A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises (...) designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics. (shrink)

Finitary sketches, i.e., sketches with finite-limit and finite-colimit specifications, are proved to be as strong as geometric sketches, i.e., sketches with finite-limit and arbitrary colimit specifications. Categories sketchable by such sketches are fully characterized in the infinitary first-order logic: they are axiomatizable by σ-coherent theories, i.e., basic theories using finite conjunctions, countable disjunctions, and finite quantifications. The latter result is absolute; the equivalence of geometric and finitary sketches requires (in fact, is equivalent to) the non-existence of measurable cardinals.

The prospect of using cell-based interventions to treat neurological conditions raises several important ethical and policy questions. In this target article, we focus on issues related to the unique constellation of traits that characterize CBIs targeted at the central nervous system. In particular, there is at least a theoretical prospect that these cells will alter the recipients' cognition, mood, and behavior—brain functions that are central to our concept of the self. The potential for such changes, although perhaps remote, is cause (...) for concern and careful ethical analysis. Both to enable better informed consent in the future and as an end in itself, we argue that early human trials of CBIs for neurological conditions must monitor subjects for changes in cognition, mood, and behavior; further, we recommend concrete steps for that monitoring. Such steps will help better characterize the potential risks and benefits of CBIs as they are tested and potentially used for treatment. (shrink)

This article is the lead piece in a special report that presents the results of a bioethical investigation into chimeric research, which involves the insertion of human cells into nonhuman animals and nonhuman animal embryos, including into their brains. Rapid scientific developments in this field may advance knowledge and could lead to new therapies for humans. They also reveal the conceptual, ethical, and procedural limitations of existing ethics guidance for human‐nonhuman chimeric research. Led by bioethics researchers working closely with an (...) interdisciplinary work group, the investigation focused on generating conceptual clarity and identifying improvements to governance approaches, with the goal of helping scholars, funders, scientists, institutional leaders, and oversight bodies (embryonic stem cell research oversight [ESCRO] committees and institutional animal care and use committees [IACUCs]) deliver principled and trustworthy oversight of this area of science. The article, which focuses on human‐nonhuman animal chimeric research that is stem cell based, identifies key ethical issues in and offers ten recommendations regarding the ethics and oversight of this research. Turning from bioethics’ previous focus on human‐centered questions about the ethics of “humanization” and this research's potential impact on concepts like human dignity, this article emphasizes the importance of nonhuman animal welfare concerns in chimeric research and argues for less‐siloed governance and oversight and more‐comprehensive public communication. (shrink)

Pancreatitis is a complex, progressively destructive inflammatory disorder. Alcohol was long thought to be the primary causative agent, but genetic contributions have been of interest since the discovery that rare PRSS1, CFTR and SPINK1 variants were associated with pancreatitis risk. We now report two associations at genome-wide significance identified and replicated at PRSS1-PRSS2 and X-linked CLDN2 through a two-stage genome-wide study. The PRSS1 variant likely affects disease susceptibility by altering expression of the primary trypsinogen gene. The CLDN2 risk allele is (...) associated with atypical localization of claudin-2 in pancreatic acinar cells. The homozygous CLDN2 genotype confers the greatest risk, and its alleles interact with alcohol consumption to amplify risk. These results could partially explain the high frequency of alcohol-related pancreatitis in men. © 2012 Nature America, Inc. All rights reserved. (shrink)

We show that a morphism of locales is open if and only if all its pullbacks are skeletal in the sense of [P.T. Johnstone, Factorization theorems for geometric morphisms, II, in: Categorical Aspects of Topology and Analysis, in: Lecture Notes in Math., vol. 915, Springer-Verlag, 1982, pp. 216–233], i.e. pulling back along them preserves denseness of sublocales . This result may be viewed as the ‘dual’ of the well-known characterization of proper maps as those which are stably closed. We (...) also investigate the circumstances in which a particular sublocale, or set of sublocales, of a given locale, may be ‘declared closed’. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Dharma Bums: The Beat Generation and the Making of Countercultural PilgrimageP. J. JohnstonI believe in the sweetness of Jesus And Buddha— I believe, In St. Francis, Avaloki Tesvara, the Saints Of First Century India A D And Scholars Santidevan And Otherwise Santayanan Everywhere.(Kerouac 1959: 15)Preliminary Polemics“PILGRIM, n. A traveler that is taken seriously.”—Ambrose Bierce, The Devil’s Dictionary 2007: 133As Beat commentator Stephen Prothero describes in his article “On the (...) Holy Road: The Beat Movement as Spiritual Protest” (1991), the Beats and their pilgrimages have most emphatically not been taken seriously. Both critics and scholars have been unkind to members of the Beat generation, and this unkindness has manifested itself in relative neglect of the Beats in all possible aspects of scholarly investigation. But nowhere does this appear more pronounced than in the area of Beat religion. Though some recent scholarship has been picking up from this earlier neglect and it is now [End Page 165] possible to find serious biographies of most of the major Beat writers and some belated attention to the movement as a literary phenomenon, the only book-length treatment of Beat Buddhism I was able to locate (Tonkinson 1995) hardly qualifies as a scholarly work and was published not by an academic press but as a special feature of the Buddhist magazine Tricycle. Prothero hypothesizes that this is because of the movement’s reputation as rebellious and antinomian—in its heyday the movement was characterized in identical unsavory terms by publications representing interests as diverse as Life and Playboy, with the latter describing the Beats as “nihilists” and the former claiming that the Beats were at war with “Mom, Dad, Politics, Marriage, the Savings Bank, Organized Religion, Literary Elegance, Law, the Ivy League Suit and Higher Education, to say nothing of the Automatic Dishwasher, the Cellophane-wrapped Soda Cracker, the Split-Level House and the clean, or peace-provoking H-bomb” (Prothero 1991: 206). Norman Podhoretz of Partisan Review went further still, claiming that the Beats were “hostile to civilization” and that the movement as a whole amounted to “a revolt of the spiritually underprivileged and crippled of soul” and “an affirmation of death” (ibid., 206). One couldn’t ask for a more passionate disavowal of the Beats or a more thorough polemic that the movement was profoundly antireligious.This could not contrast more with the Beats’ representation of their movement and its aims, with Jack Kerouac going so far as to reinterpret the crucial term “Beat” (a term for someone down and out originally borrowed from criminal street jive) as a noun derived from the adjective “beatific,” a specifically religious term familiar from such phrases as “the beatific vision” (ibid., 206–207). Several of the representative Beat writers were practicing Buddhists, influencing the entire movement to such an extent that Buddhist ideas and imagery suffused Beat literature as a whole. Ginsberg and Kerouac especially emphasized the positive and constructive elements of their spiritual vision, arguing that literature such as On the Road and Howl should be understood as religious affirmations of what is good and holy rather than as purely critical undertakings: “For the crucifix I speak out, for the Star of Israel I speak out, for the divinest man who ever lived who was German (Bach) I speak out, for sweet Mohammed I speak out, for Buddha I speak out, for Lao-tse and Chuang-tse I speak out” (ibid., 206–207). Or, as Allen Ginsberg put it less lyrically (and rather more bluntly): “Howl is an ‘Affirmation’ by individual experience of God, sex, drugs, and absurdity... the poems are religious and I meant them to be” (ibid., 207).But for the most part, Beat asseverations in no way diminished scholarly wariness about the Beat movement and its spirituality—as Prothero concludes, “the tendency among literary scholars is to see these [religious] concerns as tangential rather than constitutive” while “historians of American religion who have explored beat spirituality have tended to focus almost exclusively on the beats’ engagement with Zen and then to dismiss that engagement as haphazard” (ibid., 207).It is my contention that the mainstream scholarly neglect of Beat spirituality is in some part... (shrink)

Topos Theory is an important branch of mathematical logic of interest to theoretical computer scientists, logicians and philosophers who study the foundations of mathematics, and to those working in differential geometry and continuum physics. This compendium contains material that was previously available only in specialist journals. This is likely to become the standard reference work for all those interested in the subject.

Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and thereby to (...) demonstrate the overall unity of the subject. The material is organised in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text. (shrink)

Topos Theory is an important branch of mathematical logic of interest to theoretical computer scientists, logicians and philosophers who study the foundations of mathematics, and to those working in differential geometry and continuum physics. This compendium contains material that was previously available only in specialist journals. This is likely to become the standard reference work for all those interested in the subject.

Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and thereby to (...) demonstrate the overall unity of the subject. The material is organised in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text. (shrink)

The Euthyphro might well be given to undergraduates to read early in their philosophical training. The arguments are apparently simple, but some of them, as I shall show, lead naturally on to thorny problems of modern philosophy. Another benefit that could be gained from reading the Euthyphro is that the reader may learn to be forewarned against some common fallacies and debating tricks in moral disputes.

"No other work treating Indian philosophy on a comparable scale contains the illuminating comparisons between doctrines of Indian schools and the thought of Western philosophy ranging from Plato to Sartre and Wittgenstein...It will, moreover, contribute to the understanding of Western philosophy by Indian thinkers and vice versa...Raju has an intimate acquaintance with a remarkable range of Western thinkers and this distinguishes his work from most of what has gone before...Raju, moreover, is himself a critical thinker and consequently, although he has (...) written a history, he treats the ideas and doctrines in a philosophical mode and his assessments of positions are often original and illuminating." -- John E. Smith, Clark Professor of Philosophy, Yale University "Purpose: To deal with Indian philosophy in a fashion reflecting the way the best German historians of philosophy deal with Western philosophy...The book is remarkable for its comprehensiveness in combination with extensive critical discussions...Raju's book...is more critical than Radhakrishnan's and more philosophical than Dasgupta's. Radhakrishnan's comments are far less philosophically sophisticated and interesting than Raju's....a monument to a senior Indian philosopher's lifelong study and thoughtful critical consideration of the great classical systems of his tradition." -- Karl H. Potter, Professor of Philosophy, University of Washington "Raju's credentials are impeccable. He is one of the few scholars in the world who could presume to write a major work on Indian thought. Accordingly, his knowledge of the Indian schools is accurate and impressive. To the extent that one of his intentions is to cast those schools in terms which make them more intelligible to western readers, his work measures up very well." -- Harold H. Oliver, Professor of Philosophy, Boston University. (shrink)

The Euthyphro might well be given to undergraduates to read early in their philosophical training. The arguments are apparently simple, but some of them, as I shall show, lead naturally on to thorny problems of modern philosophy. Another benefit that could be gained from reading the Euthyphro is that the reader may learn to be forewarned against some common fallacies and debating tricks in moral disputes.

It is fortunate for my purposes that English has the two words ‘almighty’ and ‘omnipotent’, and that apart from any stipulation by me the words have rather different associations and suggestions. ‘Almighty’ is the familiar word that comes in the creeds of the Church; ‘omnipotent’ is at home rather in formal theological discussions and controversies, e.g. about miracles and about the problem of evil. ‘Almighty’ derives by way of Latin ‘omnipotens’ from the Greek word ‘pantokratōr’; and both this Greek word, (...) like the more classical ‘pankratēs’, and ‘almighty’ itself suggest God's having power over all things. On the other hand the English word ‘omnipotent’ would ordinarily be taken to imply ability to do everything; the Latin word ‘omnipotens’ also predominantly has this meaning in Scholastic writers, even though in origin it is a Latinization of ‘pantocratōr’. So there already is a tendency to distinguish the two words; and in this paper I shall make the distinction a strict one. I shall use the word ‘almighty’ to express God's power over all things, and I shall take ‘omnipotence’ to mean ability to do everything. (shrink)

Those philosophers who gave a negative answer to all four questions were called "eel-wrigglers" by the Buddhists. It was impossible to fix their position either for approval or for rejection. They would criticize any view, positive or negative, but would not themselves hold any. And it was difficult for a serious person to enter into any controversy with them.

It may be seen from the foregoing that Pauline's existence is multiply jeopardized; or rather, that my right to use 'Pauline' as a name, the way I said I was going to, is very doubtful, for I agree with Parmenides that one cannot name what is not there to be named. The words I have used to describe Pauline's various perils are full of what Ryle aptly called "systematically misleading expressions"; but we need not worry about that for the moment-enough (...) for now if the words succeed in bringing the various cases before our minds--and we can tidy up our language as we come to see things more clearly. (shrink)