An incomplete degree is cuppable if it can be joined by an incomplete degree to a complete degree. For sets fulfilling some type of simplicity property one can now ask whether these sets are cuppable with respect to a certain type of reducibilities. Several such results are known. In this paper we settle all the remaining cases for the standard notions of simplicity and all the main strong reducibilities.

The task of computing a function F with the help of an oracle X can be viewed as a search problem where the cost measure is the number of queries to X. We ask for the minimal number that can be achieved by a suitable choice of X and call this quantity the query complexity of F. This concept is suggested by earlier work of Beigel, Gasarch, Gill, and Owings on “Bounded query classes”. We introduce a fault tolerant version and (...) relate it with Ulam's game. For many natural classes of functions F we obtain tight upper and lower bounds on the query complexity of F. Previous results like the Nonspeedup Theorem and the Cardinality Theorem appear in a wider perspective. (shrink)

We present a simple proof of a Theorem of Khutoretskij on the number of incomparable one-one numberings of an r.e. family of r.e. sets. The proof directly generalizes to effective domains. In the second part, applying a Theorem of Goncharov, we show that for anyk≧ there exist total recursive functions having exactlyk recursive isomorphism classes. Using a Theorem of Selivanov, it is shown that a certain notion of computability via gödelization is different from Lacombe's notion ofV-recursiveness. Finally, we discuss the (...) complexity (w.r.t.T-degrees) of translating a Gödelnumbering into a direct sum of Friedbergnumberings. (shrink)

Weakly semirecursive sets have been introduced by Jockusch and Owings . In the present paper their investigation is pushed forward by utilizing r.e. partial orderings, which turn out to be instrumental for the study of degrees of subclasses of weakly semirecursive sets.

For a fixed set A, the number of queries to A needed in order to decide a set S is a measure of S's complexity. We consider the complexity of certain sets defined in terms of A: $ODD^A_n = \{(x_1, \dots ,x_n): {\tt\#}^A_n(x_1, \dots, x_n) \text{is odd}\}$ and, for m ≥ 2, $\text{MOD}m^A_n = \{(x_1, \dots ,x_n):{\tt\#}^A_n(x_1, \dots ,x_n) \not\equiv 0 (\text{mod} m)\},$ where ${\tt\#}^A_n(x_1, \dots ,x_n) = A(x_1)+\cdots+A(x_n)$ . (We identify A(x) with χ A (x), where χ A is (...) the characteristic function of A.) If A is a nonrecursive semirecursive set or if A is a jump, we give tight bounds on the number of queries needed in order to decide ODD A n and $\text{MOD}m^A_n: \bullet\text{ODD}^A_n$ can be decided with n parallel queries to A, but not with n - 1. $\bullet \text{ODD}^A_n$ can be decided with $\lceil log(n + 1)\rceil$ sequential queries to A but not with $\lceil log(n + 1)\rceil - 1. \bullet\text{MOD}m^A_n$ can be decided with $\lceil n/m\rceil + \lfloor n/m\rfloor$ parallel queries to A but not with $\lceil n/m\rceil + \lfloor n/m\rfloor - 1. \bullet\text{MOD}m^A_n$ can be decided with $\lceil log(\lceil n/m\rceil + \lfloor n/m\rfloor + 1)\rceil$ sequential queries to A but not with $\lceil log(\lceil n/m\rceil + \lfloor n/m\rfloor + 1)\rceil - 1$ . The lower bounds above hold for nonrecursive recursively enumerable sets A as well. (Interestingly, the lower bounds for recursively enumerable sets follow by a general result from the lower bounds for semirecursive sets.) In particular, every nonzero truth-table degree contains a set A such that ODD A n cannot be decided with n - 1 parallel queries to A. Since every truth-table degree also contains a set B such that ODD B n can be decided with one query to B, a set's query complexity depends more on its structure than on its degree. For a fixed set A, $Q(n,A) = \{S: S \text{can be decided with n sequential queries to} A\},\\Q_\parallel(n, A) = \{S: S \text{can be decided with n parallel queries to} A\}.$ We show that if A is semirecursive or recursively enumerable, but is not recursive, then these classes form non-collapsing hierarchies: $\bullet Q(0,A) \subset Q(1,A) \subset Q(2,A) \subset\cdots\\ \bullet Q_\parallel(0, A) \subset Q_\parallel(1, A) \subset Q_\parallel(2,A) \subset\cdots$ The same is true if A is a jump. (shrink)

Most theories of learning consider inferring a function f from either observations about f or, questions about f. We consider a scenario whereby the learner observes f and asks queries to some set A. If I is a notion of learning then I[A] is the set of concept classes I-learnable by an inductive inference machine with oracle A. A and B are I-equivalent if I[A] = I[B]. The equivalence classes induced are the degrees of inferability. We prove several results about (...) when these degrees are trivial, and when the degrees are omniscient. (shrink)

Since at least the advent of Jack Kevorkian’s “suicide machine” the major argument against adopting physician-assisted suicide laws has been that they will lead us down a slippery slope to state-sa...

A long-standing theme in discussion of perception and thought has been that our primary cognitive contact with individual objects and events in the world derives from our perceptual contact with them. When I look at a duck in front of me, I am not merely presented with the fact that there is at least one duck in the area, rather I seem to be presented withthisthing (as one might put it from my perspective) in front of me, which looks to (...) me to be a duck. Furthermore, such a perception would seem to put me in a position not merely to make the existential judgment that there is some duck or other present, but rather to make a singular, demonstrative judgment, that that is a duck. My grounds for an existential judgment in this case derives from my apprehension of the demonstrative thought and not vice versa. (shrink)

On Inception is a translation of Martin Heidegger's Gesamtausgabe 70. This work belongs to the crucial period, before and during WWII, when Heidegger was at work on a series of treatises that begins with "Contributions to Philosophy" and includes "The Event" and "The History of Beyng." These works are difficult, even hermetic, but represent a crucial development in Heidegger's thinking. On Inception deepens the investigation underway in the other volumes of the series and provides a unique perspective on Heidegger's (...) thinking of Being and of Event. Here, Heidegger asks, with a greater insistence than anywhere else in his work, what it might mean to think of being as event, and not as presence. Event cannot be thought without the sense of a beginning - an inception - and so, Heidegger insists, we must try to think of being as inception, as fundamentally inceptive. On Inception pursues rigorously the difficult and puzzling implications of this speculation. It does not merely extend work already undertaken but also opens doors onto wholly other pathways. (shrink)

Is it OK to lie to Siri? Is it bad to mistreat a robot for our own pleasure? Under what condition should we grant a moral status to an artificial intelligence (AI) system? This paper looks at different arguments for granting moral status to an AI system: the idea of indirect duties, the relational argument, the argument from intelligence, the arguments from life and information, and the argument from sentience. In each but the last case, we find unresolved issues with (...) the particular argument, which leads us to move to a different one. We leave the idea of indirect duties aside since these duties do not imply considering an AI system for its own sake. The paper rejects the relational argument and the argument from intelligence. The argument from life may lead us to grant a moral status to an AI system, but only in a weak sense. Sentience, by contrast, is a strong argument for the moral status of an AI system—based, among other things, on the Aristotelian principle of equality: that same cases should be treated in the same way. The paper points out, however, that no AI system is sentient given the current level of technological development. (shrink)

Over the past three decades, the philosophy of biology has emerged from the shadow of the philosophy of physics to become a respectable and thriving philosophical subdiscipline. The authors take a fresh look at the life sciences and the philosophy of biology from a strictly realist and emergentist-naturalist perspective. They outline a unified and science-oriented philosophical framework that enables the clarification of many foundational and philosophical issues in biology. This book will be of interest both to life scientists and philosophers.

We provide a battery of examples of delusions against which theoretical accounts can be tested. Then, we identify neuropsychological anomalies that could produce the unusual experiences that may lead, in turn, to the delusions in our battery. However, we argue against Maher’s view that delusions are false beliefs that arise as normal responses to anomalous experiences. We propose, instead, that a second factor is required to account for the transition from unusual experience to delusional belief. The second factor in the (...) aetiology of delusions can be described superficially as a loss of the ability to reject a candidate for belief on the grounds of its implausibility and its inconsistency with everything else that the patient knows. But we point out some problems that confront any attempt to say more about the nature of this second factor. (shrink)

Martin Heidegger's Contributions to Philosophy reflects his famous philosophical "turning." In this work, Heidegger returns to the question of being from its inception in Being and Time to a new questioning of being as event.

What exactly is hope and how does it influence our decisions? In How We Hope, Adrienne Martin presents a novel account of hope, the motivational resources it presupposes, and its function in our practical lives. She contends that hoping for an outcome means treating certain feelings, plans, and imaginings as justified, and that hope thereby involves sophisticated reflective and conceptual capacities. Martin develops this original perspective on hope--what she calls the "incorporation analysis"--in contrast to the two dominant philosophical (...) conceptions of hope: the orthodox definition, where hoping for an outcome is simply desiring it while thinking it possible, and agent-centered views, where hoping for an outcome is setting oneself to pursue it. In exploring how hope influences our decisions, she establishes that it is not always a positive motivational force and can render us complacent. She also examines the relationship between hope and faith, both religious and secular, and identifies a previously unnoted form of hope: normative or interpersonal hope. When we place normative hope in people, we relate to them as responsible agents and aspire for them to overcome challenges arising from situation or character. Demonstrating that hope merits rigorous philosophical investigation, both in its own right and in virtue of what it reveals about the nature of human emotion and motivation, How We Hope offers an original, sustained look at a largely neglected topic in philosophy. (shrink)

A ‘lottery belief’ is a belief that a particular ticket has lost a large, fair lottery, based on nothing more than the odds against it winning. The lottery paradox brings out a tension between the idea that lottery beliefs are justified and the idea that that one can always justifiably believe the deductive consequences of things that one justifiably believes – what is sometimes called the principle of closure. Many philosophers have treated the lottery paradox as an argument against the (...) second idea – but I make a case here that it is the first idea that should be given up. As I shall show, there are a number of independent arguments for denying that lottery beliefs are justified. (shrink)

A landmark discussion between two great thinkers, vital to an understanding of twentieth-century philosophy and intellectual history.

Martin Heidegger is one of the most important and influential philosophers of the 20th Century. A major figure in the development of phenomenology, his work also profoundly influenced many of the intellectual movements that followed in his wake, from Sartre's Existentialism to Derrida's deconstructionism. Towards the Definition of Philosophy brings together two seminal lectures that mark a breakthrough moment in Heidegger's thought and introduces the major themes that he would develop in his opus Being and Time.

Eric Martin and Daniel N. Osherson present a theory of inductive logic built on model theory. Their aim is to extend the mathematics of Formal Learning Theory to a more general setting and to provide a more accurate image of empirical inquiry. The formal results of their study illuminate aspects of scientific inquiry that are not covered by the commonly applied Bayesian approach.

This paper proposes a view of time that takes passage to be the most basic temporal notion, instead of the usual A-theoretic and B-theoretic notions, and explores how we should think of a world that exhibits such a genuine temporal passage. It will be argued that an objective passage of time can only be made sense of from an atemporal point of view and only when it is able to constitute a genuine change of objects across time. This requires that (...) passage can flip one fact into a contrary fact, even though neither side of the temporal passage is privileged over the other. We can make sense of this if the world is inherently perspectival. Such an inherently perspectival world is characterized by fragmentalism, a view that has been introduced by Fine in his ‘Tense and Reality’ (2005). Unlike Fine's tense-theoretic fragmentalism though, the proposed view will be a fragmentalist view based in a primitive notion of passage. (shrink)

Martin Heidegger's Nietzsche's Second Untimely Meditation presents crucial elements for understanding Heidegger's thinking from 1936 to 1940. Heidegger offers a radically different reading of a text that he had read decades earlier, showing how his relationship with Nietzche's has changed, as well as how his understandings of the differences between animals and humans, temporality and history, and the Western philosophical tradition developed. With his new reading, Heidegger delineates three Nietzschean modes of history, which should be understood as grounded in (...) the structure of temporality or historicity and also offers a metaphysical determination of life and the essence of humankind. Ullrich Hasse and Mark Sinclair offer a clear and accessible translation despite the fragmentary and disjointed quality of the original lecture notes that comprise this text. (shrink)

This book provides the first systematic presentation of anthropology's 'ontological turn', placing it in the landscape of contemporary social theory.

_ Source: _Volume 6, Issue 2-3, pp 120 - 142 This paper aims to contribute to the debate over epistemic versus non-epistemic readings of the ‘hinges’ in Wittgenstein’s _On Certainty_. I follow Marie McGinn’s and Daniele Moyal-Sharrock’s lead in developing an analogy between mathematical sentences and certainties, and using the former as a model for the latter. However, I disagree with McGinn’s and Moyal-Sharrock’s interpretations concerning Wittgenstein’s views of both relata. I argue that mathematical sentences as well as certainties are (...) true and are propositions; that some of them can be epistemically justified; that in some senses they are not prior to empirical knowledge; that they are not ineffable; and that their primary function is epistemic as much as it is semantic. (shrink)

Humanity has reached a critical moment. Our world is unsettled and rapidly changing, and we face existential risks over the next century. Various outcomes--good and bad--are possible. Yet our approach to the future is characterized by short-term thinking, polarizing debates, alarmist rhetoric, and pessimism. In this short, exhilarating book, renowned scientist and bestselling author Martin Rees argues that humanity's prospects depend on our taking a very different approach to planning for tomorrow. The future of humanity is bound to the (...) future of science and hinges on how successfully we harness technological advances to address our challenges. If we are to use science to solve our problems while avoiding its dystopian risks, we must think rationally, globally, collectively, and optimistically about the long term. Advances in biotechnology, cybertechnology, robotics, and artificial intelligence--if pursued and applied wisely--could empower us to boost the developing and developed world and overcome the threats humanity faces on Earth, from climate change to nuclear war. At the same time, further advances in space science will allow humans to explore the solar system and beyond with robots and AI. But there is no "Plan B" for Earth--no viable alternative within reach if we do not care for our home planet. Rich with fascinating insights into cutting-edge science and technology, this accessible book will captivate anyone who wants to understand the critical issues that will define the future of humanity on Earth and beyond."-- Provided by publisher. (shrink)

The Liar paradox arises when we consider a sentence that says of itself that it is not true. If such self-referential sentences exist? and examples like?This sentence is not true? certainly suggest this?, then our logic and standard notion of truth allow to infer a contradiction: The Liar sentence is true and not true. What has gone wrong? Must we revise our notion of truth and our logic? Or can we dispel the common conviction that there are such self-referential sentences? (...) The present study explores the second path.0After comparing the Liar reasoning in formal and informal logic and showing that there are no Gödelian Liar sentences, the study moves on from the semantics of self-reference to the metaphysics of expressions and proposes a novel solution to the Liar paradox: Meaningful expressions are distinct from their syntactic bases and exist only relative to contexts. Detailed semantico-metaphysical arguments show that in this dynamic setting, an object can be referred to only after it has started to exist. Hence the circular reference needed in the Liar paradox cannot occur, after all. As this solution is contextualist, it evades the expressibility problems of other proposals. (shrink)

Richard Rorty (1931 - 2007) ist einer der wichtigsten amerikanischen Philosophen der Gegenwart, der die analytische Philosophie sowohl geprägt als auch maßgeblich zu ihrer Kritik beigetragen und damit die Wiederentdeckung des Pragmatismus vorangetrieben hat. In diesem Handbuch werden alle wichtigen Aspekte seines Lebens und seiner philosophischen Arbeit dargestellt und einer wissenschaftlichen Diskussion unterzogen.

Material from this paper appears in Chap. 7 of my book Reason and Being, but there is also stuff here that isn't in the book. In particular, it discusses the claims that, for Spinoza, conceiving implies explaining and that existence is identical to or reducible to conceivability. So, if you're interested in those issues, this paper might be worth a read.