It is difficult to describe this book without praising it. Collected here in one volume are some thirty-six high quality translations into English of the most important foreign-language works in mathematical logic, as well as articles and letters by Whitehead, Russell, Norbert Weiner and Post. The contents of the volume are arranged in chronological order, beginning with Frege's Begriffsschrift—translated in its entirety—and concluding with Gödel's famous "On Formally Undecidable Propositions" and Herbrand's "On the Consistency of Arithmetic". The translation of the (...) Gödel article is a small masterpiece, and is especially welcome in view of some of the rather poor efforts which have been made to render this important work into English. But this is more than a paste-pot job of anthologizing. Van Heijenoort and others have written prefaces to each of the included selections, in which are provided background historical and bibliographical information, comments on the intellectual currents which led to the production of the article, and, in many cases, a digest of the important theorems and concepts in the article itself. Each selection is a classic in its own right. In reading through the selections in this volume, one is struck by the extent to which purely mathematical problems and issues have controlled recent logical inquiry and have determined the development of various philosophies of mathematics. In the early stages, Frege and Peano were concerned with the logical reconstruction of arithmetic, and this led to the work of Russell and the logicist philosophy. Already in the development of the new logic there were certain problems which were resolved with Russell's theory of types—a device which many mathematicians felt to be rather artificial. The use of set theory, beginning with Cantor and reaching its maturity in Zermelo's 1904 proof of the well-ordering theorem, gave rise to a new set of difficulties concerning the axioms of choice, the continuum problem, and infinite sets. The two traditions are brought together in a common nexus of foundational problems by Weiner in 1914 and by Skolem's form of the Löwenheim theorem, given in 1920. Hereafter, the way is open for the rise of mathematical inquiry into the foundations of number systems, set theory and logic by Post, Skolem, von Neumann, Hilbert, Bernays, Gödel and many others. The work was far from completed by 1931, but a new and important tradition in mathematical inquiry had been established, and had come into its own. This book is, in effect, the record of an important chapter in the history of thought. No serious student of logic or foundations of mathematics will want to be without it.—H. P. K. (shrink)

An epistemic logic is built up on the basis of an analysis of two skeptical arguments. the method used is to first construct an inference relation appropriate to epistemic contexts and introduce "a knows that..." as an operator giving rise to sentences closed with respect to this new concept of inference. soundness and completeness proofs are provided using auxiliary three-valued valuations.

PART I. -- 1. The Asian, European and the American views on destiny -- 2. Biblical fulfilment of destiny -- 3. Destiny in the Ghanaian context -- 4. Mystical effects of names on destiny -- PART II. -- 5. My childhood days and primary education -- 6. My secondary education -- 7. University education -- 8. Employment after graduation, mariage life and children -- 9. Post-graduate studies at the University of Strathclyde, Glascgow, Scotland and working experience -- 10. Resignation from (...) Cocoa processing company and employment at Tema Food Complex Corportion -- 11. Appointment as the manaing director of cocoa processing company, achievements, awards and honours received -- 12. Mysterious occurrences in my life and my wife's miraculous healing -- 13. Do you believe in fasting, prayers and dreams? -- 14. Conclusion. (shrink)

Using covariant derivatives and the operator definitions of quantum mechanics, gauge invariant Proca and Lehnert equations are derived and the Lorenz condition is eliminated in U(1) invariant electrodynamics. It is shown that the structure of the gauge invariant Lehnert equation is the same in an O(3) invariant theory of electrodynamics.

It would be difficult to name a more interesting scientific problem than that of knowledge of the brain, its overall mechanisms and its molecular nature. Rational management of the brain in the future and utilization of the principles of its functioning to construct various mechanisms to undergird present-day technological progress should follow as direct consequences of development of that sphere of knowledge.

Scientists in many fields are presently giving the closest attention to study of the potentials of the systems approach for understanding what cannot be comprehended with the analytical approach or, as V. A. Engel'gardt has put it, "an accumulation of material in reduced form." This approach is in some degree a gesture of despair. It is quite obvious that we now face the danger of drowning in the abundance of data accumulated in terms of "special" problems not tied into a (...) system, and that this threatens loss of general direction. (shrink)

These Essays Look Afresh At The Varying Connotations Of Social Justice In Its Moral, Legal, Economic, Political And Historic Perspectives. They Consider Social Justice Vis-A-Vis Democracy, Gender Questions, Justice-Making Mechanisms, Retribution And The Hindu Karma.

The Vatican palimpsest omits the word enthymemate and leaves a lacuna, thus showing that the scribe found it written as Greek in his exemplar. Now A has been shown to belong to the fourth century, and therefore its authority must be greater than that of the other manuscripts available for this part of Gellius. The same problem occurs in 12.2.14, non pro enthymemate aliquo, where Hertz goes against the Greek of the manuscripts and adopts the reading of Carrio. Yet an (...) examination of the use of the Greek dative in Cicero's Letters will show that it can be used fully as the equivalent of a Latin ablative, can be governed by prepositions taking the ablative in Latin, and can be qualified by a Latin adjective in the ablative. (shrink)

THE HOLY GAL - and European, medieval legends - a mysterious vessel, for the sake of approaching and engaging in its good deeds, the knights performed their exploits. It was commonly believed that this is the Cup with the blood of Jesus Christ, which Joseph of Arimathea gathered, who removed from the cross the body of the crucified Christ. It was often assumed that this cup originally served Christ and the Apostles at the time of the Last Supper; was the (...) Cup for the communion of the first Liturgy. Gral is a mystery, invisible to the unworthy, but also worthy of being different. Gral has the ability to miraculously fill his elect with unearthly things, which was first discovered during the imprisonment of Joseph Artmofeysky. (shrink)

Childhood obesity is a serious problem for increasing numbers of children around the world. According to the International Obesity Task Force, 1 of 10 schoolaged children worldwide is overweight or obese, a number totaling 155 million; of these, 2-3% are obese. Prevalence is highest in the Americas and Europe, followed by the Near/Middle East, with smaller but growing numbers in the Asia-Pacific and Sub-Saharan regions of the world.In the United States, which provides the data for much of this report, prevalence (...) continues to rise. The most recent nationally representative data indicate that 33.6% of individuals aged 2-19 years were overweight and 17.1% were at risk for overweight in 2003-2004, compared to 28.2% and 13.9% in 1999-2000, respectively. In this age group, the prevalence of overweight or at risk for overweight was highest among Mexican Americans, followed by Non-Hispanic blacks and Non-Hispanic whites, and a higher percentage of males were overweight compared to females. (shrink)

This paper attempts to argue for the theory-ladenness of evidence. It does so by employing and analysing an episode from the history of eighteenth century chemistry. It delineates attempts by Joseph Priestley and Antoine Lavoisier to construct entirely different kinds of evidence for and against a particular hypothesis from a set of agreed upon observations or (raw) data. Based on an augmented version of a distinction, drawn by J. Bogen and J. Woodward, between data and phenomena it is shown that (...) the role of theoretical auxiliary assumptions is very important in constructing evidence for (or against) a theory from observation or (raw) data. In revolutionary situations, rival groups hold radically different theories and theoretical auxiliary assumptions. These are employed to construct very different evidence from the agreed upon set of observations or (raw) data. Hence, theory resolution becomes difficult. It is argued that evidence construction is a multi-layered exercise and can be disputed at any level. What counts as unproblematic observation or (raw) data at one level may become problematic at another level. The contingency of these constructions and the (un)problematic nature of evidence are shown to be partially dependent upon the scientific knowledge that the scientific community possesses. (shrink)