_'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.'_ _– The Guardian_ In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system. The importance of Godel's Proof rests upon its radical implications and has echoed throughout many fields, from maths (...) to science to philosophy, computer design, artificial intelligence, even religion and psychology. While others such as Douglas Hofstadter and Roger Penrose have published bestsellers based on Godel’s theorem, this is the first book to present a readable explanation to both scholars and non-specialists alike. A gripping combination of science and accessibility, _Godel’s Proof_ by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity. _Kurt Godel_ Born in Brunn, he was a colleague of physicist Albert Einstein and professor at the Institute for Advanced Study in Princeton, N.J. (shrink)

H. G. Wells has long occupied a curious place in the literary history of the early twentieth century, positioned as an extremely popular yet myopic outsider whose seeming miscalculation of the post-1910 literary zeitgeist acted in a directly inverse relation to his uncannily accurate technological predictions of the world to come. Wells’s reputation as a literary innovator in this period sunk in opposite relation to his rising stature as a futurologist, a shift whose repercussions for the author’s legacy are, as (...) both Roger Luckhurst and Steven McLean have recently noted, still largely evident in the ways his work is positioned, studied, and debated in the contemporary academy.1 As Wells’s 1890s scientific romances .. (shrink)

_'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.'_ _– The Guardian_ In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system. The importance of Godel's Proof rests upon its radical implications and has echoed throughout many fields, from maths (...) to science to philosophy, computer design, artificial intelligence, even religion and psychology. While others such as Douglas Hofstadter and Roger Penrose have published bestsellers based on Godel’s theorem, this is the first book to present a readable explanation to both scholars and non-specialists alike. A gripping combination of science and accessibility, _Godel’s Proof_ by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity. _Kurt Godel_ Born in Brunn, he was a colleague of physicist Albert Einstein and professor at the Institute for Advanced Study in Princeton, N.J. (shrink)

_'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.'_ _– The Guardian_ In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system. The importance of Godel's Proof rests upon its radical implications and has echoed throughout many fields, from maths (...) to science to philosophy, computer design, artificial intelligence, even religion and psychology. While others such as Douglas Hofstadter and Roger Penrose have published bestsellers based on Godel’s theorem, this is the first book to present a readable explanation to both scholars and non-specialists alike. A gripping combination of science and accessibility, _Godel’s Proof_ by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity. _Kurt Godel_ Born in Brunn, he was a colleague of physicist Albert Einstein and professor at the Institute for Advanced Study in Princeton, N.J. (shrink)

About this book Hilary Whitehall Putnam was one of the leading philosophers of the second half of the 20th century. As student of Rudolph Carnap's and Hans Reichenbach's, he went on to become not only a major figure in North American analytic philosophy, who made significant contributions to the philosophy of mind, language, mathematics, and physics but also to the disciplines of logic, number theory, and computer science. He passed away on March 13, 2016. The present volume is a memorial (...) to his extraordinary intellectual contributions, honoring his contributions as a philosopher, a thinker, and a public intellectual. It features essays by an international team of leading philosophers, covering all aspects of Hilary Putnam's philosophy from his work in ethics and the history of philosophy to his contributions to the philosophy of science, logic, and mathematics. Each essay is an original contribution. -/- Author information James Conant, Univ. of Chicago/Univ. of Leipzig, USA/Germany; Sanjit Chakraborty, IISER Kolkata/VIT-AP University, India. (shrink)

1. Kierkegaard on saying and showing. The paper explores certain parallels between Kierkegaard's Concluding Unscientific Postscript and Wittgenstein's Tractatus. The following five parallels appear to exist between these two works: both draw a distinction between sense and nonsense; both distinguish between what can be said and what can only be shown; both aspire to show what cannot be said by drawing limits to what can be said; both end by retracting themselves; both imply that silence is the only correct form (...) of answer to certain questions they pose. I argue that the standard interpretation of each of these works has them inside out: a proper understanding of parallels and reveals both works to be concerned with undermining a doctrine of ineffability. I try to show that although parallels , , and depend upon a misreading of these works they, too, are nevertheless connected to deep and interesting genuine parallels in the respective philosophical undertakings of these two authors. ;2. Nietzsche's perfectionism. Nietzsche has been read as advancing a form of perfectionism in both moral and political philosophy. I argue against the standard reading of Nietzsche as defending some form of moral or political elitism. The argument is based on a careful examination of Nietzsche's third Untimely Meditation--a text frequently drawn upon to support an extreme elitist interpretation of Nietzsche. I go on to suggest that Nietzsche's views are, nonetheless, aptly characterized as perfectionist in certain respects and that they represent a striking development of certain strains of perfectionist thought that have been either widely neglected or prematurely dismissed in contemporary moral and political philosophy. ;3. The James/Royce Debate on the theory of truth. The paper argues that to understand William James' mature views one needs to situate his writing within the polemical context of the period in which he wrote and, in particular, to view his development against the background of his ongoing dialogue with Josiah Royce. I outline three successive arguments Royce deploys in an attempt to show that James' pragmatic theory of truth is self-refuting. I argue that the pressure these arguments exert on James leads him to develop a more nuanced and original form of pragmatism than has hitherto generally been appreciated. (shrink)

The development of ethical and practice guidelines related to mental health service on the Internet has lagged behind the movement of practitioners into this area. Even for clinicians who are not offering services on the Web, the Internet has led to confusion and concern about proper roles and responsibilities. This article discusses an actual experience we had with a self-described rationally suicidal man with multiple sclerosis. After presenting some background on MS, we report initial interactions with the man verbatim and (...) summarize subsequent correspondence in an analysis of the man's claim that his decision to die was well reasoned and that he should be allowed a physician's assistance. (shrink)

We explore the formal foundations of recent studies comparing aural pattern recognition capabilities of populations of human and non-human animals. To date, these experiments have focused on the boundary between the Regular and Context-Free stringsets. We argue that experiments directed at distinguishing capabilities with respect to the Subregular Hierarchy, which subdivides the class of Regular stringsets, are likely to provide better evidence about the distinctions between the cognitive mechanisms of humans and those of other species. Moreover, the classes of the (...) Subregular Hierarchy have the advantage of fully abstract descriptive (model-theoretic) characterizations in addition to characterizations in more familiar grammar- and automata-theoretic terms. Because the descriptive characterizations make no assumptions about implementation, they provide a sound basis for drawing conclusions about potential cognitive mechanisms from the experimental results. We review the Subregular Hierarchy and provide a concrete set of principles for the design and interpretation of these experiments. (shrink)

We sketch an axiomatic reformalization of Generalized Phrase StructureGrammar (GPSG) – a definition purely within the language ofmathematical logic of the theory GPSG embodies. While this treatment raisesa number of theoretical issues for GPSG, our focus is not thereformalization itself but rather the method we employ. The model-theoreticapproach it exemplifies can be seen as a natural step in the evolution ofconstraint-based theories from their grammar-based antecedents. One goal ofthis paper is to introduce this approach to a broader audience and todemonstrate (...) its application to an existing theory. As such, it joins agrowing literature of similar studies. Prior studies, however, have had anumber of weaknesses – they generally offer little in the way ofconcrete examples of the advantages the approach has to offer, theytypically ignore significant portions of the theories they address, and, byfully abstracting away from the notion of grammar mechanism, they largelyabandon the possibility of establishing meaningful complexity results. Thesecond goal of the paper is to address these issues. Our thrust is to sketchthe reformalization sufficiently to illustrate the way in which it capturesFeature Specification Defaults (FSDs) and the Exhaustive Constant PartialOrdering (ECPO) property. Our definition of FSDs is considerably simplifiedrelative to the original formalization and is free of the procedural flavorthat has led some to assume that FSDs are inherently dynamic. Our treatmentof ECPO uncovers a gap in its definition in the context of partialcategories that has heretofore gone unnoticed. We offer these as ademonstration of the kind of insight that a model-theoretic reinterpretationcan bring to an existing theory. Further, since these are the types ofproperties that prior studies in this genre have failed to address, FSDs andECPO provide a means for us to explore the limitations of these approachesand to offer ways of overcoming them. Finally, the logical framework weemploy has a well defined generative capacity – definability in thisframework characterizes strong context-freeness in a particular sense. Thus,despite being more abstract than its constraint-based predecessors, themodel-theoretic approach, as exemplified here, can offer stronger complexityresults than are typically available in the constraint-based framework. (shrink)

The Scottish Philosophy of Common Sense originated as a protest against the philosophy of the greatest Scottish philosopher. Hume's sceptical conclusions did not excite as much opposition as might have been expected. But in Scotland especially there was a good deal of spoken criticism which was never written; and some who would have liked to denounce Hume's doctrines in print were restrained by the salutary reflection that if they were challenged to give reasons for their criticism they would find it (...) uncommonly difficult to do so. Hume's scepticism was disliked, but it was difficult to see how it could be adequately met. At this point Thomas Reid stepped into the field. He was the only man of his time who really understood the genesis of Hume's scepticism and succeeded in locating its sources. At first sight it would seem that this discovery required no peculiar perspicuity. It would seem that nobody could help seeing that Hume's sceptical conclusions were based on Locke's premises, and that Hume could never be successfully opposed by any critic who accepted Locke's assumptions. But this is precisely one of those obvious things that is noticed by nobody. And in fact Reid was the first man to see it clearly. It thus became his duty to question the assumptions on which all his own early thought had been based. The result of this reflection was the conclusion that, since the "ideal theory" of Locke and Berkeley logically led to Hume's scepticism, and since scepticism was intolerable, that theory would have to be amended, or, if necessary, abandoned. This volume contains works by Thomas Reid, Adam Ferguson, James Beattie, and Dugald Stewart. (shrink)

We provide first-order axioms for the theories of finite trees with bounded branching and finite trees with arbitrary (finite) branching. The signature is chosen to express, in a natural way, those properties of trees most relevant to linguistic theories. These axioms provide a foundation for results in linguistics that are based on reasoning formally about such properties. We include some observations on the expressive power of these theories relative to traditional language complexity classes.

In the target article, Bowers et al. dispute deep artificial neural network (ANN) models as the currently leading models of human vision without producing alternatives. They eschew the use of public benchmarking platforms to compare vision models with the brain and behavior, and they advocate for a fragmented, phenomenon-specific modeling approach. These are unconstructive to scientific progress. We outline how the Brain-Score community is moving forward to add new model-to-human comparisons to its community-transparent suite of benchmarks.

This collection of original essays presents diverse perspectives on the hybrid, evolving traditions of Confucianism. The chapters explore contemporary harmony across philosophy, religion, politics, linguistics, diplomacy, international relations, and education, with writers from numerous cultural and national backgrounds.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This paper introduces a special issue of Cognitive Science initiated on the 25th anniversary of the publication of Parallel Distributed Processing (PDP), a two-volume work that introduced the use of neural network models as vehicles for understanding cognition. The collection surveys the core commitments of the PDP framework, the key issues the framework has addressed, and the debates the framework has spawned, and presents viewpoints on the current status of these issues. The articles focus on both historical roots and contemporary (...) developments in learning, optimality theory, perception, memory, language, conceptual knowledge, cognitive control, and consciousness. Here we consider the approach more generally, reviewing the original motivations, the resulting framework, and the central tenets of the underlying theory. We then evaluate the impact of PDP both on the field at large and within specific subdomains of cognitive science and consider the current role of PDP models within the broader landscape of contemporary theoretical frameworks in cognitive science. Looking to the future, we consider the implications for cognitive science of the recent success of machine learning systems called “deep networks”—systems that build on key ideas presented in the PDP volumes. (shrink)

This article provides a critical comparative analysis of the substantive and procedural values and ethical concepts articulated in guidelines for allocating scarce resources in the COVID-19 pandemic. We identified 21 local and national guidelines written in English, Spanish, German and French; applicable to specific and identifiable jurisdictions; and providing guidance to clinicians for decision making when allocating critical care resources during the COVID-19 pandemic. US guidelines were not included, as these had recently been reviewed elsewhere. Information was extracted from each (...) guideline on: 1) the development process; 2) the presence and nature of ethical, medical and social criteria for allocating critical care resources; and 3) the membership of and decision-making procedure of any triage committees. Results of our analysis show the majority appealed primarily to consequentialist reasoning in making allocation decisions, tempered by a largely pluralistic approach to other substantive and procedural values and ethical concepts. Medical and social criteria included medical need, co-morbidities, prognosis, age, disability and other factors, with a focus on seemingly objective medical criteria. There was little or no guidance on how to reconcile competing criteria, and little attention to internal contradictions within individual guidelines. Our analysis reveals the challenges in developing sound ethical guidance for allocating scarce medical resources, highlighting problems in operationalising ethical concepts and principles, divergence between guidelines, unresolved contradictions within the same guideline, and use of naïve objectivism in employing widely used medical criteria for allocating ICU resources. (shrink)