GENERALIZED RECUBION THEORY II © North-Holland Publishing Company (1978) MONOTONE QUANTIFIERS AND ADMISSIBLE SETS Ion Barwise University of Wisconsin ...

Oliver Sacks MD, Clinical Professor of Neurology at the Albert Einstein College of Medicine in New York, talked with Anthony Freeman during his visit to London in January 1995 to publicize his recently published book An Anthropologist on Mars. The interview is preceded by an overview of the book.

Contents: Recursive Enumerability and the Jump Operator; On the Degrees Less Than 0'; A Simple Set Which Is Not Effectively Simple; The Recursively Enumerable Degrees Are Dense; Metarecursive Sets (with G Kreisel); Post's Problem, Admissible Ordinals and Regularity; On a Theorem of Lachlan and Marlin; A Minimal Hyperdegree (with R O Gandy); Measure-Theoretic Uniformity in Recursion Theory and Set Theory; Forcing with Perfect Closed Sets; Recursion in Objects of Finite Type; The a-Finite Injury Method (with S G Simpson); Remarks Against (...) Foundational Activity; Countable Admissible Ordinals and Hyperdegrees; The 1-Section of a Type n Object; The k-Section of a Type n Object; Post's Problem, Absoluteness and Recursion in Finite Types; Effective Bounds on Morley Rank; On the Number of Countable Models; Post's Problem in E-Recursion; The Limits of E-Recursive Enumerability; Effective Versus Proper Forcing. (shrink)

The first two parts of Objectivity and Insight explore the prospects for objectivity on the standard ontological conception, and find that they are not good. In Part I, under the heading of subject-driven scepticism, Sacks addresses the problem of securing epistemic reach that extends beyond subjective content. In so doing, he considers models of mind proposed by Locke, Hume, Kant, James, and Bergson. Part II, under the heading of world-driven scepticism, discusses the scope for universality of normative structure-a problem (...) which survives even after the assumption of an epistemologically significant breach between subject and object has been rejected. In the third part of the book Sacks introduces an alternative conception of objectivity, and shows that there is good reason to accept it. This conception turns on an insight which is taken to be implicit in transcendental idealism, and responsible for its abiding appeal; but Sacks's articulation of that insight is neither idealist nor metaphysical. (shrink)

While most business ethics texts focus exclusively on individual decision making--what should an individual do--this resource presents the whole business ethics story. Highly realistic, readable, and down-to-earth, it moves from the individual to the managerial to the organizational level, focusing on business ethics in an organizational context to promote an understanding of complex influences on behavior. The new Fifth Edition is the perfect text for students entering the workplace, those seeking to become professionals in training, communications, compliance, in addition to (...) chief ethics officers, corporate counsel, heads of human resources, and senior executives. (shrink)

The notion of a weakly scattered theory T is defined. T need not be scattered. For each a model of T, let sr() be the Scott rank of . Assume sr() ≤ ω\sp A \sb 1 for all a model of T. Let σ\sp T \sb 2 be the least Σ₂ admissible ordinal relative to T. If T admits effective k-splitting as defined in this paper, then θσ\cal Aθ\cal A$ a model of T.

The battle of Salamis can be dated with a high degree of certainty. Probably about the time of that battle, Cleombrotus was at the Isthmus, constructing the defences there. At some point while building the wall, he considered giving chase to the Persian army. When his sacrifice was answered by a solar eclipse, he took this as a bad omen and immediately returned to Lacedaemon. The eclipse visible to Cleombrotus could only have been that of 2 October 480. Now it (...) is generally supposed that Cleombrotus would not have thought to abandon the construction of the wall and pursue Xerxes unless the latter had just begun his retreat from Athens. Thus, as Herodotus says that a few days () after the battle of Salamis Xerxes withdrew from Attica, the battle of Salamis probably occurred before 2 October 480. (shrink)

What I take to be the consummation of rhythmic music, which music parlance describes as "being in the groove", is here regarded as an experience that symbolically manifests a "highest good" which is a perennial theme in western metaphysics. This Good is a contemporaneity between terms of fundamental oppositions that constitute the human condition. From Kant's critical project, this ideal is traced from its origins in Socratic dialectic, through Schelling's principle of "Identity", and into Kierkegaard's notion of "resting transparently." Musical (...) performance is successful, I argue, to the degree to which it manages to play this "both-at-once.". (shrink)

There exists a countable structure of Scott rank where and where the -theory of is not ω-categorical. The Scott rank of a model is the least ordinal β where the model is prime in its -theory. Most well-known models with unbounded atoms below also realize a non-principal -type; such a model that preserves the Σ1-admissibility of will have Scott rank . Makkai [M. Makkai, An example concerning Scott heights, J. Symbolic Logic 46 301–318. [4]] produces a hyperarithmetical model of Scott (...) rank whose -theory is ω-categorical. A computable variant of Makkai’s example is produced in [W. Calvert, S.S. Goncharov, J.F. Knight, J. Millar, Categoricity of computable infinitary theories, Arch. Math. Logic . [1]; J. Knight, J. Millar, Computable structures of rank J. Math. Logic . [2]]. (shrink)

This book contains the material for a first course in pure model theory with applications to differentially closed fields.

In chapter 3 of Wild Animal Ethics Johannsen argues for a collective obligation based on beneficence to intervene in nature in order to reduce the suffering of wild animals. In the same chapter he claims that the non-identity problem is merely a “theoretical puzzle” which doesn’t affect our reasons for intervention. In this paper I argue that the non-identity problem affects both the strength and the nature of our reasons to intervene. By intervening in nature on a large scale we (...) change which animals come into existence. In doing so, we enable harmful animals to inflict harms on other animals, and we put other animals in harm’s way. The harms that these animals will inflict and endure are foreseeable. Furthermore, since non-human animals aren’t moral agents, harmful animals cannot be morally responsible for their harmful actions. I argue therefore that by causing animals to exist, knowing that they will inflict and suffer harms, we become morally responsible for those harms. By engaging in identity-affecting actions then we take on secondary moral duties towards the animals we have thereby caused to exist, and these secondary moral duties may be extremely demanding, even more so than the initial costs of intervention. Finally, these duties are duties of justice rather than duties of beneficence, and as such are more stringent than purely beneficence-based moral reasons. Furthermore, this conclusion flows naturally from several plausible principles which Johannsen explicitly endorses. (shrink)

Book reviewed in this article: The Man Who Mistook His Wife for a Hat and Other Clinical Tales. By Oliver Sacks.

Our ultimate purpose is to give an axiomatic treatment of recursion theory sufficient to develop the priority method. The direct or abstract approach is to keep in mind as clearly as possible the methods actually used in recursion theory, and then to formulate them explicitly. The indirect or experimental approach is to look first for other mathematical theories which seem similar to recursion theory, to formulate the analogies precisely, and then to search for an axiomatic treatment which covers not only (...) recursion theory but also the analogous theories as particular cases.The first approach is more general because it does not depend on the existence of analogues. A concrete mathematical theory, it seems, need have no such analogues and still be important, as e.g. classical number theory. In such a case, an axiomatic treatment may still be useful for exhibiting the mathematical structure of the theory considered and the assumptions on which it rests. However, it will lack one of the most heavily advertised advantages of the axiomatic method, namely, the “economy of thought” which results from an uniform theory for several different and interesting cases: we cannot hope for this if, by hypothesis, we know of only one particular case. In contrast, the second approach, if successful at all, is bound to achieve such “economy” because we start out with several interesting particular cases. Another possible virtue of the second approach is that of field work over insight: the abstract pattern that we are looking for and hoping to formalize in axioms, may not be evident in any one mathematical theory, but may spring to the eye if one happens to look simultaneously at several theories which happen to realize the pattern. (shrink)

This article reviews the history of marketing thought in relation to social responsibility and business ethics. The main objective of the article is to show that business can be profitable and socially responsible at the same time by practising the societal marketing concept. More specifically, it presents the development of a marketing philosophy, discusses the influence of consumerism on the marketing concept and deals with ethics and social responsibility in marketing. It is argued that organisations who adopt the societal marketing (...) concept will be the ones most likely to make long-run profits as well as be beneficial to society as a whole. (shrink)

Research into the neural correlates of consciousness (NCCs) has blossomed, due to the advent of new and increasingly sophisticated brain research tools. Neuroimaging has uncovered a variety of brain processes that relate to conscious perception, obtained in a range of experimental paradigms. But methods such as functional magnetic resonance imaging or electroencephalography do not always afford inference on the functional role these brain processes play in conscious vision. Such empirical NCCs could reflect neural prerequisites, neural consequences, or neural substrates of (...) a conscious experience. Here, we take a closer look at the use of non-invasive brain stimulation (NIBS) techniques in this context. We discuss and review how NIBS methodology can enlighten our understanding of brain mechanisms underlying conscious vision by disentangling the empirical NCCs. (shrink)

National Book Award Finalist. How did humanity originate and why does a species like ours exist on this planet? Do we have a special place, even a destiny in the universe? Where are we going, and perhaps, the most difficult question of all, "Why?" In The Meaning of Human Existence, his most philosophical work to date, Pulitzer Prize–winning biologist Edward O. Wilson grapples with these and other existential questions, examining what makes human beings supremely different from all other species. Searching (...) for meaning in what Nietzsche once called "the rainbow colors" around the outer edges of knowledge and imagination, Wilson takes his readers on a journey, in the process bridging science and philosophy to create a twenty-first-century treatise on human existence—from our earliest inception to a provocative look at what the future of mankind portends. Continuing his groundbreaking examination of our "Anthropocene Epoch," which he began with The Social Conquest of Earth, described by the New York Times as "a sweeping account of the human rise to domination of the biosphere," here Wilson posits that we, as a species, now know enough about the universe and ourselves that we can begin to approach questions about our place in the cosmos and the meaning of intelligent life in a systematic, indeed, in a testable way. Once criticized for a purely mechanistic view of human life and an overreliance on genetic predetermination, Wilson presents in The Meaning of Human Existence his most expansive and advanced theories on the sovereignty of human life, recognizing that, even though the human and the spider evolved similarly, the poet's sonnet is wholly different from the spider's web. Whether attempting to explicate "The Riddle of the Human Species," "Free Will," or "Religion"; warning of "The Collapse of Biodiversity"; or even creating a plausible "Portrait of E.T.," Wilson does indeed believe that humanity holds a special position in the known universe. The human epoch that began in biological evolution and passed into pre-, then recorded, history is now more than ever before in our hands. Yet alarmed that we are about to abandon natural selection by redesigning biology and human nature as we wish them, Wilson soberly concludes that advances in science and technology bring us our greatest moral dilemma since God stayed the hand of Abraham. (shrink)

Esta dissertação encontra-se construída em torno de um núcleo central - a exposição, aná-lise e discussão do chamado 'Argumento da linguagem privada', de Wittengstein. A dinâmica própria da abordagem e discussão do tema leva necessariamente a percorrer o conjunto da obra de Wittengstein, o que motiva um notável aprofundamento do assunto e torna ainda mais aliciante este ensaio.

This paper adds temporal logic to public announcement logic (PAL) and dynamic epistemic logic (DEL). By adding a previous-time operator to PAL, we express in the language statements concerning the muddy children puzzle and sum and product. We also express a true statement that an agent’s beliefs about another agent’s knowledge flipped twice, and use a sound proof system to prove this statement. Adding a next-time operator to PAL, we provide formulas that express that belief revision does not take place (...) in PAL. We also discuss relationships between announcements and the new knowledge agents thus acquire; such relationships are related to learning and to Fitch’s paradox. We also show how inverse programs and hybrid logic each can be used to help determine whether or not an arbitrary structure represents the play of a game. We then add a past-time operator to DEL, and discuss the importance of adding yet another component to the language in order to prove completeness. (shrink)

The paper aims to cast light on the kind of proof involved in central transcendental arguments. It is suggested that some of the difficulty associated with such arguments may result from the tendency to construe them simply as articulating relations between concepts or propositional contents. A different construal, connected with phenomenological description, is outlined, as a way of bringing out the force of these arguments. It is suggested that it can be fruitful to think in terms of this construal in (...) understanding some of Kant's transcendental proofs. The recommended construal also helps to understand the nature of the link between transcendental arguments and transcendental idealism. (shrink)

The most important clarification we bring in our reply to commentators concerns the problem of the “explanatory gap”: that is, the gulf that separates physical processes in the brain from the experienced quality of sensations. By adding two concepts (bodiliness and grabbiness) that were not stressed in the target article, we strengthen our claim and clarify why we think we have solved the explanatory gap problem, – not by dismissing qualia, but, on the contrary, by explaining why sensations have a (...) “feel” and why “feels” feel the way they do. We additionally clarify our views on: internal representations (we claim internal representations cannot explain why sensation has a feel), on behaviorism (we are not behaviorists), on perception and action (we believe there can be perception without action), and on the brain (we believe the brain does do something important in perception). (shrink)

This paper aims to extend in two directions the probabilistic dynamic epistemic logic provided in Kooi’s paper (J Logic Lang Inform 12(4):381–408, 2003) and to relate these extensions to ones made in van Benthem et al. (Proceedings of LOFT’06. Liverpool, 2006). Kooi’s probabilistic dynamic epistemic logic adds to probabilistic epistemic logic sentences that express consequences of public announcements. The paper (van Benthem et al., Proceedings of LOFT’06. Liverpool, 2006) extends (Kooi, J Logic Lang Inform 12(4):381–408, 2003) to using action models, (...) but in both papers, the probabilities are discrete, and are defined on trivial σ -algebras over finite sample spaces. The first extension offered in this paper is to add a previous-time operator to a probabilistic dynamic epistemic logic similar to Kooi’s in (J Logic Lang Inform 12(4):381–408, 2003). The other is to involve non-trivial σ -algebras and continuous probabilities in probabilistic dynamic epistemic logic. (shrink)

This is the first modern, annotated and scholarly edition of Jean-Baptiste Du Bos’ _Critical Reflections on Poetry and Painting_, one of the seminal works of modern aesthetics in any language.

One of the most respected religious thinkers of our time makes an impassioned plea for the return of religion to its true purpose—as a partnership with God in the work of ethical and moral living. What are our duties to others, to society, and to humanity? How do we live a meaningful life in an age of global uncertainty and instability? In To Heal a Fractured World, Rabbi Jonathan Sacks offers answers to these questions by looking at the ethics (...) of responsibility. In his signature plainspoken, accessible style, Rabbi Sacks shares with us traditional interpretations of the Bible, Jewish law, and theology, as well as the works of philosophers and ethicists from other cultures, to examine what constitutes morality and moral behavior. “We are here to make a difference,” he writes, “a day at a time, an act at a time, for as long as it takes to make the world a place of justice and compassion.” He argues that in today’s religious and political climate, it is more important than ever to return to the essential understanding that “it is by our deeds that we express our faith and make it real in the lives of others and the world.” To Heal a Fractured World—inspirational and instructive, timely and timeless—will resonate with people of all faiths. (shrink)

This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.

Preprint of Cole, Sacks, and Waterman. 2000. "On the immunity principle: A view from a robot." Trends in Cognitive Science 4 (5): 167, a response to Shaun Gallagher, S. 2000. "Philosophical conceptions of the self: implications for cognitive science," Trends in Cognitive Science 4 (1):14-21. Also see Shaun Gallagher, Reply to Cole, Sacks, and Waterman Trends in Cognitive Science 4, No. 5 (2000): 167-68.

This paper provides a sound and complete proof system for a language that adds to Dynamic Epistemic Logic a discrete previous-time operator as well as single symbol formulas that partially reveal the most recent event that occurred. The completeness theorem is by filtration followed by model unraveling and other model transformations. Decidability follows from the completeness proof. The degree to which it is important to include the additional single symbol formulas is addressed in a discussion about the difficulties of the (...) completeness for a language that only adds the previous-time operator to DEL. Discussion is also given regarding the completeness for a language obtained by removing common knowledge operators from. (shrink)