Rhymed text and movable pictures present a variety of amusing situations.

The volume collects classics of Marxist historiography of science, including a new translation of Boris Hessen's “The Social and Economic Roots of Newton's ...

We give new proofs of both incompleteness theorems. We do not use the diagonalization lemma, but work with some quickly growing functions instead.

We take I.Q. tests but not Compassion Aptitude tests. Yet mind and emotions need to be seen as two different parts of the same spectrum if the battered human psyche is to be mended. Skolimowski sees the opportunity for a new order to be brought about if the Western mind can return to, then reintegrate, the spiritual.

The ArgumentFranz Borkenau's book,The Transition from Feudal to Modern Thought(Der Übergang vom feudalen zum bürgerlichen Weltbild[literally:The Transition from the Feudal to the Bourgeois World-Picture]), serves as background for Grossmann's study. The objective of this book was to trace the sociological origins of the mechanistic categories of modern thought as developed in the philosophy of Descartes and his successors. In the beginning of the seventeenth century, according to Borkenau, mechanistic thinking triumphed over medieval philosophy which emphasized qualitative, not quantitative considerations. This (...) transition from medieval and feudal methods of thought to modern principles is the general theme of Borkenau's book, and is traced to the social changes of this time. According to this work, the essential economic change that marked the transition from medieval to modern times was the destruction of the handicraft system and the organization of labor under one roof and under one management. The roots of the change in thought are to be sought here. With the dismemberment of the handicraft system and the division of labor into relatively unskilled, uniform, and therefore comparable activities, the conception of abstract homogeneous social labor arises. The division of the labor process into simple repeated movements permits a comparison of hours of labor. Calculation with such abstract social unities, according to Borkenau, was the source from which modern mechanistic thinking in general derived its origin.Grossmann, although he considers Borkenau's work a valuable and important contribution, does not believe that the author has achieved his purpose. First of all, he contends that the period that Borkenau describes as the period of the triumph of modern thought over medieval should not be placed at the beginning of the seventeenth century, but in the Renaissance, and that not Descartes and Hobbes but Leonardo da Vinci was the initiator of modern thought. Leonardo's theories, evolved from a study of machines, were the source of the mechanistic categories that culminated in modern thought.If Borkenau's conception as to the historical origin of these categories is incorrect in regard to time, Grossmann claims it follows that it is incorrect also in regard to the social sources to which it is ascribed. In the beginning, the factory system did not involve a division of labor into comparable homogeneous processes, but in general only united skilled handicraftsmen under one roof. The development of machinery, not the calculation with abstract hours of labor, is the immediate source of modern scientific mechanics. This goes back to the Renaissance and has relatively little to do with the original factory system that was finally superseded by the Industrial Revolution.While Borkenau, in tracing the social background of the thought of the period, relies chiefly on the conflicts and strife of political parties, Grossmann regards this as one element only in the formation of the general social situation, which in its entirety and in the interaction of its elements explains the development of modern thought. (shrink)

We transform the proof of the second incompleteness theorem given in [3] to a proof-theoretic version, avoiding the use of the arithmetized completeness theorem. We give also new proofs of old results: The Arithmetical Hierarchy Theorem and Tarski's Theorem on undefinability of truth; the proofs in which the construction of a sentence by means of diagonalization lemma is not needed.

Historically, Ehrenfest’s theorem is the first one which shows that classical physics can emerge from quantum physics as a kind of approximation. We recall the theorem in its original form, and we highlight its generalizations to the relativistic Dirac particle and to a particle with spin and izospin. We argue that apparent classicality of the macroscopic world can probably be explained within the framework of standard quantum mechanics.

The geography of religion is one of the younger areas of religious studies. The subject of her interests is the reciprocal ties that stand between religion and the geographical environment. On the one hand, the influence of the geographical environment on the formation of religious imaginations is investigated, and on the other hand, feedback, that is, what kind of religion does the change in the geographical environment. In addition, this area of ​​religious studies is engaged in the distribution of individual (...) religions, demographic and statistical issues, as well as analysis of the topography of holy places, problems of religious migration, pilgrimage, missions, religious tourism, etc. (shrink)

This book presents a detailed treatment of ordinal combinatorics of large sets tailored for independence results. It uses model theoretic and combinatorial methods to obtain results in proof theory, such as incompleteness theorems or a description of the provably total functions of a theory. In the first chapter, the authors first discusses ordinal combinatorics of finite sets in the style of Ketonen and Solovay. This provides a background for an analysis of subsystems of Peano Arithmetic as well as for combinatorial (...) independence results. Next, the volume examines a variety of proofs of Gödel's incompleteness theorems. The presented proofs differ strongly in nature. They show various aspects of incompleteness phenomena. In additon, coverage introduces some classical methods like the arithmetized completeness theorem, satisfaction predicates or partial satisfaction classes. It also applies them in many contexts. The fourth chapter defines the method of indicators for obtaining independence results. It shows what amount of transfinite induction we have in fragments of Peano arithmetic. Then, it uses combinatorics of large sets of the first chapter to show independence results. The last chapter considers nonstandard satisfaction classes. It presents some of the classical theorems related to them. In particular, it covers the results by S. Smith on definability in the language with a satisfaction class and on models without a satisfaction class. Overall, the book's content lies on the border between combinatorics, proof theory, and model theory of arithmetic. It offers readers a distinctive approach towards independence results by model-theoretic methods. (shrink)

L'uomo si rivela in varie dimensioni, ma la sua dignità è un aspetto che ai nostri tempi viene sottolineato in modo del tutto particolare. L'uomo è consapevole di avere una dignità per il semplice fatto di essere uomo. La nostra cultura è molto sensibile a questa dimensione che si svela come una conquista nei diversi campi. Dove entra il senso del dover essere all’altezza della propria natura, cioe nel comportamento, nella conquista e nel raggiungimento dei fini, li si rivolge alla (...) dimensione etica della dignità dell'uomo. La dignità umana deve esser riconosciuta dagli altri, rispettata e promossa nella vita sociale. In questo caso si accede cosi alla radice dei diritti deiruomo. Quest'articolo tratta invece della dimensione metafisica della dignità dell’uomo in San Tommaso d'Aquino. (shrink)

Henryk Elzenberg is one of the most prominent Polish philosophers of this century. His main publications are: the brilliant Foundations of Leibniz’s Metaphysics of 1917; a philosophical diary published in 1963 as Trouble with Being; and a collection of papers Man and Value. Elzenberg’s principal field of inquiry was axiology, in which he put forward a deep and original conception of his own. That, however, remains still mostly in the form of manuscripts and lecture notes, of which we publish (...) two pieces above: a critique of the utilitarian concept of value, and an analysis of Meinong’s position on the same topic. (shrink)

We study cofinal extensions of models of arithmetic, in particular we show that some properties near to expandability are preserved under cofinal extensions.