"A valuable collection both for original source material as well as historical formulations of current problems."-- The Review of Metaphysics "Much more than a mere collection of papers . . . a valuable addition to the literature."-- Mathematics of Computation An anthology of fundamental papers on undecidability and unsolvability by major figures in the field, this classic reference opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by (...) Godel, Church, Turing, and Post single out the class of recursive functions as computable by finite algorithms. Additional papers by Church, Turing, and Post cover unsolvable problems from the theory of abstract computing machines, mathematical logic, and algebra, and material by Kleene and Post includes initiation of the classification theory of unsolvable problems. Suitable for graduate and undergraduate courses. 1965 ed. (shrink)

Gödel has emphasized the important role that his philosophical views had played in his discoveries. Thus, in a letter to Hao Wang of December 7, 1967, explaining why Skolem and others had not obtained the completeness theorem for predicate calculus, Gödel wrote:This blindness of logicians is indeed surprising. But I think the explanation is not hard to find. It lies in a widespread lack, at that time, of the required epistemological attitude toward metamathematics and toward non-finitary reasoning. …I may (...) add that my objectivist conception of mathematics and metamathematics in general, and of transfinite reasoning in particular, was fundamental also to my other work in logic.How indeed could one think of expressing metamathematics in the mathematical systems themselves, if the latter are considered to consist of meaningless symbols which acquire some substitute of meaning only through metamathematics?Or how could one give a consistency proof for the continuum hypothesis by means of my transfinite model Δ if consistency proofs have to be finitary?In a similar vein, Gödel has maintained that the “realist” or “Platonist” position regarding sets and the transfinite with which he is identified was part of his belief system from his student days. This can be seen in Gödel's replies to the detailed questionnaire prepared by Burke Grandjean in 1974. Gödel prepared three tentative mutually consistent replies, but sent none of them. (shrink)

This essay is a response to Michael Martin’s “Why the Resurrection Is Initially Improbable,” Philo, Vol. 1, No.1. I argue that Martin has not succeeded in achieving his aim of showing that the Resurrection is initially improbable and thus, by Bayes’s Theorem, implausible. I respond to five of Martin’s arguments: the “particular time and place argument”; the claim that there is no plausible Christian theory of why Jesus should have been incarnated and resurrected; the claim that (...) the Resurrection accounts in the New Testament are unreliable; Martin’s assumptions about how one establishes the initial probability of Resurrection; and the use Martin makes of Bayes’s Theorem to discredit belief in the Resurrection. (shrink)

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)

Argument mapping is a way of diagramming the logical structure of an argument to explicitly and concisely represent reasoning. The use of argument mapping in critical thinking instruction has increased dramatically in recent decades. This paper overviews the innovation and provides a procedural approach for new teaches wanting to use argument mapping in the classroom. A brief history of argument mapping is provided at the end of this paper.

What is critical thinking, especially in the context of higher education? How have research and scholarship on the matter developed over recent past decades? What is the current state of the art here? How might the potential of critical thinking be enhanced? What kinds of teaching are necessary in order to realize that potential? And just why is this topic important now? These are the key questions motivating this volume. We hesitate to use terms such as “comprehensive” or “complete” or (...) “definitive,” but we believe that, taken in the round, the chapters in this volume together offer a fair insight into the contemporary understandings of higher education worldwide. We also believe that this volume is much needed, and we shall try to justify that claim in this introduction. (shrink)

Cognitive approaches contribute to our understanding of delusions by providing an explanatory framework that extends beyond the personal level to the sub personal level of information-processing systems. According to one influential cognitive approach, two factors are required to account for the content of a delusion, its initial adoption as a belief, and its persistence. This chapter reviews Bayesian developments of the two-factor framework.

Anosognosia is literally ‘unawareness of or failure to acknowledge one’s hemi- plegia or other disability’ (OED). Etymology would suggest the meaning ‘lack of knowledge of disease’ so that anosognosia would include any denial of impairment, such as denial of blindness (Anton’s syndrome). But Babinski, who introduced the term in 1914, applied it only to patients with hemiplegia who fail to acknowledge their paralysis. Most commonly, this is failure to acknowledge paralysis of the left side of the body following damage to (...) the right hemisphere of the brain. In this paper, we shall mainly be concerned with anosognosia for hemiplegia. But we shall also use the term ‘anosognosia’ in an inclusive way to encompass lack of knowledge or acknowledgement of any impairment. Indeed, in the construction ‘anosognosia for X’, X might even be anosognosia for some Y. (shrink)

The situation of historical knowledge: the historicized world -- The technology of historical knowledge: management-systems -- The logic of historical knowledge: causality, rationality, identity -- The organization of historical knowledge: categorical coordinators; rhetorical strategy -- The purpose of historical knowledge: comprehension.

The Palgrave Handbook of Critical Thinking in Higher Education provides a single compendium on the nature, function, and applications of critical thinking. This book brings together the work of top researchers on critical thinking worldwide, covering questions of definition, pedagogy, curriculum, assessment, research, policy, and application.

Shaking the respect for history? -- Imprisoned by history -- The historical unconscious -- History: a self-centred science -- History: deception as cultural practice.

The nonvisual self-touch rubber hand paradigm elicits the compelling illusion that one is touching one’s own hand even though the two hands are not in contact. In four experiments, we investigated spatial limits of distance and alignment on the nonvisual self-touch illusion and the well-known visual rubber hand illusion. Common procedures and common assessment methods were used. Subjective experience of the illusion was assessed by agreement ratings for statements on a questionnaire and time of illusion onset. The nonvisual self-touch illusion (...) was diminished though never abolished by distance and alignment manipulations, whereas the visual rubber hand illusion was more robust against these manipulations. We assessed proprioceptive drift, and implications of a double dissociation between subjective experience of the illusion and proprioceptive drift are discussed. (shrink)

Inattentional blindness studies have shown that an unexpected object may go unnoticed if it does not share the property specified in the task instructions. Our aim was to demonstrate that observers develop an attentional set for a property not specified in the task instructions if it allows easier performance of the primary task. Three experiments were conducted using a dynamic selective-looking paradigm. Stimuli comprised four black squares and four white diamonds, so that shape and colour varied together. Task instructions specified (...) shape but observers developed an attentional set for colour, because we made the black–white discrimination easier than the square–diamond discrimination. None of the observers instructed to count bounces by squares reported an unexpected white square, whereas two-thirds of observers instructed to count bounces by diamonds did report the white square. When attentional set departs from task instructions, you may fail to see what you were told to look for. (shrink)

Complementary and alternative therapiesThere has long been debate about the degree to which conventional health professionals should work closely with complementary and alternative medicine practitioners, if patients choose treatment from both. Some doctors are trained in conventional and alternative therapies but often, liaison depends on the type of therapy, whether it is regulated by law and whether it supplements conventional methods of diagnosis and treatment or claims to provide an alternative to them. Among the therapies often used by patients to (...) supplement conventional medicine, but which do not claim to have a diagnostic purpose, are aromatherapy, massage, stress therapy, reflexology and hypnotherapy. Chinese medicine and homoeopathy are among those which are not statutorily regulated but claim to provide diagnosis and treatment. Practitioners of conventional medicine are often wary of unregulated treatments that supplant evidence-based therapy—even though not all conventional medicine has been proven by randomised controlled trials.The role of complementary and alternative therapies came under scrutiny in England in February 2010 when the Parliamentary Science and Technology Committee published a critical report on NHS funding for homoeopathy. 1 Focusing on whether government policy on homoeopathy was evidence-based, the Committee found a mismatch between the evidence and policy. Its main conclusion was that the evidence indicates that homoeopathy is not efficacious and does not produce results beyond the placebo effect. The Committee said that explanations for why homoeopathy was thought to work were implausible and that further homoeopathic clinical trials could not be justified. The amount that the NHS actually spends on homoeopathic therapies was left unclear and was subject to varying claims from the Society of Homoeopaths and the Health Minister.2 The Parliamentary report recommended that there should be a clear policy on prescribing placebos, including homoeopathic medicines, but the government has been …. (shrink)

First, I discuss cross-cultural evidence showing that a good deal of enculturation takes place outside of thinking through other minds. Second, I review evidence challenging the claim that humans seek to minimize entropy. Finally, I argue that optimality claims should be avoided, and that descriptive Bayesianism offers a more promising avenue for the development of a Bayesian theory of culture.

[Crispin Wright] Two kinds of epistemological sceptical paradox are reviewed and a shared assumption, that warrant to accept a proposition has to be the same thing as having evidence for its truth, is noted. 'Entitlement', as used here, denotes a kind of rational warrant that counter-exemplifies that identification. The paper pursues the thought that there are various kinds of entitlement and explores the possibility that the sceptical paradoxes might receive a uniform solution if entitlement can be made to reach sufficiently (...) far. Three kinds of entitlement are characterised and given prima facie support, and a fourth is canvassed. Certain foreseeable limitations of the suggested anti-sceptical strategy are noted. The discussion is grounded, overall, in a conception of the sceptical paradoxes not as directly challenging our having any warrant for large classes of our beliefs but as crises of intellectual conscience for one who wants to claim that we do. /// [ Martin Davies] Wright's account of sceptical arguments and his use of the idea of epistemic entitlement are reviewed. His notion of non-transmission of epistemic warrant is explained and a concern about his notion of entitlement is developed. An epistemological framework different from Wright's is described and several notions of entitlement are introduced. One of these, negative entitlement, is selected for more detailed comparison with Wright's notion. Thereafter, the paper shows how the two notions of entitlement have contrasting consequences for non-transmission of warrant and how they go naturally with two conceptions of the presuppositions of epistemic projects. Problems for negative entitlement are explained and solutions are proposed. (shrink)

In recent years consciousness has become a significant area of study in the cognitive sciences. The Frontiers of Consciousness is a major interdisciplinary exploration of consciousness. The book stems from the Chichele lectures held at All Souls College in Oxford, and features contributions from a 'who's who' of authorities from both philosophy and psychology. The result is a truly interdisciplinary volume, which tackles some of the biggest and most impenetrable problems in consciousness. The book includes chapters considering the apparent explanatory (...) gap between science and consciousness, our conscious experience of emotions such as fear, and of willed actions by ourselves and others. It looks at subjective differences between two ways in which visual information guides behaviour, and scientific investigation of consciousness in non-human animals. It looks at the challenges that the mind-brain relation presents for clinical practice as well as for theories of consciousness. The book draws on leading research from philosophy, experimental psychology, functional imaging of the brain, neuropsychology, neuroscience, and clinical neurology. Distinctive in its accessibility, authority, and its depth of coverage, Frontiers of Consciousness will be a groundbreaking and influential addition to the consciousness literature. (shrink)

Classic text considersgeneral theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, computable functionals, classification of unsolvable decision problems and more.

Many philosophers and psychologists argue that normal adult human beings possess a primitive or 'folk' psychological theory. Recently, however, this theory has come under challenge from the simulation alternative. This alternative view says that human bings are able to predict and explain each others' actions by using the resources of their own minds to simuate the psychological etiology of the actions of others. The thirteen essays in this volume present the foundations of theory of mind debate, and are accompanied by (...) an extensive introduction. (shrink)

[Crispin Wright] Two kinds of epistemological sceptical paradox are reviewed and a shared assumption, that warrant to accept a proposition has to be the same thing as having evidence for its truth, is noted. 'Entitlement', as used here, denotes a kind of rational warrant that counter-exemplifies that identification. The paper pursues the thought that there are various kinds of entitlement and explores the possibility that the sceptical paradoxes might receive a uniform solution if entitlement can be made to reach sufficiently (...) far. Three kinds of entitlement are characterised and given prima facie support, and a fourth is canvassed. Certain foreseeable limitations of the suggested anti-sceptical strategy are noted. The discussion is grounded, overall, in a conception of the sceptical paradoxes not as directly challenging our having any warrant for large classes of our beliefs but as crises of intellectual conscience for one who wants to claim that we do. /// [Martin Davies] Wright's account of sceptical arguments and his use of the idea of epistemic entitlement are reviewed. His notion of non-transmission of epistemic warrant is explained and a concern about his notion of entitlement is developed. An epistemological framework different from Wright's is described and several notions of entitlement are introduced. One of these, negative entitlement, is selected for more detailed comparison with Wright's notion. Thereafter, the paper shows how the two notions of entitlement have contrasting consequences for non-transmission of warrant and how they go naturally with two conceptions of the presuppositions of epistemic projects. Problems for negative entitlement are explained and solutions are proposed. (shrink)

Martin Davies; II*—Perceptual Content and Local Supervenience, Proceedings of the Aristotelian Society, Volume 92, Issue 1, 1 June 1992, Pages 21–46, https://do.

In this book, psychologists and philosophers describe and discuss a range of case studies of delusional beliefs, drawing out general lessons both for the cognitive architecture of the mind and for the notion of rationality, and exploring connections between the delusional beliefs that occur in schizophrenia and the flawed understanding of beliefs that is characteristic of autism.

INTRODUCTION: In accounts of the two-factor theory of delusional belief, the second factor in this theory has been referred to only in the most general terms, as a failure in the processes of hypothesis evaluation, with no attempt to characterise those processes in any detail. Coltheart and Davies attempted such a characterisation, proposing a detailed eight-step model of how unexpected observations lead to new beliefs based on the concept of abductive inference as introduced by Charles Sanders Peirce. METHODS: In this (...) paper, we apply that model to the explanation of various forms of delusional belief. RESULTS: We provide evidence that in cases of delusion there is a specific failure of the seventh step in our model: the step at which predictions from hypotheses are considered in the light of relevant evidence. CONCLUSIONS: In the two-factor theory of delusional belief, the second factor consists of a failure to reject hypotheses in the face of disconfirmatory evidence. (shrink)

Consciousness is, perhaps, the aspect of our mental lives that is the most perplexing for both psychologists and philosophers. Daniel Dennett has described it as 'both the most obvious and the most mysterious feature of our minds' and attempts at definition often seem to move in circles. Thomas Nagel famously remarked that 'without consciousness the mind-body problem would be much less interesting. With consciousness it seems hopeless.'. These observations might suggest that consciousness - indefinable and mysterious - falls outside the (...) scope of rational enquiry, defying both scientific and philosophical investigation. In reality, however, the topic has been a focus of psychological investigation since William James and is increasingly vital in philosophical research. This book illustrates the various, interdisciplinary approaches to the problem, providing both pointers to a solution and a summary of the key positions. (shrink)