, image). Section seven considers the difference between Cassirer’s and Nishitani’s respective accounts of myth. Section nine examines the nature and function of philosophy, science, and religion in terms of their relation to myth and in terms of how they understand interdependent origination. Section, ten ends the paper by considering what is called the “fracturing” of culture and the advent of nihilism. (shrink)

This brief article is intended to introduce the reader to the field of algebraic set theory, in which models of set theory of a new and fascinating kind are determined algebraically. The method is quite robust, applying to various classical, intuitionistic, and constructive set theories. Under this scheme some familiar set theoretic properties are related to algebraic ones, while others result from logical constraints. Conventional elementary set theories are complete with respect to algebraic models, which arise in a variety of (...) ways, including topologically, type-theoretically, and through variation. Many previous results from topos theory involving realizability, permutation, and sheaf models of set theory are subsumed, and the prospects for further such unification seem bright. (shrink)

In this paper the machinery and results developed in [Awodey et al, 2004] are extended to the study of constructive set theories. Specifically, we introduce two constructive set theories BCST and CST and prove that they are sound and complete with respect to models in categories with certain structure. Specifically, basic categories of classes and categories of classes are axiomatized and shown to provide models of the aforementioned set theories. Finally, models of these theories are constructed in the category of (...) ideals. (shrink)

We show how to interpret the language of first-order set theory in an elementary topos endowed with, as extra structure, a directed structural system of inclusions . As our main result, we obtain a complete axiomatization of the intuitionistic set theory validated by all such interpretations. Since every elementary topos is equivalent to one carrying a dssi, we thus obtain a first-order set theory whose associated categories of sets are exactly the elementary toposes. In addition, we show that the full (...) axiom of Separation is validated whenever the dssi is superdirected. This gives a uniform explanation for the known facts that cocomplete and realizability toposes provide models for Intuitionistic Zermelo-Fraenkel set theory. (shrink)

In this short note we give a glimpse of homotopy type theory, a new field of mathematics at the intersection of algebraic topology and mathematical logic, and we explain Vladimir Voevodsky’s univalent interpretation of it. This interpretation has given rise to the univalent foundations program, which is the topic of the current special year at the Institute for Advanced Study.

As McKinsey and Tarski showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for propositional modal logic, in which the “necessity” operation is modeled by taking the interior of an arbitrary subset of a topological space. In this article, the topological interpretation is extended in a natural way to arbitrary theories of full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to such topological semantics.

We show how to interpret the language of first-order set theory in an elementary topos endowed with, as extra structure, a directed structural system of inclusions (dssi). As our main result, we obtain a complete axiomatization of the intuitionistic set theory validated by all such interpretations. Since every elementary topos is equivalent to one carrying a dssi, we thus obtain a first-order set theory whose associated categories of sets are exactly the elementary toposes. In addition, we show that the full (...) axiom of Separation is validated whenever the dssi is superdirected. This gives a uniform explanation for the known facts that cocomplete and realizability toposes provide models for Intuitionistic Zermelo—Fraenkel set theory (IZF). (shrink)

The Oxford Handbook of Japanese Philosophy is by all counts an ambitious work. Its primary goal is to provide the reader with a foundational framework in which to engage interpretively the tradition of Japanese philosophy. It would be impossible to summarize, let alone do justice to, the thirty-six rich and illuminating chapters written by many of the most prominent scholars in the field from Japan, Europe, Australia, and North America.Navigating between the "violence of inclusion" that would reduce the philosophically other (...) to our own conception of philosophy and the "violence of exclusion" that would fail to recognize what we share with this other, Bret Davis... (shrink)

We define the notion of a model of higher-order modal logic in an arbitrary elementary topos E. In contrast to the well-known interpretation of higher-order logic, the type of propositions is not interpreted by the subobject classifier ΩE, but rather by a suitable complete Heyting algebra H. The canonical map relating H and ΩE both serves to interpret equality and provides a modal operator on H in the form of a comonad. Examples of such structures arise from surjective geometric morphisms (...) f : F → E, where H = f∗ΩF. The logic differs from non-modal higher-order logic in that the principles of functional and propositional extensionality are not longer valid but may be replaced by modalized versions. The usual Kripke, neighborhood, and sheaf semantics for propositional and first-order modal logic are subsumed by this notion. (shrink)

This work is a step toward the development of a logic for types and computation that includes not only the usual spaces of mathematics and constructions, but also spaces from logic and domain theory. Using realizability, we investigate a configuration of three toposes that we regard as describing a notion of relative computability. Attention is focussed on a certain local map of toposes, which we first study axiomatically, and then by deriving a modal calculus as its internal logic. The resulting (...) framework is intended as a setting for the logical and categorical study of relative computability. (shrink)

This paper constructs models of intuitionistic set theory in suitable categories. First, a Basic Intuitionistic Set Theory (BIST) is stated, and the categorical semantics are given. Second, we give a notion of an ideal over a category, using which one can build a model of BIST in which a given topos occurs as the sets. And third, a sheaf model is given of a Basic Intuitionistic Class Theory conservatively extending BIST. The paper extends the results in [2] by introducing a (...) new and perhaps more natural notion of ideal, and in the class theory of part three. (shrink)

The failed criterion of logical truth proposed by Carnap in the Logical Syntax of Language was based on the determinateness of all logical and mathematical statements. It is related to a conception which is independent of the specifics of the system of the Syntax, hints of which occur elsewhere in Carnap’s writings, and those of others. What is essential is the idea that the logical terms are invariant under reinterpretation of the empirical terms, and are therefore semantically determinate. A certain (...) objection to Carnap’s version of the invariance conception has been repeated several times in the literature. It is based on Gödel incompleteness, which is puzzling, since Carnap’s Syntax is otherwise quite careful to take account of Gödel. We show here that, in fact, the objection is invalid and is based on a confusion about determinacy. Sorting this out is worthwhile not only for the purpose of better understanding Carnap’s thinking in the Syntax, though. The invariance conception is also related to recent work in the philosophy of logic regarding “logicality”—the characterization of logical concepts—following a proposal of Tarski’s. It is even connected to some very recent developments in the foundations of mathematics. (shrink)

The fundamental duality theories relating algebra and geometry that were discovered in the mid-twentieth century can also be applied to logic via its algebraization under categorical logic. They thereby result in known and new completeness theorems. This idea can be taken even further via what is sometimes called “categorification” to establish a new connection between logic and geometry, a glimpse of which can also be had in topos theory.

This paper is the first in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...) so as to shed new light on the relevant strengths and limits of higher-order logic. (shrink)

In 2016, a Cincinnati Zoo worker shot and killed a Western lowland gorilla to protect a three-year-old boy who had fallen into the animal’s enclosure. This incident involves a variant of the classical trolley problem, one in which the death of a human being on the main track might be avoided by selecting an alternate track containing a member of an endangered species. This problem raises two important questions for environmental ethics. First, what, if anything, imbues a human child with (...) greater value than a member of a critically endangered species? Second, is it ethical for zoos to house species such as gorillas? With regard to the first question, at a minimum, it is not obvious whether a human child or a gorilla has the greater value. With regard to the second question, an appeal can be made to Japanese environmental philosophy, particularly the ethical paradigm of kyōsei and the aesthetics of Yuriko Saitō. Members of endangered species have intrinsic value, which entails human obligations to protect the species as a whole and minimize harm to its specimens. (shrink)

This volume collects the best and most influential essays that Stephen Stich has published in the last 40 years on topics in the philosophy of mind and the philosophy of language. They discuss a wide range of topics including grammar, innateness, reference, folk psychology, eliminativism, connectionism, evolutionary psychology, simulation theory, social construction, and psychopathology. However, they are unified by two central concerns. The first is the viability of the commonsense conception of the mind in the face of challenges posed (...) by both philosophical arguments and empirical findings. The second is the philosophical implications of research in the cognitive sciences which, in the last half century, has transformed both our understanding of the mind and the ways in which the mind is studied. The volume includes a new introductory essay that elaborates on these themes and offers an overview of the papers that follow. (shrink)

This book introduces the history of third way ideology, surveys its various contrasting forms and locates it within the context of a recurrent crisis of modern European ideologies.

Successive UK governments have adopted failure as a strategy in the reform of public education in England: first, to construct crises in order to blame professionals/parents/children for a failing system; and second, to provide rescue solutions that are designed to fail in order to sustain the change imperative. We describe this as policy mortality, or the integration of systemic and organisational ‘death’ within reform design. Our research demonstrates the interplay between the blame for the ‘wrong’ type of school, leader, teacher, (...) pupil, parent, and the claimed ‘solutions’ in the form of new schools (e.g., between 70 and 90 different types in England), organisations (e.g., MATs), professionals (e.g., CEOs), pupils (e.g., branded access to a school place), and parents (e.g., consumer choice). Our research contribution is conceptual through the development of new thinking about policy mortality, whereby the claim is for ‘success’ but the reality is that some professionals, schools, children and parents are required to fail. (shrink)

Image factorizations in regular categories are stable under pullbacks, so they model a natural modal operator in dependent type theory. This unary type constructor [A] has turned up previously in a syntactic form as a way of erasing computational content, and formalizing a notion of proof irrelevance. Indeed, semantically, the notion of a support is sometimes used as surrogate proposition asserting inhabitation of an indexed family. We give rules for bracket types in dependent type theory and provide complete semantics using (...) regular categories. We show that dependent type theory with the unit type, strong extensional equality types, strong dependent sums, and bracket types is the internal type theory of regular categories, in the same way that the usual dependent type theory with dependent sums and products is the internal type theory of locally Cartesian closed categories. We also show how to interpret first-order logic in type theory with brackets, and we make use of the translation to compare type theory with logic. Specifically, we show that the propositions-as-types interpretation is complete with respect to a certain fragment of intuitionistic first-order logic, in the sense that a formula from the fragment is derivable in intuitionistic first-order logic if, and only if, its interpretation in dependent type theory is inhabited. As a consequence, a modified double-negation translation into type theory (without bracket types) is complete, in the same sense, for all of classical first-order logic. (shrink)

Negative attack ads used in political compaigns have been attacked as being unethical because they contribute to voter cynicism and apathy and as being manipulative. From a rhetorical perspective these advertisements serve a positive societal function by creating alternative rhetorical visions that can contribute to the marketplace of ideas.