It is a paradox, whose importance familiarity fails to diminish, that the most highly developed and useful scientific theories are ostensibly expressed in terms of objects never encountered in experience. The line traced by a draughtsman, no matter how accurate, is seen beneath the microscope as a kind of corrugated trench, far removed from the ideal line of pure geometry. And the “point-planet” of astronomy, the “perfect gas” of thermodynamics, or the “pure species” of genetics are equally remote from exact (...) realization. Indeed the unintelligibility at the atomic or sub-atomic level of the notion of a rigidly demarcated boundary shows that such objects not merely are not but could not be encountered. While the mathematician constructs a theory in terms of “perfect” objects, the experimental scientist observes objects of which the properties demanded by theory are and can, in the very nature of measurement, be only approximately true. As Duhem remarks, mathematical deduction is not useful to the physicist if interpreted rigorously. It is necessary to know that its validity is unaltered when the premise and conclusion are only “approximately true.” But the indeterminacy thus introduced, it is necessary to add in criticism, will invalidate the deduction unless the permissible limits of variation are specified. To do so, however, replaces the original mathematical deduction by a more complicated mathematical theory in respect of whose interpretation the same problem arises, and whose exact nature is in any case unknown. (shrink)

A Man whose height is four feet is short; adding one tenthof an inch to a short man's height leaves him short; therefore, a man whose height is four feet and one tenth of an inch is short. Now begin again and argue in the same pattern. A man whose height is four feet and one tenth of an inch is short; adding one tenth of an inch to a short man's height leaves him short; therefore, a man whose height (...) is four feet and two tenths of an inch is short. In this way, it seems, we can reach the absurd result that a man whose height is four feet plus any number of tenths of an inch is short. For, if the first argument is sound, so is the second; and if the second, so is the third; and so on. There appears to be no good reason for stopping at any one point rather than at another; it is hard to see why the chain of arguments should ever be broken. But the conclusion is ridiculous; it is, for example, preposterous to say that a man whose height is seven feet is, nevertheless, short. (shrink)

It is a commonly raised argument against the family resemblance account of concepts that there is no limit to a concept's extension. An account of family resemblance which attempts to provide a solution to this problem by including both similarity among instances and dissimilarity to non-instances has been developed by the philosopher of science Thomas Kuhn. Similar solutions have been hinted at in the literature on family resemblance concepts, but the solution has never received a detailed investigation. I shall provide (...) a reconstruction of Kuhn's theory and argue that his solution necessitates a developmental perspective wchich builds on both the transmission of taxonomies between generations and a progressive development through history. (shrink)

Editorial preface to the fourth edition and modified translation -- The text of the Philosophische Untersuchungen -- Philosophische untersuchungen = Philosophical investigations -- Philosophie der psychologie, ein fragment = Philosophy of psychology, a fragment.

The primary purpose of this book is to provide the reader with a comprehensive coverage of theoretical foundations of fuzzy set theory and fuzzy logic, as well as a broad overview of the increasingly important applications of these novel areas of mathematics. Although it is written as a text for a course at the graduate or upper division undergraduate level, the book is also suitable for self-study and for industry-oriented courses of continuing education. No previous knowledge of fuzzy set theory (...) and fuzzy logic is required for understanding the material covered in the book. Although knowledge of basic ideas of classical set theory and classical logic is useful, fundamentals of these subject areas are briefly overviewed in the book. In addition, basic ideas of neural networks, genetic algorithms, and rough sets are also explained. This makes the book virtually self-contained. Throughout the book, many examples are used to illustrate concepts, methods, and generic applications as they are introduced. Each chapter is followed by a set of exercises, which are intended to enhance readers' understanding of the material presented in the chapter. Extensive and carefully selected bibliography, together with bibliographical notes at the end of each chapter and a bibliographical subject index, is an invaluable resource for further study of fuzzy theory and applications. (shrink)

Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Godel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of (...) philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gode1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Godel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.". (shrink)

Nietzsche's mature masterpiece, Beyond Good and Evil considers the origins and nature of Judeo-Christian morality; the end of philosophical dogmatism and beginning of perspectivism; the questionable virtues of science and scholarship; liberal democracy, nationalism, and women's emancipation. A superb and new translation by Marion Faber, this highly annotated edition is complemented by a lucid introduction by one of the most eminent of Nietzsche scholars, Robert C. Holub.

The notions of health, illness, and disease are fuzzy-theoretically analyzed. They present themselves as non-Aristotelian concepts violating basic principles of classical logic. A recursive scheme for defining the controversial notion of disease is proposed that also supports a concept of fuzzy disease. A sketch is given of the prototype resemblance theory of disease.

It is a commonly raised argument against thefamily resemblance account of concepts that, on thisaccount, there is no limit to a concept's extension.An account of family resemblance which attempts toprovide a solution to this problem by including bothsimilarity among instances and dissimilarity tonon-instances has been developed by the philosopher ofscience Thomas Kuhn. Similar solutions have beenhinted at in the literature on family resemblanceconcepts, but the solution has never received adetailed investigation. I shall provide areconstruction of Kuhn's theory and argue that (...) hissolution necessitates a developmental perspective withbuilds on both the transmission of taxonomies betweengenerations and a progressive development throughhistory. (shrink)

/ Part INTRODUCTION Fuzziness is not a priori an obvious concept and demands some explanation. "Fuzziness" is what Black (NF) calls "vagueness" when ...

The sociological dimension of science is studied using the discovery of the Wasserman reaction and its accidental application as a test for syphilis as a basis, ...

This book, a joint publication of the Institute of Physics Publishing and Oxford University Press, is the third in a series of three works that form part of the Oxford/IOP Computational Intelligence Library project. The other two works are the Handbook of Neural Computation and the Handbook of Evolutionary Computation. Each of the three handbooks is available in loose-leaf print form, as well as in an electronic version that combines both CD-ROM and on-line (World Wide Web) access to the contents. (...) In each case, regularly published supplements will be available on a subscription basis. (shrink)

This book is the result of over 30 years of collaboration among its authors. It uses the systematic account of our common morality developed by one of its authors to provide a useful foundation for dealing with the moral problems and disputes that occur in the practice of medicine. The analyses of impartiality, rationality, and of morality as a public system not only explain why some bioethical questions, such as the moral acceptability of abortion, cannot be resolved, but also provide (...) a method for determining the correct answer for those occasions when a bioethical question has a unique correct answer. This new edition includes an entire chapter that has been added to address the controversial issue of abortion within the authors' distinct framework. This book presents the latest revisions of the authors' orignial analyses of the concepts of death and disease, analyses that have had a significant impact on the field of bioethics. It also includes an added chapter on mental disorders, where the authors' definition influenced what psychiatry classifies as a mental disorder, and so has had an impact that reveals beyond the field of bioethics. In this edition, the authors also offer a new, more developed perspective on the concept of valid or informed consent by considering what information physicians should be required to know before proposing screening, diagnostic testing, prescribing medications, or performing surgery. The book also integrates some of the important insights of the field of clinical epidemiology into its discussion of valid consent. Its account of paternalism and its justification, perhaps the most ubiquitous moral problem in medical ethics, has had considerable influence. Its discussion of euthanasia and physician assisted suicide challenges the standard views that have been put forward by both proponents and opponents of physician assisted suicide and voluntary active euthanasia. (shrink)

In the general theory of logic built up by Whitehead and Russell to furnish a basis for all mathematics there is a certain subtheory which is unique in its simplicity and precision; and though all other portions of the work have their roots in this subtheory, it itself is completely independent of them. Whereas the complete theory requires for the enunciation of its propositions real and apparent variables, which represent both individuals and propositional functions of different kinds, and as a (...) result necessitates- the introduction of the cumbersome theory of types, this subtheory uses only real variables, and these real variables represent but one kind of entity—which the authors have chosen to call elementary propositions. The most general statements are formed by merely combining these variables by means of the two primitive propositional functions of propositions Negation and Disjunction; and the entire theory is concerned with the process of asserting those combinations which it regards as true propositions, employing for this purpose a few general rules which tell how to assert new combinations from old, and a certain number of primitive assertions from which to begin. (shrink)

The hypothesis of the study was that the domains of color and form are structured into nonarbitrary, semantic categories which develop around perceptually salient “natural prototypes.” Categories which reflected such an organization (where the presumed natural prototypes were central tendencies of the categories) and categories which violated the organization (natural prototypes peripheral) were taught to a total of 162 members of a Stone Age culture which did not initially have hue or geometric-form concepts. In both domains, the presumed “natural” categories (...) were consistently easier to learn than the “distorted” categories. Even when not central, natural prototype stimuli tended to be more rapidly learned and more often chosen as the most typical example of the category than were other stimuli. Implications for general differences between natural categories and the artificial categories of concept formation research were discussed. (shrink)