Let CH be the class of compacta (i.e., compact Hausdorff spaces), with BS the subclass of Boolean spaces. For each ordinal α and pair $\langle K,L\rangle$ of subclasses of CH, we define Lev ≥α K,L), the class of maps of level at least α from spaces in K to spaces in L, in such a way that, for finite α, Lev ≥α (BS,BS) consists of the Stone duals of Boolean lattice embeddings that preserve all prenex first-order formulas of quantifier rank (...) α. Maps of level ≥ 0 are just the continuous surjections, and the maps of level ≥ 1 are the co-existential maps introduced in [8]. Co-elementary maps are of level ≥α for all ordinals α; of course in the Boolean context, the co-elementary maps coincide with the maps of level ≥ω. The results of this paper include: (i) every map of level ≥ω is co-elementary; (ii) the limit maps of an ω-indexed inverse system of maps of level ≥α are also of level ≥α; and (iii) if K is a co-elementary class, k ≥ k (K,K) = Lev ≥ k+1 (K,K), then Lev ≥ k (K,K) = Lev ≥ω (K,K). A space X ∈ K is co-existentially closed in K if Lev ≥ 0 (K, X) = Lev ≥ 1 (K, X). Adapting the technique of "adding roots," by which one builds algebraically closed extensions of fields (and, more generally, existentially closed extensions of models of universal-existential theories), we showed in [8] that every infinite member of a co-inductive co-elementary class (such as CH itself, BS, or the class CON of continua) is a continuous image of a space of the same weight that is co-existentially closed in that class. We show here that every compactum that is co-existentially closed in CON (a co-existentially closed continuum) is both indecomposable and of covering dimension one. (shrink)

Many properties of compacta have “textbook” definitions which are phrased in lattice-theoretic terms that, ostensibly, apply only to the full closed-set lattice of a space. We provide a simple criterion for identifying such definitions that may be paraphrased in terms that apply to all lattice bases of the space, thereby making model-theoretic tools available to study the defined properties. In this note we are primarily interested in properties of continua related to unicoherence; i.e., properties that speak to the existence of (...) “holes” in a continuum and in certain of its subcontinua. (shrink)

By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the "reduced coproduct", which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the "ultracoproduct" can be obtained from the usual topological ultraproduct via a compactification process in the style of Wallman and Frink. We prove theorems dealing with (...) the topological structure of reduced coproducts (especially ultracoproducts) and show in addition how one may use this construction to gain information about the category of compact Hausdorff spaces. (shrink)

The Chang-Łoś-Suszko theorem of first-order model theory characterizes universal-existential classes of models as just those elementary classes that are closed under unions of chains. This theorem can then be used to equate two model-theoretic closure conditions for elementary classes; namely unions of chains and existential substructures. In the present paper we prove a topological analogue and indicate some applications.

A topological classification scheme consists of two ingredients: (1) an abstract class K of topological spaces; and (2) a "taxonomy", i.e. a list of first order sentences, together with a way of assigning an abstract class of spaces to each sentence of the list so that logically equivalent sentences are assigned the same class. K is then endowed with an equivalence relation, two spaces belonging to the same equivalence class if and only if they lie in the same classes prescribed (...) by the taxonomy. A space X in K is characterized within the classification scheme if whenever Y ∈ K and Y is equivalent to X, then Y is homeomorphic to X. As prime example, the closed set taxonomy assigns to each sentence in the first order language of bounded lattices the class of topological spaces whose lattices of closed sets satisfy that sentence. It turns out that every compact two-complex is characterized via this taxonomy in the class of metrizable spaces, but that no infinite discrete space is so characterized. We investigate various natural classification schemes, compare them, and look into the question of which spaces can and cannot be characterized within them. (shrink)

Given a finite lexicon L of relational symbols and equality, one may view the collection of all L-structures on the set of natural numbers ω as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on ω. For example, (...) in every sense of relative ubiquity considered here, the set of dense linear orderings on ω is ubiquitous in the set of linear orderings on ω. (shrink)

The languages of finitary and infinitary logic over the alphabet of bounded lattices have proven to be of considerable use in the study of compacta. Significant among the sentences of these languages are the ones that are base free, those whose truth is unchanged when we move among the lattice bases of a compactum. In this paper we define syntactically the expansive sentences, and show each of them to be base free. We also show that many well-known properties of compacta (...) may be expressed using expansive sentences; and that any property so expressible is closed under inverse limits and co-existential images. As a byproduct, we conclude that co-existential images of pseudo-arcs are pseudo-arcs. This is of interest because the corresponding statement for confluent maps is still open, and co-existential maps are often—but not always—confluent. (shrink)

An error has been found in the cited paper; namely, Theorem 3.1 is false.

A first order representation (f.o.r.) in topology is an assignment of finitary relational structures of the same type to topological spaces in such a way that homeomorphic spaces get sent to isomorphic structures. We first define the notions "one f.o.r. is at least as expressive as another relative to a class of spaces" and "one class of spaces is definable in another relative to an f.o.r.", and prove some general statements. Following this we compare some well-known classes of spaces and (...) first order representations. A principal result is that if X and Y are two Tichonov spaces whose posets of zero-sets are elementarily equivalent then their respective rings of bounded continuous real-valued functions satisfy the same positive-universal sentences. The proof of this uses the technique of constructing ultraproducts as direct limits of products in a category theoretic setting. (shrink)

Noam Chomsky and Frances Egan argue that David Marr’s computational theory of vision is not intentional, claiming that the formal scientific theory does not include description of visual content. They also argue that the theory is internalist in the sense of not describing things physically external to the perceiver. They argue that these claims hold for computational theories of vision in general. Beyond theories of vision, they argue that representational content does not figure as a topic within formal computational theories (...) in cognitive science. I demonstrate that Chomsky’s and Egan’s claims about Marr’s theory are false. Marr’s computational theory contains a mathematical theory of visual content, based on empirical psychophysical evidence. It also contains mathematical descriptions of distal physical surfaces and objects, and of their optic projection to the perceiver. Much computational research on vision contains these types of intentional and externalist components within the formal, mathematical, theories. Chomsky’s and Egan’s claims demonstrate inadequate study and understanding of Marr’s work and other research in this area. Computational theories of vision, by containing empirically based mathematical theories of visual content, to this extent present naturalizations of semantics. (shrink)

Deleuze's concept of 'becoming' provides the key to his notoriously complex metaphysics, yet it has not been systematized until now. Bankston tracks the concept of becoming and its underlying temporal processes across Deleuze's writings, arguing that expressions of becoming(s) appear in two modes of temporality: an appropriation of Nietzsche's eternal return (the becoming of the event), and Bergsonian duration (the becoming of sensation). Overturning the criticisms launched by Žižek and Badiou, with conceptual encounters between Bergson, Nietzsche, Leibniz, Borges, Klossowski, (...) and Proust, the newly charted concept of double becoming provides a roadmap to the totality of Deleuze's philosophy. Bankston systematizes Deleuze's multi-mirrored universe where form and content infinitely refract in a vital kaleidoscope of becoming" -- Amazon.com. (shrink)

The ontologies of Slavoj Žižek and Gilles Deleuze are incommensurable. Rather than appropriate one at the expense of the other, this essay uses Žižek’s notion of parallax to think the two philosophers together, without mediation. Both Deleuze and Žižek provide mirrored philosophical images, with the point of divergence being absolute lack. Deleuze argues that lack, or the being of negation, is an error of representational understanding, while Žižek conceives his philosophy as being driven by absolute lack. A stark opponent of (...) Žižek’s precursor, Hegel, Deleuze rejects opposition as a constitutive feature of reality. However, Žižek mirrors Deleuze’s very concepts in his Lacanian reading of Hegel, while said concepts retain identical terms. For instance, Žižek calls l’objet petit a “difference,” while his term for absolute negation is “repetition,” and finally, he refers to his philosophical system as the “non-All”. These singular concepts in Žižek’s thought share an identical language with that of Deleuze. Deleuze’s philosophy is one of “difference,” while its mode of proliferation is “repetition,” and finally, he often refers to his philosophy as the “One-All”. Mapping these common terms that do not denote a common language, but incommensurable, inverse logics, it becomes evident that Deleuze and Žižek are mirror images of one another, infinitely fragmenting across the expanse of their respective positions. Thus, by triangulating ontology from their unique perspectives, a new ontological shift emerges—one that resists mediation and admixture. (shrink)

The study of anarchism as a philosophical, political, and social movement has burgeoned both in the academy and in the global activist community in recent years. Taking advantage of this boom in anarchist scholarship, Nathan J. Jun and Shane Wahl have compiled twenty-six cutting-edge essays on this timely topic in New Perspectives on Anarchism.

This edition includes a new introduction by Peter J. Gomes that reflects on the impact of this book in the years since it was written.

We are witnessing increasing use of the Internet, particular social media, to criticize (perceived or actual) moral failings and misdemeanors. This phenomenon of so-called ‘online public shaming’ could provide a powerful tool for reinforcing valuable social norms. But it also threatens unwarranted and severe punishments meted out by online mobs. This paper analyses the dangers associated with the informal enforcement of norms, drawing on Locke, but also highlights its promise, drawing on recent discussions of social norms. We then consider two (...) crucial conditions that online public shaming must meet in order to be justifiable: proportionality and accountability. We argue that these requirements are in fact frequently violated, rendering most cases of online public shaming unjustified. While the use of online public shaming against others’ vices has some apparent virtues, it is currently rarely justified, given its own vices. (shrink)

Reasons and reasoning were central to the work of Paul Grice, one of the most influential and admired philosophers of the late twentieth century. In the John Locke Lectures that Grice delivered in Oxford at the end of the 1970s, he set out his fundamental thoughts about these topics; Aspects of Reason is the long-awaited publication of those lectures. This immensely rich work, powerfully evocative of the mind of its author, will refresh and illuminate discussions in many areas of (...) contemporary philosophy. (shrink)

Forced to Fail traces the long legal history of first racial segregation, and then racial desegregation in America. The authors explain how rapidly changing demographics and family structure in the United States have greatly complicated the project of top-down government efforts to achieve an "ideal" racial balance in schools. It describes how social capital—a positive outcome of social interaction between and among parents, children, and teachers—creates strong bonds that lead to high academic achievement.

This is a collection in translation of essays by Paul Ricoeur which presents a comprehensive view of his philosophical hermeneutics, its relation to the views of his predecessors in the tradition and its consequences for the social sciences. The volume has three parts. The studies in the first part examine the history of hermeneutics, its central themes and the outstanding issues it has to confront. In Part II, Ricoeur's own current, constructive position is developed. A concept of the text (...) is formulated as the implications of the theory are pursued into the domains of sociology, psychoanalysis and history. Many of the essays appear here in English for the first time; the editor's introduction brings out their background in Ricoeur's thought and the continuity of his concerns. The volume will be of great importance for those interested in hermeneutics and Ricoeur's contribution to it, and will demonstrate how much his approach offers to a number of disciplines. (shrink)

The ethical issues raised by cybersecurity practices and technologies are of critical importance. However, there is disagreement about what is the best ethical framework for understanding those issues. In this paper we seek to address this shortcoming through the introduction of a principlist ethical framework for cybersecurity that builds on existing work in adjacent fields of applied ethics, bioethics, and AI ethics. By redeploying the AI4People framework, we develop a domain-relevant specification of five ethical principles in cybersecurity: beneficence, non-maleficence, autonomy, (...) justice, and explicability. We then illustrate the advantages of this principlist framework by examining the ethical issues raised by four common cybersecurity contexts: penetration testing, distributed denial of service attacks (DDoS), ransomware, and system administration. These case analyses demonstrate the utility of this principlist framework as a basis for understanding cybersecurity ethics and for cultivating the ethical expertise and ethical sensitivity of cybersecurity professionals and other stakeholders. (shrink)

In this chapter a new problem about rule-following is outlined, one that is distinct both from Kripke’s and Wright’s versions of the problem. This new problem cannot be correctly responsed to, as Kripke’s can, by invoking Wright’s Intentional Account of rule-following. The upshot might be called, following Kant, an antinomy of pure reason: we both must — and cannot — make sense of someone’s following a rule. The chapter explores various ways out of this antinomy without here endorsing any of (...) them. (shrink)

Foreword William Schweiker Paul Tillich, one of the great Protestant theologians of the twentieth century, addresses in Morality and Beyond a basic problem ...

In this study of space and power and knowledge in France from the 1830s through the 1930s, Rabinow uses the tools of anthropology, philosophy, and cultural criticism to examine how social environment was perceived and described. Ranging from epidemiology to the layout of colonial cities, he shows how modernity was revealed in urban planning, architecture, health and welfare administration, and social legislation.

Paul Thom's book presents Kilwardby's science of logic as a body of demonstrative knowledge about inferences and their validity, about the semantics of non-modal and modal propositions, and about the logic of genus and species. This science is thoroughly intensional. It grounds the logic of inference on "that in virtue of which" the inference holds. It bases the truth conditions of propositions on relations between conceptual entities. It explains the logic of genus and species through the notion of essence. (...) Thom interprets this science as a formal logic of intensions with its own proof theory and semantics. This comprehensive reconstruction of Kilwardby's logic shows the medieval master to be one of the most interesting logicians of the thirteenth century. (shrink)

De milieuproblematiek staat pas sinds kort op de agenda als een fenomeen dat de mensheid bedreigt. Toch blijkt het negentiende-eeuwse gedachtegoed van Karl Marx verrassende inzichten te bieden om deze actuele problemen te duiden. Marx laat zien dat het menselijk ingrijpen in de natuur leidt tot zelfvervreemding: de mens ondermijnt zijn bestaan als een wezen dat zelf deel uitmaakt van de natuur. Deze zelfvervreemding cumuleert in de kapitalistische samenleving. Marx lezend zien we dat de milieuproblematiek geen historische vergissing is, maar (...) fundamenteel samenhangt met de mens als redelijk wezen. Onze beheersingsrede heeft geleid tot de vervreemding van de natuur. Toch geeft dezelfde rede die de mens de vrijheid biedt zich boven het ecologische evenwicht te verheffen, hem de mogelijkheid zich te verzoenen met de natuur. Marx verwijst naar dit dubbele gezicht van de rede als hij stelt dat het 'rijk van de vrijheid' in de schoot van het kapitalisme wordt geboren. In dit boek onderzoekt Paul Cobben welke aanzetten de huidige samenleving biedt om vorm te geven aan de verzoening met de natuur. Paul Cobben is emeritus hoogleraar geschiedenis van de moderne filosofie aan Tilburg University. Momenteel is hij gastonderzoeker aan de Vrije Universiteit Amsterdam en redacteur van de serie 'Critical Studies in German Idealism'. Van zijn hand verscheen o.a. 'Value in Capitalist Society. Rethinking Marx's Criticism of Capitalism' (2015)."-- Publisher information. (shrink)

The Renaissance was a period of great intellectual change and innovation as philosophers rediscovered the philosophy of classical antiquity and passed it on to the modern age. Renaissance philosophy is distinct both from the medieval scholasticism, based on revelation and authority, and from philosophers of the seventeenth and eighteenth centuries who transformed it into new philosophical systems. Despite the importance of the Renaissance to the development of philosophy over time, it has remained largely understudied by historians of philosophy and professional (...) philosophers. This anthology aims to correct this by providing scholars and students of philosophy with representative translations of the most important philosophers of the Renaissance. Its purpose is to help readers appreciate philosophy in the Renaissance and its importance in the history of philosophy. The anthology includes translations from philosophers from the thirteenth to the seventeenth centuries, and it ranges from works on moral and political philosophy, to metaphysics, epistemology, and natural philosophy, thereby providing historians and students of philosophy with a sense for the nature, breadth, and complexity of philosophy in the Renaissance. Each translation is accompanied by an introduction by a historian of Renaissance philosophy, as well as select secondary sources, in order to encourage further study. (shrink)

Paul Helm investigates what religious faith is and what makes it reasonable.

Logic brings elementary logic out of the academic darkness into the light of day. Paul Tomassi makes logic fully accessible for anyone trying to come to grips with the complexities of this challenging subject. This book is written in a patient and user-friendly way which makes both the nature and value of formal logic crystal clear. This textbook proceeds from a frank, informal introduction to fundamental logical notions to a system of formal logic rooted in the best of our (...) natural deductive reasoning in daily life. The book includes plenty of exercise to put the students' reading to test, summay boxes of key points, a glossary and many illustrations. This book will be useful to any student who needs a patient and comprehensible introduction to what otherwise can be a daunting subject. (shrink)

We sometimes strive to achieve difficult goals when our evidence suggests that success is unlikely – not just because it will require strength of will, but because we are targets of prejudice and discrimination or because success will require unusual ability. Optimism about one’s prospects can be useful for persevering in these cases. That said, excessive optimism can be dangerous; when our evidence is unfavourable, we should be at most agnostic about whether we will succeed. This paper explores the nature (...) and rational significance of agnostic practical commitments. Most importantly, the rationality of striving against the odds can depend on investing in a plan for failure: a plan B. I aim to make headway on an account of what backup plans are, how they are related to primary plans, and whether the standard norms of plan rationality apply to our agnostic commitments. (shrink)

One dimension of the controversy over whether evaluative properties are presented in perceptual content has general roots in the debate over whether perceptual content, in general, is rich or austere. I argue that we need to recognise a level of rich non-sensory perceptual content, drawing on experiences of chicken sexing and speech perception, to capture what our experience is like and our epistemic entitlements. In both cases (and many others), we are not conscious of the precise perceptual cues that are (...) the basis for discriminations and, thus, the characterisation of the phenomenal content of such experiences must go beyond sensory properties. Nevertheless, this point is arguably insufficient to establish the perception of evaluative properties. Their representation requires the subject to respond in certain ways. I discuss how this should go for the case of pain and then, in outline, for moral properties. (shrink)

This paper introduces constitutivism about practical reason, which is the view that we can justify certain normative claims by showing that agents become committed to these claims simply in virtue of acting. According to this view, action has a certain structural feature – a constitutive aim, principle, or standard – that both constitutes events as actions and generates a standard of assessment for action. We can use this standard of assessment to derive normative claims. In short, the authority of certain (...) normative claims arises from the bare fact that we are agents. This essay explains the constitutivst strategy, surveys the extant attempts to generate constitutivist theories, and considers the problems and prospects for the theory. (shrink)

The relationship between abstract formal procedures and the activities of actual physical systems has proved to be surprisingly subtle and controversial, and there are a number of competing accounts of when a physical system can be properly said to implement a mathematical formalism and hence perform a computation. I defend an account wherein computational descriptions of physical systems are high-level normative interpretations motivated by our pragmatic concerns. Furthermore, the criteria of utility and success vary according to our diverse purposes and (...) pragmatic goals. Hence there is no independent or uniform fact to the matter, and I advance the ‘anti-realist’ conclusion that computational descriptions of physical systems are not founded upon deep ontological distinctions, but rather upon interest-relative human conventions. Hence physical computation is a ‘conventional’ rather than a ‘natural’ kind. (shrink)

Freud claimed that the concept of drive is "at once the most important and the most obscure element of psychological research." It is hard to think of a better proof of Freud's claim than the work of Nietzsche, which provides ample support for the idea that the drive concept is both tremendously important and terribly obscure. Although Nietzsche's accounts of agency and value everywhere appeal to drives, the concept has not been adequately explicated. I remedy this situation by providing an (...) account of drives. I argue that Nietzschean drives are dispositions that generate evaluative orientations, in part by affecting perceptual saliences. In addition, I show that drive psychology has important implications for contemporary accounts of reflective agency. Contemporary philosophers often endorse a claim that has its origins in Locke and Kant: self-conscious agents are capable of reflecting on and thereby achieving a distance from their motives; therefore, these motives do not determine what the agent will do. Nietzsche's drive psychology shows that the inference in the preceding sentence is illegitimate. The drive psychology articulates a way in which motives can determine the agent's action by influencing the course of the agent's reflective deliberations. An agent who reflects on a motive and decides whether to act on it may, all the while, be surreptitiously guided by the very motive upon which he is reflecting. I show how this point complicates traditional models of the role of reflection in agency. (shrink)

[Significantly updated in Chapter 6 of Awareness and the Substructure of Knowledge] In order for a reason to justify an action or attitude it must be one that is possessed by an agent. Knowledge-centric views of possession ground our possession of reasons, at least partially, either in our knowledge of them or in our being in a position to know them. On virtually all accounts, knowing P is some kind of non-accidental true belief that P. This entails that knowing P (...) is a kind of non-accidental true representation that P. I outline a novel theory of the epistemic requirement on possession in terms of this more general state of non-accidental true representation. It is just as well placed to explain the motivations behind knowledge-centric views of possession, and it is also better placed to explain the extent of the reasons we possess in certain cases of deductive belief-updates and cases involving environmental luck. I conclude with three reflections. First, I indicate how my arguments generate a dilemma for Errol Lord’s view that possessing reasons is just a matter of being in a position to manifest one’s knowledge how to use them. Second, I explain how my view can simultaneously manage cases of environmental luck without falling prey to lottery cases. Finally, I sketch the direction for a further range of counterexamples to knowledge-centric theories of possession. (shrink)

The Oxford Handbook of Epistemology contains 19 previously unpublished chapters by today's leading figures in the field. These chapters function not only as a survey of key areas, but as original scholarship on a range of vital topics. Written accessibly for advanced undergraduates, graduate students, and professional philosophers, the Handbook explains the main ideas and problems of contemporary epistemology while avoiding overly technical detail.

Conservatism about perceptual justification tells us that we cannot have perceptual justification to believe p unless we also have justification to believe that perceptual experiences are reliable. There are many ways to maintain this thesis, ways that have not been sufficiently appreciated. Most of these ways lead to at least one of two problems. The first is an over-intellectualization problem, whereas the second problem concerns the satisfaction of the epistemic basing requirement on justified belief. I argue that there is at (...) least one Conservative view that survives both difficulties, a view which has the further ability to undercut a crucial consideration that has supported Dogmatist views about perceptual justification. The final section explores a tension between Conservatism and the prospects of having a completely general account of propositional justification. Ironically, the problem is that Conservatives seem committed to making the acquisition of propositional justification too easy. My partial defense of Conservatism concludes by suggesting possible solutions to this problem. (shrink)

Paul M. Pietroski, University of Maryland I had heard it said that Chomsky’s conception of language is at odds with the truth-conditional program in semantics. Some of my friends said it so often that the point—or at least a point—finally sunk in.

Vorrangig als der "strengste Methodenfanatiker und Logizist" der Marburger Schule des Neukantianismus bekannt, trat Natorp jedoch genau an diesem Punkt mit der selbständigen Form seines späten Philosophierens hervor: der Überschreitung der Methode in der Idee einer allgemeinen Logik. Unter allgemeiner Logik versteht er die streng einheitliche logische Grundlegung der Gegenstandssetzung, ja aller irgendwie logisch erfaßlichen Setzung. Damit war ein Zugang geschaffen zu der von Natorp angestrebten Erkenntnis des Geistigen in seiner Ureinheit, aus der erst die Besonderungen hervorgehen.

Le philosophe, collègue et ami de Michel Foucault, fait le portrait de ce dernier et présente les grands thèmes de sa pensée philosophique et politique.

The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers.