Critical Realism and Marxism addresses controversial debates, revealing a potentially fruitful relationship; deepening our understanding of the social world and contibuting towards eliminating barbarism in contemporary capitalism.

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.

I argue that, contrary to intuition, it would be both possible and permissible to design people - whether artificial or organic - who by their nature desire to do tasks we find unpleasant.

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)

"The Knowledge Book" is a unique interdisciplinary reference work for students and researchers concerned with the nature of knowledge. It is the first work of its kind to be organized on the assumption that whatever else knowledge might be, it is intrinsically social. The book consists of 42 alphabetically arranged entries on key concepts at the intersection of philosophy and sociology - what used to be called "sociology of knowledge" but is now increasingly called "social epistemology". The entries include concepts (...) common to disciplines that in recent years have devoted more of their attention to knowledge: cultural studies, communication studies, information science, education, policy studies and business studies. Special attention is given to concepts from the emerging field of science and technology studies. Each entry presents a short, self-contained essay providing an overview of a concept and concludes with suggestions for further reading. All the entries are fully cross-referenced, allowing readers to both make connections and follow their own interests. (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)

of type theory has been used successfully to formalize large parts of constructive mathematics, such as the theory of generalized recursive definitions [NPS90, ML79]. Moreover, it is also employed extensively as a framework for the development of high-level programming languages, in virtue of its combination of expressive strength and desirable proof-theoretic properties [NPS90, Str91]. In addition to simple types A, B, . . . and their terms x : A b(x) : B, the theory also has dependent types x : (...) A B(x), which are regarded as indexed families of types. There are simple type forming operations A × B and A → B, as well as operations on dependent types, including in particular the sum x:A B(x) and product x:A B(x) types (see the appendix for details). The Curry-Howard interpretation of the operations A × B and A → B is as propositional conjunction and.. (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 (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)

Bostrom and Ord’s reversal test has been appealed to by many philosophers to substantiate the charge that preferences for status quo options are motivated by status quo bias. I argue that their characterization of the reversal test needs to be modified, and that their description of the burden of proof it imposes needs to be clarified. I then argue that there is a way to meet that burden of proof which Bostrom and Ord fail to recognize. I also argue that (...) the range of circumstances in which the reversal test can be usefully applied is narrower than they recognize. (shrink)

In the spirit of the pragmatic account of quotation and reporting offered by Macagno and Walton (2017), we outline a systematic pragmatic account of rephrasing. For this purpose, we combine two interrelated methods of inquiry into the variety of uses of rephrase as a persuasive device: (i) the annotation of rephrase types to identify locutionary and illocutionary aspects of rephrase, (ii) the crowd–sourced examination of rephrase types to investigate their perlocutionary effects. As it draws on Waltonian insights and on empirical (...) and experimental research on the (mis)use of rephrase, our approach allows us to ground a novel theoretically–informed and data–driven pragmatic account of rephrase. (shrink)

In the spirit of the pragmatic account of quotation and reporting offered by Macagno and Walton (2017), we outline a systematic pragmatic account of rephrasing. For this purpose, we combine two interrelated methods of inquiry into the variety of uses of rephrase as a persuasive device: (i) the annotation of rephrase types to identify locutionary and illocutionary aspects of rephrase, (ii) the crowd–sourced examination of rephrase types to investigate their perlocutionary effects. As it draws on Waltonian insights and on empirical (...) and experimental research on the (mis)use of rephrase, our approach allows us to ground a novel theoretically–informed and data–driven pragmatic account of rephrase. (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 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)

The present paper shows that the clearest formulation of J. M. E. McTaggart's antipassage argument, that of D. H. Mellor in _Real Time II, is unsound when its premises are interpreted so that it is valid. This argument need mislead us no longer. The crucial item in the interpretation of the premises is the copula 'is', as in 'E is past'. The copula may be either tensed or tenseless. While this ambiguity of the copula has been noted before, its implications (...) for McTaggart's argument had not been adequately exploited. This paper does that job. (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)

In what sense is a person addicted to drugs or alcohol incompetent, and so a legitimate object of coercive treatment? The standard tests for competence do not pick out the capacity that is lost in addiction: the capacity to properly regulate consumption. This paper is an attempt to sketch a justificatory framework for understanding the conditions under which addicted persons may be treated against their will. These conditions rarely obtain, for they apply only when addiction is extremely severe and great (...) harm threatens. It will be argued also that to widen the measures currently in place in some jurisdictions, though philosophically well-motivated, would require very strong evidence of a set of conditions disposing a person to an addictive future. It is doubtful that any such currently available evidence is strong enough to justify coercive treatment. Nevertheless, coercive treatment of addiction is already a reality, with the potential for more, and so some discussion will be presented regarding the extraordinary safeguards necessary to prevent misapplication of such treatment policies. (shrink)

This article explores the role of changing memes in large systems change toward marriage equality—popularly referred to as same-sex marriage—in the United States. Using an abbreviated case history of the transformation, the article particularly explores the shifting memes or core units of culture, in this case, word phrases associated with marriage equality over time, influencing the social change process. Using both the case history and the empirical work on memes, the article identifies nine lessons to support others tackling large systems (...) change challenges. (shrink)

The purpose of the Cambridge Edition is to offer translations of the best modern German edition of Kant's work in a uniform format suitable for Kant scholars. When complete the edition will include all of Kant's published writings and a generous selection from the unpublished writings such as the Opus postumum, handschriftliche Nachlass, lectures, and correspondence. This volume contains the first translation into English of notes from Kant's lectures on metaphysics. These lectures, dating from the 1760s to the 1790s, touch (...) on all the major topics and phases of Kant's philosophy. Most of these notes have appeared only recently in the German Academy Edition; this translation offers many corrections of that edition. As is standard with the volumes in the Cambridge Edition there is an extensive editorial apparatus, including extensive linguistic and explanatory notes, a detailed subject index, and glossaries of key terms. (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.

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.

Aims to find the common language between two of the most important philosophical thinkers of the twentieth century.

Three different styles of foundations of mathematics are now commonplace: set theory, type theory, and category theory. How do they relate, and how do they differ? What advantages and disadvantages does each one have over the others? We pursue these questions by considering interpretations of each system into the others and examining the preservation and loss of mathematical content thereby. In order to stay focused on the “big picture”, we merely sketch the overall form of each construction, referring to the (...) literature for details. Each of the three steps considered below is based on more recent logical research than the preceding one. The first step from sets to types is essentially the familiar idea of set theoretic semantics for a syntactic system, i.e. giving a model; we take a brief glance at this step from the current point of view, mainly just to fix ideas and notation. The second step from types to categories is known to categorical logicians as the construction of a “syntactic category”; we give some specifics for the benefit of the reader who is not familiar with it. The third step from categories to sets is based on quite recent work, but captures in a precise way an intuition from the early days of foundational studies. With these pieces in place, we can then draw some conclusions regarding the differences between the three schemes, and their relative merits. In particular, it is possible to state more precisely why the methods of category theory are more appropriate to philosophical structuralism. (shrink)

This book examines Whitehead’s process aesthetics focusing on two categories, the penumbral beauty of darkness and the tragic beauty of perishability, while establishing parallels with the Japanese sense of evanescent beauty. It clarifies how both traditions develop a religio-aesthetic vision of tragic beauty and its reconciliation in the supreme ecstasy of peace.

It is suggested that some limitations of current designs for medical AI systems stem from the failure of those designs to address issues of artificial consciousness. Consciousness would appear to play a key role in the expertise, particularly the moral expertise, of human medical agents, including, for example, autonomous weighting of options in diagnosis; planning treatment; use of imaginative creativity to generate courses of action; sensorimotor flexibility and sensitivity; empathetic and morally appropriate responsiveness; and so on. Thus, it is argued, (...) a plausible design constraint for a successful ethical machine medical or care agent is for it to at least model, if not reproduce, relevant aspects of consciousness and associated abilities. In order to provide theoretical grounding for such an enterprise we examine some key philosophical issues that concern the machine modelling of consciousness and ethics, and we show how questions relating to the first research goal are relevant to medical machine ethics. We believe that this will overcome a blanket skepticism concerning the relevance of understanding consciousness, to the design and construction of artificial ethical agents for medical or care contexts. It is thus argued that it would be prudent for designers of MME agents to reflect on issues to do with consciousness and medical expertise; to become more aware of relevant research in the field of machine consciousness ; and to incorporate insights gained from these efforts into their designs. (shrink)

The notion of a continuously variable quantity can be regarded as a generalization of that of a particular (constant) quantity, and the properties of such quantities are then akin to, and derived from, the..

The [lambda]-calculus can be represented topologically by assigning certain spaces to the types and certain continuous maps to the terms. Using a recent result from category theory, the usual calculus of [lambda]-conversion is shown to be deductively complete with respect to such topological semantics. It is also shown to be functionally complete, in the sense that there is always a ‘minimal’ topological model in which every continuous function is [lambda]-definable. These results subsume earlier ones using cartesian closed categories, as well (...) as those employing so-called Henkin and Kripke [lambda]-models. (shrink)

Knowledge is a collective enterprise, all of whose members potentially benefit from any one of them managing to achieve, or at least approximate, the truth. However, it does not follow that the best way to do this is by trying to establish the truth for oneself as a fixed belief and then making it plain for all to hear or see, so that it might spread like a virus, or “meme”, as Richard Dawkins might say.

William Cronon has recently argued that the current debate concerning justifications for protecting wilderness relies upon conceptions of natural value premised upon a nature/society dualism that originated in older nature writing but which still animates contemporary thinking. This dualism, he argues, prevents adequate realization of the human and social places in nature, and is ultimately counterproductiveto the task of articulating the proper relationship between humans and the natural world. While the origin of one of these conceptions of natural value (the (...) frontier) can be traced back to Rousseau, I argue that Rousseau’s writings reveal a far more complex and nuanced treatment of the value of nature in and for society (and the persons that compose it) than has thus far been acknowledged. Moreover, by unpacking several arguments made by Rousseau on behalf of the stewardship and accessibility of natural areas, one can not only gain a more accurate view of Rousseau’s environmental thought than is ordinarily recognized by authors who focus on his primitivism and anti-modern critique, but also some insights that may help bridge the nature/society dualism plaguing contemporary environmental ethics and noted by Cronon. (shrink)

The politics of food illustrates an enduring tension within environmental ethics and green political theory: the oft-assumed division between those thinkers for whom humanitarian goals remain prominent but who situate them within a normative framework stressing environmental sustainability and those thinkers who reject any distinctively humanitarian interests as untenably anthropocentric. In posing the problem as a moral dilemma between feeding people and saving nature, light and dark green value theories are made to appear in stark contrast, with the former prescribing (...) the delivery of food aid to relieve hunger-related suffering, and the latter rejecting that call. This supposed dilemma between feeding people and saving nature is a false one. The real problem is a moral elitism on the part of developed countries where an insidious form of selfishness overemphasizes the role of population and obscures the roles of highly variable rates of consumption upon current environmental ills. An examination of theexemplary case of food politics shows that the exaggerated differences in policy implications of these two value theories can be diminished and that there is potential for common cause. (shrink)

Many political philosophers today think of justice as fundamentally about fairness, while those who defend capital punishment typically hold that justice is fundamentally about desert. In this paper I show that justice as fairness calls for capital punishment because the continued existence of murderers increases unfairness between themselves and their victims, increasing the harm to murdered persons. Rescuing murdered persons from increasing harm is prima facie morally required, and so capital punishment is a prima facie duty of society and sentencing (...) judges.1. (shrink)