Berger, U., Total sets and objects in domain theory, Annals of Pure and Applied Logic 60 91-117. Total sets and objects generalizing total functions are introduced into the theory of effective domains of Scott and Ersov. Using these notions Kreisel's Density Theorem and the Theorem of Kreisel-Lacombe-Shoenfield are generalized. As an immediate consequence we obtain the well-known continuity of computable functions on the constructive reals as well as a domain-theoretic characterization of the Heriditarily Effective Operations.

The paper presents a refined method of extracting reasonable and sometimes unexpected programs from classical proofs of formulas of the form ∀x∃yB . We also generalize previously known results, since B no longer needs to be quantifier-free, but only has to belong to a strictly larger class of so-called “goal formulas”. Furthermore we allow unproven lemmas D in the proof of ∀x∃yB , where D is a so-called “definite” formula.

We present an extension of Heyting arithmetic in finite types called Uniform Heyting Arithmetic that allows for the extraction of optimized programs from constructive and classical proofs. The system has two sorts of first-order quantifiers: ordinary quantifiers governed by the usual rules, and uniform quantifiers subject to stronger variable conditions expressing roughly that the quantified object is not computationally used in the proof. We combine a Kripke-style Friedman/Dragalin translation which is inspired by work of Coquand and Hofmann and a variant (...) of the refined A-translation due to Buchholz, Schwichtenberg and the author to extract programs from a rather large class of classical first-order proofs while keeping explicit control over the levels of recursion and the decision procedures for predicates used in the extracted program. (shrink)

This paper describes formalizations of Tait's normalization proof for the simply typed λ-calculus in the proof assistants Minlog, Coq and Isabelle/HOL. From the formal proofs programs are machine-extracted that implement variants of the well-known normalization-by-evaluation algorithm. The case study is used to test and compare the program extraction machineries of the three proof assistants in a non-trivial setting.

Building on previous work by Coquand and Spiwack [T. Coquand, A. Spiwack, A proof of strong normalisation using domain theory, in: Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science, LICS’06, IEEE Computer Society Press, 2006, pp. 307–316] we construct a strict domain-theoretic model for the untyped λ-calculus with pattern matching and term rewriting which has the property that a term is strongly normalising if its value is not . There are no disjointness or confluence conditions imposed (...) on the rewrite rules, and under a mild but necessary condition completeness of the method is proven. As an application, we prove strong normalisation for barrecursion in higher types combined with polymorphism and non-deterministic choice. (shrink)

We study, from a classical point of view, how the truth of a statement about higher type functionals depends on the underlying model. The models considered are the classical set-theoretic finite type hierarchy and the constructively more meaningful models of continuous functionals, hereditarily effective operations, as well as the closed term model of Gödel's system T. The main results are characterisations of prenex classes for which truth in the full set-theoretic model transfers to truth in the other models. As a (...) corollary we obtain that the axiom of choice is not conservative over Gödel's system T with classical logic for closed ∃2-formulas. We hope that this study will contribute to a clearer delineation and perception of constructive mathematics from a classical perspective. (shrink)

We study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract computational content from proofs about abstract structures specified by arbitrary classically true disjunction free formulas. The interpretation is shown to be sound with respect to a domain-theoretic denotational semantics and a corresponding lazy operational semantics of a functional language for extracted programs. We also show how (...) extracted programs can be translated into Haskell. As an application we extract a program converting the signed digit representation of real numbers to infinite Gray code from a proof of inclusion of the corresponding coinductive predicates. (shrink)

According to what Birch (2022) calls the theory-heavy approach to investigating nonhuman-animal consciousness, we select one of the well-developed theories of consciousness currently debated within contemporary cognitive science and investigate whether animals exhibit the neural structures or cognitive abilities posited by that theory as sufficient for consciousness. Birch argues, however, that this approach is in general problematic because it faces what he dubs the dilemma of demandingness—roughly, that we cannot use theories that are based on the human case to assess (...) consciousness in nonhuman animals and vice versa. We argue here that, though this dilemma may problematize the application of many current accounts of consciousness to nonhuman animals, it does not challenge the use of standard versions of the higher-order thought theory (“HOTT”) of consciousness, according to which a creature is in a conscious mental state just in case it is aware of being in that state via a suitable higher-order thought (“HOT”). We show this in two ways. First, we argue that, unlike many extant theories of consciousness, HOTT is typically motivated by a commonsense, and more importantly, neutral condition on consciousness that applies to humans and animals alike. Second, we offer new empirical and theoretical reasons to think that many nonhuman animals possess the relevant HOTs necessary for consciousness. Considering these issues not only reveals the explanatory power of HOTT and some of its advantages over rival accounts, but also enables us to further extend and clarify the theory. (shrink)

Perceptual experiences justify beliefs. A perceptual experience of a dog justifies the belief that there is a dog present. But there is much evidence that perceptual states can occur without being conscious, as in experiments involving masked priming. Do unconscious perceptual states provide justification as well? The answer depends on one’s theory of justification. While most varieties of externalism seem compatible with unconscious perceptual justification, several theories have recently afforded to consciousness a special role in perceptual justification. We argue that (...) such views face a dilemma: either consciousness should be understood in functionalist terms, in which case our best current theories of consciousness do not seem to imbue consciousness with any special epistemic features, or it should not, in which case it is mysterious why only conscious states are justificatory. We conclude that unconscious perceptual justification is quite plausible. (shrink)

For over twenty years Douglas Berger has advanced research and reflection on Indian philosophical traditions from both classical and cross-cultural perspectives. This volume reveals the extent of his contribution by bringing together his perspectives on these classical Indian philosophies and placing them in conversation with Confucian, Chinese Buddhist and medieval Indian Sufi traditions. Delving into debates between Nyaya and Buddhist philosophers on consciousness and identity, the nature of Sankara's theory of the self, the precise character of Nagarjuna's idea of (...) emptiness, and the relationship between awareness and embodiment in the broad spectrum of Indian thought, chapters exhibit Berger's unusually broad range of expertise. They connect Chinese Confucian and Buddhist texts with classical Indian theories of ethics and consciousness, contrast the ideas of seminal European thinkers like Nietzsche and Derrida from prevailing themes in Buddhism, and shed light on the spiritual and political dimensions of the Mughal prince Dara Shukoh's immersion into Vedantic thought. Always approaching the arguments from an intercultural perspective, Berger shows how much relevance and resonance classical Indian thought has with ancient Confucian views of ethics, Chinese Buddhist depictions of consciousness and medieval Mughal conceptions of divinity. The result is a volume celebrating the rigor, vitality and intercultural resonance of India's rich philosophical heritage. (shrink)

Ulrich Meyer defends a novel theory about the nature of time, and argues against the consensus view that time and space are fundamentally alike. He presents the first comprehensive defense of a 'modal' account, which emphasizes the similarities between times and possible worlds in modal logic, and is easily reconciled with the theory of relativity.

David Rosenthal explains conscious mentality in terms of two independent, though complementary, theories—the higher-order thought (“HOT”) theory of consciousness and quality-space theory (“QST”) about mental qualities. It is natural to understand this combination of views as constituting a kind of representationalism about experience—that is, a version of the view that an experience’s conscious character is identical with certain of its representational properties. At times, however, Rosenthal seems to resist this characterization of his view. We explore here whether and to what (...) extent it makes sense to construe Rosenthal’s views as representationalist. Our goal is not merely terminological—discerning how best to use the expression ‘representationalism’. Rather, we argue that understanding Rosenthal’s account as a kind of representationalism permits us not only to make sense of broader debates within the philosophy of mind, but also to extend and clarify aspects of the view itself. (shrink)

Discusses the journey of Buddhist ideas on awareness and personhood from India to China. Encounters of Mind explores a crucial step in the philosophical journey of Buddhism from India to China, and what influence this step, once taken, had on Chinese thought in a broader scope. The relationship of concepts of mind, or awareness, to the constitution of personhood in Chinese traditions of reflection was to change profoundly after the Cognition School of Buddhism made its way to China during the (...) sixth century. India’s Buddhist philosophers had formulated the idea that, in order for human beings to achieve perfect enlightenment, they had to produce a state of awareness through practice that they described as “luminous.” However, once introduced to the Chinese tradition, the concept of the “luminous mind” was to become a condition already found within human nature for the possibility of achieving human ideals. This notion of the luminous mind was to have far-reaching significance both for Chinese Buddhism and for medieval Confucianism. Douglas L. Berger follows the transforming path of conceptions of the luminosity of consciousness and the perfectibility of personhood in order to bring into clearer relief the history of Indian and Chinese philosophical dialogue, as well as in the hope that such dialogue will be reignited. (shrink)

Locating stance -- Structures of stance in lived experience -- Stance and others, stance and lives -- The social life of stance and the politics of expressive culture.

Just as noncapacitated decision making will forever be a feature of clinical medicine, so will the quest for effective advance care planning and serviceable documentation of these preferences. “Re-...

Thoughtprints Anne E. Berger andMarta Segarra I admit to it in the name of autobiography and in order to confide in you the following: [...] I have a particularly animalist perception and interpretation of what I do, think, write, live, ...

Drawing on the thought of Heidegger, this book puts forward a new conception of attention as human presence, showing how its state determines the efficacy of public spaces in articulating and achieving visions of the common good. A valuable resource for scholars of philosophy of mind, political philosophy, phenomenology, and cognitive science.

Periods of transition are often symbolically associated with death, making the latter the paradigm of liminality. Yet, many volumes on death in the social sciences and humanities do not specifically address liminality. This book investigates these "ultimate ambiguities," assuming they can pose a threat to social relationships because of the disintegrating forces of death, but they are also crucial periods of creativity, change, and emergent aspects of social and religious life. Contributors explore death and liminality from an interdisciplinary perspective and (...) present a global range of historical and contemporary case studies outlining emotional, cognitive, artistic, social, and political implications. (shrink)

Acknowledgements Andrea Scarantino, Nicholas Shea, Mark Sprevak, and three anonymous referees provided incisive and constructive comments, for which I am very grateful. In 2012, earlier versions of this paper were delivered in Edinburgh, at the Joint Session in Stirling, and at a workshop on natural information in Aberdeen. I thank participants for their feedback.

It is to an over-all situation based upon the complex play of political, social, economic and scientific factors, along with technological and mass media factors unique to our own era, that we owe the general trend toward multi-pluri-inter-trans-disciplinary questions so generally prevalent in our world today.

This book develops an original interpretation of the relationship between F.W.J. Schelling and G.W.F. Hegel. It argues that the difference between these philosophers must be understood in light of their shared commitment to the philosophy of nature and the idea that spirit, or humanity, emerges from the natural world. The author makes a case for the contemporary relevance of German idealist philosophy of nature by walking the reader through its major themes, motivations, and arguments. Along the way, Schelling and Hegel (...) are shown to develop key insights about the structure of reality and the dependence of living things and human beings upon inorganic natural processes. In elucidating the details of Schelling's and Hegel's respective philosophies of nature, the book challenges some of our most basic assumptions about the scope of philosophical inquiry and the relationship between matter, life, and human existence. Schelling, Hegel, and the Philosophy of Nature will appeal to scholars and advanced students working on German idealism, as well as those interested in contemporary philosophies of nature and the topic of emergence. (shrink)

Notions abstraites qu'engendre la vie.--Mobiles du comportement humain.--Pacte social.--Conclusion pour les trois études.

This book takes its point of departure from the work of the French sociologist Pierre Bourdieu, whose book 'Distinction' is considered a classic work of sociological analysis. The topics dealt with are shown in the table of contents below. The book is distinctive in that it offers discussions of four methodologies/theories used in discussing taste: semiotics, psychoanalytic theory, sociological theory and Marxist theory and then applies these theories in the second part of the book to a variety of topics involving (...) taste, such as yogurt, dogs, the singer Celine Dion, ocean cruises, brands, smartphones, men's facial hair, and so on. Readers of the book will learn four methodologies they can use in analyzing taste and see how these methodologies were applied. (shrink)

Many have claimed that epistemic rationality sometimes requires us to have imprecise credal states (i.e. credal states representable only by sets of credence functions) rather than precise ones (i.e. credal states representable by single credence functions). Some writers have recently argued that this claim conflicts with accuracy-centered epistemology, i.e., the project of justifying epistemic norms by appealing solely to the overall accuracy of the doxastic states they recommend. But these arguments are far from decisive. In this essay, we prove some (...) new results, which show that there is little hope for reconciling the rationality of credal imprecision with accuracy-centered epistemology. (shrink)

The conception of disinterested pleasure is not only central to Kant’s theory of beauty but also highly influential in contemporary philosophical discourse about beauty. However, it remains unclear, what exactly disinterested pleasure is and what role it plays in experiences of beauty. This volume sheds new light on the conception of disinterested pleasure from the perspectives of both Kant scholarship and contemporary aesthetics. In the first part, the focus is on Kant’s theory of beauty as grounded on the conception of (...) disinterested pleasure. In the second part, disinterested pleasure is investigated in the light of contemporary debates on beauty. The third part is dedicated to the relation of theories of disinterested pleasure to the meta-aesthetical debate between realism and anti-realism. The volume clarifies the meaning, role, and implications of one of the most influential conceptions in traditional as well as contemporary approaches to beauty. (shrink)

Ce texte tente de tisser ensemble, entre les 2 auteurs, des lectures, des expériences, des échanges. C'est un texte d'éducation sur l'éducation. Chaque démarche exige des engagements, des remaniements conceptuels et une reprise d'élaborations toujours inachevées.--[Memento].