Theorems in automated theorem proving are usually proved by formal logical proofs. However, there is a subset of problems which humans can prove by the use of geometric operations on diagrams, so called diagrammatic proofs. Insight is often more clearly perceived in these proofs than in the corresponding algebraic proofs; they capture an intuitive notion of truthfulness that humans find easy to see and understand. We are investigating and automating such diagrammatic reasoning about mathematical theorems. Concrete, rather than general diagrams (...) are used to prove particular concrete instances of the universally quantified theorem. The diagrammatic proof is captured by the use of geometric operations on the diagram. These operations are the inference steps of the proof. An abstracted schematic proof of the universally quantified theorem is induced from these proof instances. The constructive -rule provides the mathematical basis for this step from schematic proofs to theoremhood. In this way we avoid the difficulty of treating a general case in a diagram. One method of confirming that the abstraction of the schematic proof from the proof instances is sound is proving the correctness of schematic proofs in the meta-theory of diagrams. These ideas have been implemented in the system, called Diamond, which is presented here. (shrink)

The concept of virtual machine allows us to combine the dynamical and computational hypotheses in an investigation of cognition. Van Gelder explicitly rejects this approach, but not only does it allow us to use the modelling technique most appropriate to the task, it also opens up a new range of phenomena where these techniques interact.

This article describes a quantitative examination of corporate volunteering research in the form of a bibliometric analysis. Using author, journal, geography, epistemological, and industry data from 115 refereed and 445 non-refereed publications published during 1990–2015, we identify corporate volunteering as a rather young research field. Although the field has progressively developed, it is still limited in magnitude, with recent signs of stagnation. The current state is characterized by moderate publication and author activity rates, with a shift toward more peer-reviewed publications (...) conducted in coauthorship, mostly in the disciplines of business, management, and ethics; a focus on financial services as well as the professional service sector; few high-impact studies; and a narrow geographic spread, with North America as the market leader and a rising interest in Western European countries. Findings on the field's prevalent research orientation further indicate a strong employee-centered focus emphasizing the underlying business case. However, in contrast to the overarching concept of corporate social responsibility research, a relatively large share of the corporate volunteering literature also addresses society-related issues, namely, corporates' relationship with non-profits. (shrink)

Reflecting Alan Robinson's fundamental contribution to computational logic, this book brings together seminal papers in inference, equality theories, and logic programming. It is an exceptional collection that ranges from surveys of major areas to new results in more specialized topics. Alan Robinson is currently the University Professor at Syracuse University. Jean-Louis Lassez is a Research Scientist at the IBM Thomas J. Watson Research Center. Gordon Plotkin is Professor of Computer Science at the University of Edinburgh. Contents: Inference. Subsumption, (...) A Sometimes Undervalued Procedure, Larry Wos, Ross Overbeek, and Ewing Lusk. The Markgraf Karl Refutation Procedure, Hans Jurgen Ohlbach and Jorg H. Siekmann. Modal Logic Should Say More than it Does, Melvin Fitting. Interactive Proof Presentation, W. W. Bledsoe. Intelligent Backtracking Revisited, Maurice Bruynooghe. A Science of Reasoning, Alan Bundy. Inductive Inference of Theories from Facts, Ehud Y. Shapiro. Equality. Solving Equations in Abstract Algebras: A Rule-based Survey of Unification, Jean-Pierre Jouannaud and Claude Kirchner. Disunification: A Survey, Hubert Comon. A Case Study of the Completion Procedure: Proving Ring Commutativity Problems, Deepak Kapur and Hantao Zhang. Computations in Regular Rewriting Systems I and II, Girard Huet and JeanJacques Levy. Unification and ML Type Reconstruction, Paris Kanellakis, Harry Mairson, and John Mitchell. Automatic Dimensional Analysis, Mitchell Wand. Logic Programming. Logic Programming Schemes and Their Implementations, Keith Clark. A Near-Horn Prolog for Compilation, Donald Loveland and David Reed. Unfold/Fold Transformations of Logic Programs, P. A. Gardner and J. C. Shepherdson. An Algebraic Representation of Logic Program Computations, Andrea Corradini and Ugo Montanari. Theory of Disjunctive Logic Programs, Jack Minker, Arcot Rajasekar, and Jorge Lobo. Bottom-Up Evaluation of Logic Programs, Jeffrey Naughton and Raghu Ramakrishnan. Absys, the First Logic Programming Language: A View of the Inevitability of Logic Programming, E. W. Elcock. (shrink)

In this new edition of his acclaimed autobiography — long out of print and rare until now — Alan Watts tracks his spiritual and philosophical evolution from a child of religious conservatives in rural England to a freewheeling spiritual teacher who challenged Westerners to defy convention and think for themselves. From early in this intellectual life, Watts shows himself to be a philosophical renegade and wide-ranging autodidact who came to Buddhism through the teachings of Christmas Humphreys and D. T. (...) Suzuki. Told in a nonlinear style, In My Own Way wonderfully combines Watts’ own brand of unconventional philosophy and often hilarious accounts of gurus, celebrities, psychedelic drug experiences, and wry observations of Western culture. A charming foreword written by Watts’ father sets the tone of this warm, funny, and beautifully written story of a compelling figure who encouraged readers to “follow your own weird” — something he always did himself, as his remarkable account of his life shows. (shrink)

I revisit my 1993 paper on Putnam and mathematical realism focusing on the indispensability argument and how it has fared over the years. This argument starts from the claim that mathematics is an indispensable part of science and draws the conclusion, from holistic considerations about confirmation, that the ontology of science includes abstract objects as well as the physical entities science deals with.

In this collection of essays, Watts displays the playfulness of thought and simplicity of language that has made him one of the most popular lecturers and authors on the spiritual traditions of the East. Watts draws on a variety of religious traditions and explores the limits of language in the face of spiritual truth.

White searches for the subtler side of Nietzsche beyond his ambiguous support for violence and oppression. He looks at the `yes saying teachings' articulated with the `voice of beauty'.

Featuring the edited transcripts of eight lectures delivered by Alan Watts from 1960 to 1973. The Tao of Philosophy offers a rich introduction to the wit and wisdom of one of the foremost philosophers of the twentieth century.

“Life exists only at this very moment, and in this moment it is infinite and eternal. For the present moment is infinitely small; before we can measure it, it has gone, and yet it exists forever…. You may believe yourself out of harmony with life and its eternal Now; but you cannot be, for you are life and exist Now.”–from Become What You Are In this collection of writings, including nine new chapters never before available in book form, Watts displays (...) the intelligence, playfulness of thought, and simplicity of language that has made him so perennially popular as an interpreter of Eastern thought for Westerners. He draws on a variety of religious traditions, and covers topics such as the challenge of seeing one’s life “just as it is,” the Taoist approach to harmonious living, the limits of language in the face of ineffable spiritual truth, and the psychological symbolism of Christian thought. (shrink)

Bridging the gap between the world of science and the realm of the spiritual, B. Alan Wallace introduces a natural theory of human consciousness that has its roots in contemporary physics and Buddhism. Wallace's "special theory of ontological relativity" suggests that mental phenomena are _conditioned_ by the brain, but do not _emerge_ from it. Rather, the entire natural world of mind and matter, subjects and objects, arises from a unitary dimension of reality that is more fundamental than these dualities, (...) as proposed by Wolfgang Pauli and Carl Jung. To test his hypothesis, Wallace employs the Buddhist meditative practice of _samatha_, refining one's attention and metacognition, to create a kind of telescope to examine the space of the mind. Drawing on the work of the physicist John Wheeler, he then proposes a more general theory in which the participatory nature of reality is envisioned as a self-excited circuit. In comparing these ideas to the Buddhist theory known as the Middle Way philosophy, Wallace explores further aspects of his "general theory of ontological relativity," which can be investigated by means of _vipasyana_, or insight, meditation. Wallace then focuses on the theme of symmetry in reference to quantum cosmology and the "problem of frozen time," relating these issues to the theory and practices of the Great Perfection school of Tibetan Buddhism. He concludes with a discussion of the general theme of complementarity as it relates to science and religion. The theories of relativity and quantum mechanics were major achievements in the physical sciences, and the theory of evolution has had an equally deep impact on the life sciences. However, rigorous scientific methods do not yet exist to observe mental phenomena, and naturalism has its limits for shedding light on the workings of the mind. A pioneer of modern consciousness research, Wallace offers a practical and revolutionary method for exploring the mind that combines the keenest insights of contemporary physicists and philosophers with the time-honored meditative traditions of Buddhism. (shrink)

In order to come to your senses, Alan Watts often said, you sometimes need to go out of your mind. Perhaps more than any other teacher in the West, this celebrated author, former Anglican priest, and self-described spiritual entertainer was responsible for igniting the passion of countless wisdom seekers to the spiritual and philosophical delights of India, China, and Japan. With Out of Your Mind, you are invited to immerse yourself in six of this legendary thinker's most engaging teachings (...) on how to break through the limits of the rational mind and expand your awareness and appreciation for the great game unfolding all around us. Distilled from Alan Watts’s pinnacle lectures, Out of Your Mind brings you an inspiring new resource that captures the true scope of this brilliant teacher in action. For those both new and familiar with Watts, this book invites us to delve into his favorite pathways out of the trap of conventional awareness, including: • The art of the “controlled accident”—what happens when you stop taking your life so seriously and start enjoying it with complete sincerity • How we come to believe “the myth of myself”—that we are skin-encapsulated egos separate from the world around us—and how to transcend that illusion • Why we must fully embrace chaos and the void to find our deepest purpose • Unconventional and refreshing insights into the deeper principles of Buddhism, Hinduism, Western philosophy, Christianity, and much more. (shrink)

This compilation offers a unique synthesis of the traditional branches of Eastern thought by drawing upon their historical connections and common foundations in mystical experience.

In his newly updated version of The Anatomy of a Constitutional Law Case, Alan F. Westin provides a documentary portrait of historically important constitutional law case, 'Youngstown Sheet & Tube Co. v. Sawyer, ' from its rise in a bargaining dispute in the steel industry during 1952 to the aftermath of its decision by the United States Supreme Court. Westin has added to his classic book additional materials and personal commentaries collected since the work was first published. The new (...) information covers what went on within the Truman administration, what went on within the Supreme Court when analyzing and resolving issues that come before it. Westin includes selections from transcripts, briefs and other official proceedings, adds notes describing each phase of the constitutional process, and a section of commentary and questions relating this case to others. (shrink)

In "Epistemic Permissiveness", Roger White presents several arguments against Extreme Permissivism, the view that there are possible cases where, given one's total evidence, it would be rational to either believe P, or to believe ~P. In this paper, we carefully reconstruct White's arguments and then argue that they do not succeed.

All this is tightly reasoned, the argument is packed, but the language is clear."—Christian Century "The man value of this book seems to me to be that it ...

Pre-Socratic philosophy. - Plato. - Aristotle. - Post-Aristotelian philosophy. - The Theory of art: Quintilian, Longinus, and Philostratus. - Plotinus. - The lesser Neoplatonists. - Neoplatonic views of three early Christians. - Mediaeval descriptive psychology. - The psychology of the mystics. - Dante's theory of vision. - Conclusion.

People high in depressive or anxious symptom severity show repetitive negative thinking, including worry and rumination. They also show various cognitive phenomena, including probability, cost, and interpretation biases. Since there is conceptual overlap between these cognitive biases and repetitive negative thinking – all involve thinking about potential threats and misfortunes – we wondered whether repetitive negative thinking could account for (mediate) these cognitive biases’ associations with depressive and anxious symptom severity. In three studies, conducted in two languages and cultures, cost (...) bias and (in two studies) interpretation bias only predicted symptom severity via worry and repetitive negative thinking; this suggests these biases are actually associated with repetitive negative thinking, rather than with symptoms. In contrast, probability bias showed direct relationships with depressive (all studies) and anxious (two studies) symptom severity, suggesting its relationships with symptoms are partly independent of repetitive negative thinking. These results show the value of studying relationships among the various cognitive features of psychopathology. Furthermore, new interventions which target cognitive biases in depression or anxiety must show that they can improve upon cognitive behavioural therapy, which is already widely available, targets both repetitive negative thinking and probability bias, and is highly effective. (shrink)

In this wide-ranging interview Alan Norrie discusses how he became involved with Critical Realism, his work on Dialectical Critical Realism, and responses to it amongst the Critical Realist communi...