We show that the lattice L 20 is not embeddable into the lattice of ideals of computably enumerable Turing degrees (J). We define a structure called a pseudolattice that generalizes the notion of a lattice, and show that there is a Π 2 necessary and sufficient condition for embedding a finite pseudolattice into J.

De Interpretatione is among Aristotle's most influential and widely read writings; C. W. A. Whitaker presents the first systematic study of this work, and offers a radical new view of its aims, its structure, and its place in Aristotle's system. He shows that De Interpretatione is not a disjointed essay on ill-connected subjects, as traditionally thought, but a highly organized and systematic treatise on logic, argument, and dialectic.

Perceptual experience, that paradigm of subjectivity, constitutes our most immediate and fundamental access to the objective world. At least, this would seem to be so if commonsense realism is correct — if perceptual experience is (in general) an immediate awareness of mind-independent objects, and a source of direct knowledge of what such objects are like. Commonsense realism raises many questions. First, can we be more precise about its commitments? Does it entail any particular conception of the nature of perceptual experience (...) and its relation to perceived objects, or any particular view of the way perception yields knowledge? Second, what explains the apparent intuitive appeal of commonsense realism? Should we think of it as a kind of folk theory held by most human adults or is there a sense in which we are pre-theoretically committed to it — in virtue of the experience we enjoy or in virtue of the concepts we use or in virtue of the explanations we give? Third, is commonsense realism defensible, in the face of formidable challenges from epistemology, metaphysics and cognitive science? The project of the present volume is to advance our understanding of these issues and thus to shed light on the commitments and credentials of commonsense realism. As you may have guessed from the title, the volume also aims to highlight the key role the concept of causation plays in these debates. Central issues to be addressed include the status and nature of causal requirements on perception, the causal role of perceptual experience, and the relation between objective perception and causal thinking — issues that, as many chapters in the volume bring out, are inseparable from concerns with the very nature of causation. (shrink)

The authors present a case study involving truth telling responsibilities in the setting of nonepileptic seizures. Specifically, over the course of several suspected nonepileptic seizures, a patient’s seizures stopped after he received a saline flush meant to precede the administration of anti-seizure medication. The patient and his surrogate believed he had received the medication each time, and the team wondered whether they should disclose the truth. Some worried that disclosure would reinforce the suspected psychogenic behavior, exacerbating the patient’s condition. In (...) this way, the case study presents a twist on the traditional truth telling archetype. While most truth telling cases center on navigating cultural differences or worries about emotional harm, this case presented concerns about medical harm in the form of exacerbating the patient’s condition. The authors describe the complex patient-family-team dynamic that preceded this ethical dilemma, describe the case, analyze the ethical issue, and describe the outcome. (shrink)

I first seriously contemplated writing a book on degree theory in 1976 while I was visiting the University of Illinois at Chicago Circle. There was, at that time, some interest in ann-series book about degree theory, and through the encouragement of Bob Soare, I decided to make a proposal to write such a book. Degree theory had, at that time, matured to the point where the local structure results which had been the mainstay of the earlier papers in the area (...) were finding a steadily increasing number of applications to global degree theory. Michael Yates was the first to realize that the time had come for a systematic study of the interaction between local and global degree theory, and his papers had a considerable influence on the content of this book. During the time that the book was being written and rewritten, there was an explosion in the number of global theorems about the degrees which were proved as applications of local theorems. The global results, in turn, pointed the way to new local theorems which were needed in order to make further progress. I have tried to update the book continuously, in order to be able to present some of the more recent results. It is my hope to introduce the reader to some of the fascinat ing combinatorial methods of Recursion Theory while simultaneously showing how to use these methods to prove some beautiful global theorems about the degrees. (shrink)

We investigate homomorphisms of degree structures with various relations, functions and constants. Our main emphasis is on pseudolattices, i.e., partially ordered sets with a join operation and relations simulating the meet operation. We show that there are no finite quotients of the pseudolattice of degrees or of the pseudolattice of degrees 0′, but that many finite distributive lattices are pseudolattice quotients of the pseudolattice of computably enumerable degrees.

In recent years, there has been a substantial amount of work in reverse mathematics concerning natural mathematical principles that are provable from RT, Ramsey's Theorem for Pairs. These principles tend to fall outside of the "big five" systems of reverse mathematics and a complicated picture of subsystems below RT has emerged. In this paper, we answer two open questions concerning these subsystems, specifically that ADS is not equivalent to CAC and that EM is not equivalent to RT.

According to John McDowell and Bill Brewer, our experiences have the type of content which can be the content of judgements - content which is the result of the actualization of specific conceptual abilities. They defend this view by arguing that our experiences must have such content in order for us to be able to think about our environment. In this paper I show that they do not provide a conclusive argument for this view. Focusing on Brewer’s version of the (...) argument, I show that it rests on a questionable assumption - namely, that if a subject can recognize the normative bearing of a mental content upon what she should think and do, then this content must be the result of the actualization of conceptual capacities (and in this sense conceptual). I argue that considerations regarding the roles played by experience and concepts in our mental lives may require us to reject this assumption. (shrink)

Both Carnap and Quine made significant contributions to the philosophy of mathematics despite their diversedviews. Carnap endorsed the dichotomy between analytic and synthetic knowledge and classified certainmathematical questions as internal questions appealing to logic and convention. On the contrary, Quine wasopposed to the analytic-synthetic distinction and promoted a holistic view of scientific inquiry. The purpose of thispaper is to argue that in light of the recent advancement of experimental mathematics such as Monte Carlosimulations, limiting mathematical inquiry to the domain of (...) logic is unjustified. Robustness studies implemented inMonte Carlo Studies demonstrate that mathematics is on par with other experimental-based sciences. (shrink)

We define a class of finite partial lattices which admit a notion of rank compatible with embedding constructions, and present a necessary and sufficient condition for the embeddability of a finite ranked partial lattice into the computably enumerable degrees.

Postcolonial science studies entails ostensibly contradictory critical and empirical commitments. Science studies scholars influenced by Bruno Latour and Isabelle Stengers embrace forms of realist, radical empiricism, while postcolonial studies scholars influenced by Jacques Derrida trace the limits of the knowable. This essay takes their common use of the term cosmopolitics as an unexpected point of departure for reconciling Derrida’s program with Stengers’s and Latour’s. I read Derrida’s critique of hospitality and Stengers’s and Latour’s ontological politics as necessary complements for conceiving (...) a care-oriented subalternist cosmopolitics, a process of composing common worlds that remains attentive to the limits of representation. (shrink)

Do famous athletes have special obligations to act virtuously? A number of philosophers have investigated this question by examining whether famous athletes are subject to special role model obligations (Wellman 2003; Feezel 2005; Spurgin 2012). In this paper we will take a different approach and give a positive response to this question by arguing for the position that sport and gaming celebrities are ‘ambassadors of the game’: moral agents whose vocations as rule-followers have unique implications for their non-lusory lives. According (...) to this idea, the actions of a game’s players and other stakeholders—especially the actions of its stars—directly affect the value of the game itself, a fact which generates additional moral reasons to behave in a virtuous manner. We will begin by explaining the three main positions one may take with respect to the question: moral exceptionalism, moral generalism, and moral exemplarism. We will argue that no convincing case for moral exemplarism has thus far been made, which gives us reason to look for new ways to defend this position. We then provide our own ‘ambassadors of the game’ account and argue that it gives us good reason to think that sport and game celebrities are subject to special obligations to act virtuously. (shrink)

We present a necessary and sufficient condition for the embeddability of a principally decomposable finite lattice into the computably enumerable degrees. This improves a previous result which required that, in addition, the lattice be ranked. The same condition is also necessary and sufficient for a finite lattice to be embeddable below every non-zero computably enumerable degree.

An examination of David Hume's philosophy of religion that situates his conception "true religion" within the context of his overall science of human nature, his rejection of popular religion, and his Ciceronian influence"--Provided by publisher.

John McDowell (in Mind and World) and Bill Brewer (in Perception and Reason) argue that the content of our perceptual experience is conceptual in the following sense. It is of the type of content that could be the content of a judgement – that is, a content which results from the actualization of two (or more) conceptual abilities. Specifically, they suggest that the conceptual abilities actualized in experience are demonstrative abilities, and thus the resulting content is of the type we (...) may express by means of sentences of the form ‘this is thus’. In this paper I argue that we cannot construe experiential contents in this way. I first outline a construal of the ability to think about a thing being thus which is based on Brewer's discussion of conceptual experiential contents, and which I take to be the best construal available to the conceptualist. I then show that on this construal the demonstrative abilities that account for our experience of properties require intentional focused attention to the relevant properties. The conceptualist is thus committed to holding that we experience only the properties we are intentionally attending to, and I argue that this is implausible. The interest in examining Brewer's conceptualist construal of experiential content and pointing out its shortcoming is not limited merely to an interest in whether there is a workable conceptualist account of experiential content. I suggest that certain aspects of Brewer's construal capture important (and often neglected) aspects of our perceptual experience, and that understanding why the account fails can contribute to our understanding of both experiential content and demonstrative thought. (shrink)

Both introspection and empirical studies suggest that visual attention can affect the phenomenology of our visual experience. However, the exact character of such effects is far from clear. My aim in this chapter is to spell out the main difficulties involved in attempting to achieve a clearer view of these effects, and to make some suggestions as to how we can make progress with this issue while avoiding tempting mistakes. I do this by discussing the question of whether there is (...) a sense in which attention to a seen object can be said to contribute to the object’s visual phenomenal salience. It is often suggested that focusing visual attention on a seen object renders the object phenomenally salient. I look at potential evidence for this suggestion, and consider what form, if any, of visual phenomenal salience it may support. (shrink)

We all experience loneliness at some time in our lives and it often motivates people, consciously or otherwise, to enter treatment. Yet it is rarely explicitly addressed in psychoanalytic literature. Loneliness and Longing rectifies this oversight by thoroughly exploring this painful psychological state. In this book contributors address the inner sense of loneliness âe" that is feeling alone even in the company of others âe" by drawing on different aspects of loneliness and longing. Topics covered include: loneliness in the consulting (...) room the relationship between loneliness and love the effects of social networking and the internet how loneliness changes throughout the life-cycle healing the analystâe(tm)s loneliness. Loneliness and Longing draws on both theory and practice to discuss ways to help people to understand and cope with this important emotional state, encouraging them to make loneliness and longing less pervasive in their lives. This will be ideal reading for analysts, psychotherapists, and related practitioners facing the challenges of loneliness in their consulting rooms. (shrink)

In ancient China, a revered Taoist sage named Zhuangzi told many parables. In Existential Psychology and the Way of the Tao, a selection of these parables will be featured. Following each parable, an eminent existential psychologist will share a personal and scholarly reflection on the meaning and relevance of the parable for psychotherapy and contemporary life. The major tenets of Zhuangzi's philosophy are featured. Taoist concepts of emptiness, stillness, Wu Wei (i.e. intentional non-intentionality), epistemology, dreams and the nature of reality, (...) character building in the midst of pain, meaning and the centrality of relationships, authenticity, self-care, the freedom that can come from one's willingness to confront death, spiritual freedom, and gradations of therapeutic care are topics highlighted in this book. (shrink)

This book presents a unifying framework for using priority arguments to prove theorems in computability. Priority arguments provide the most powerful theorem-proving technique in the field, but most of the applications of this technique are ad hoc, masking the unifying principles used in the proofs. The proposed framework presented isolates many of these unifying combinatorial principles and uses them to give shorter and easier-to-follow proofs of computability-theoretic theorems. Standard theorems of priority levels 1, 2, and 3 are chosen to demonstrate (...) the framework's use, with all proofs following the same pattern. The last section features a new example requiring priority at all finite levels. The book will serve as a resource and reference for researchers in logic and computability, helping them to prove theorems in a shorter and more transparent manner"--Provided by publisher. (shrink)

A choice set for a computable linear ordering is a set which contains one element from each maximal block of the ordering. We obtain a partial characterization of the computable linear order-types for which each computable model has a computable choice set, and a full characterization in the relativized case; Every model of the linear order-type α of degree ≤ d has a choice set of degree ≤ d iff α can written as a finite sum of order-types, each of (...) which either has finitely many blocks, or has order-type n · η for some integer n. (shrink)