The paper examines the difference between János Bolyai’s and Lobachevskii’s notion of non-Euclidean parallelism. The examination starts with the summary of a widespread view of historians of mathematics on János Bolyai’s notion of non-Euclidean parallelism used in the first paragraph of his Appendix. After this a novel position of the location and meaning of Bolyai’s term “parallela” in his Appendix is put forward. After that János Bolyai’s Hungarian manuscript, the Commentary on Lobachevskii’s Geometrische Untersuchungen is elaborated (...) in order to see how Bolyai and Lobachevskii’s notions of parallelism differ. The careful examination of the Commentary reveals a seeming incoherence of Bolyai’s translation, and finally the explanation of this incoherence offered by the Received View and that of the novel position will be compared and assessed. L’article examine la différence entre la notion du parallélisme non-Euclidean de János Bolyai et celle de Lobachevskii. Tout d’abord le travail s’occupe de l’opinion répendue parmi les historiens de géometrie (le « Received View » ), selon laquelle János Bolyai précise la notion du parallélisme non-Euclidean dans le premier paragraph de l’Appendix. Ensuite une pointe de vue toute neuve sera présentée concernant la place et le sens du terminus technicus,,paralella” de Bolyai dans l’Appendix. Enfin on va analyser les Commentaires (un manuscrit hongrois) de János Bolyai sur le livre Geometrische Untersuchungen de Lobachevskii àfin de voir jusqu’à quel point la notion de parallelisme de Bolyai se diffère de celle de Lobachevskii. L’analyse bien fondue des Commentaires va nous relever un apparent incohérence de la traduction de Bolyai. On examine et on compare l’opinion répendue dans le vaste public avec la nouvelle interpretation de l’Appendix, et on discute les explications probables de cet incohérence. (shrink)

The universal homogeneous triangle-free graph, constructed by Henson [A family of countable homogeneous graphs, Pacific J. Math.38(1) (1971) 69–83] and denoted H3, is the triangle-free analogue of the Rado graph. While the Ramsey theory of the Rado graph has been completely established, beginning with Erdős–Hajnal–Posá [Strong embeddings of graphs into coloured graphs, in Infinite and Finite Sets. Vol.I, eds. A. Hajnal, R. Rado and V. Sós, Colloquia Mathematica Societatis János Bolyai, Vol. 10 (North-Holland, 1973), pp. 585–595] and culminating in (...) work of Sauer [Coloring subgraphs of the Rado graph, Combinatorica26(2) (2006) 231–253] and Laflamme–Sauer–Vuksanovic [Canonical partitions of universal structures, Combinatorica26(2) (2006) 183–205], the Ramsey theory of H3 had only progressed to bounds for vertex colorings [P. Komjáth and V. Rödl, Coloring of universal graphs, Graphs Combin.2(1) (1986) 55–60] and edge colorings [N. Sauer, Edge partitions of the countable triangle free homogenous graph, Discrete Math.185(1–3) (1998) 137–181]. This was due to a lack of broadscale techniques. We solve this problem in general: For each finite triangle-free graph G, there is a finite number T(G) such that for any coloring of all copies of G in H3 into finitely many colors, there is a subgraph of H3 which is again universal homogeneous triangle-free in which the coloring takes no more than T(G) colors. This is the first such result for a homogeneous structure omitting copies of some nontrivial finite structure. The proof entails developments of new broadscale techniques, including a flexible method for constructing trees which code H3 and the development of their Ramsey theory. (shrink)

Entangled states provide the necessary tools for conceptual tests of quantum mechanics and other alternative theories. These tests include local hidden variables theories, pre- and postselective quantum mechanics, QND measurements, complementarity, and tests of quantum mechanics itself against, e.g., the so-called causal communication constraint. We show how to produce various nonlocal entangled states of multiple cavity fields that are useful for these tests, using cavity QED techniques. First, we discuss the generation of the Bell basis states in two entangled cavities, (...) when there is at most one photon in either of the cavities, and then a straightforward generalization to similar N-cavity states. We then show how to produce a nonlocal entangled state when there is precisely one photon hiding in three cavities. These states can be produced by sending appropriately prepared atoms through the cavities. As applications we briefly review two proposals: one to test quantum mechanics against the causal communication constraint using a two-cavity entangled state and the other to test pre- and postselective quantum mechanics using a three-cavity entangled state. The outcome of the latter experiment can be discussed from the viewpoint of the consistent histories interpretation of quantum mechanics and therefore provides an opportunity to subject quantum cosmological ideas to laboratory tests. Finally, we point out the relation between these schemes and the schemes suggested for quantum computing, teleportation, and quantum copying. (shrink)

The application of evolutionary perspectives to analyzing sex differences in aggressive behavior and dominance hierarchies has been found useful in multiple areas. We draw attention to the parallel of gender differences in the worsening health status of restructuring societies. Drastic socio-economic changes are interpreted as examples of hierarchy disruption, having differential psychological and behavioral impact on women and men, and leading to different changes in health status.

Recent neurophysiological observations are giving rise to the expectation that in the near future genuine biological experiments may contribute more than will premature speculations to the understanding of global and cognitive functions. The classical reflex principle — as the basis of neural functions — has to yield to new ideas, like autopoiesis and/or self-organization, as the basic paradigm in the framework of which the essence of the neural can be better understood. Neural activity starts in the very earliest stages of (...) development well before receptors and afferent input become functional. Under suitable conditions, both in nervous tissue cultures and in embryonic tissue recombination experiments, the conditions of such initial autopoietic activity can be studied. This paper tries to generalize this elementary concept for various neural centers, notably for the spinal segmental apparatus and the cerebral cortex. (shrink)

János Kornai, a distinguished Hungarian economist, began his adult life as an ardent believer in socialism and then became a critic of the communist political and economic system. He lost family members in the Holocaust, contributed to the ideological preparation for the 1956 Hungarian Revolution, and became an influential theorist of the post-Soviet economic transition. He has been a journalist, a researcher prohibited from teaching in his home country, and a tenured professor at Harvard. By Force of Thought traces Kornai's (...) lifelong intellectual journey and offers a subjective complement to his academic research.Disenchanted with communism, Kornai published Overcentralization, the first book written by someone living behind the Iron Curtain to be openly critical of Soviet-style economics. Although it was attacked in Hungary, it was hailed by Western economists. The Kornai-Lipták theory on two-level planning captured the attention of mathematical economists. Kornai went on to publish the controversial Anti-Equilibrium, a critique of the general equilibrium theory underpinning mainstream economic analyses of markets, Economics of Shortage, The Road to a Free Economy, and the summary of his lifetime research, The Socialist System. An intellectual emissary between East and West, Kornai commuted between Harvard and Budapest for many years.Kornai's memoir describes his research--including his present-day evaluation of his past work--as well as the social and political environments in which he did his work. The difficulties faced by a critic of central planning in a communist country are made especially vivid by material from newly opened secret police files and informers' reports on his activities. By Force of Thought will be an essential resource for students of economic thought, socialist systems, and postsocialist transition, and for readers interested in Eastern European intellectual life before, during, and after communism. (shrink)

This essay tries to review the main elements of the concept of public reason as presented by John Rawls with reference to his latest book (The Law of Peoples with The Idea of Public Reason Revisited) and simultaneously brings up the arguments for and against this concept that have been put forward by the literature. Many of the arguments presented here are not new, but what this essay aims at is a reassessment of the debate by confronting many of the (...) interpretations and points of view raised around the concept of public reason. Based on the argumentation that if ‘right’ precedes this leaves room for the (different existences of) ‘good’ I propose that public reason ought to be conceived more as a political concept and less of a comprehensive account of morality. (shrink)

Pál Makó was a prominent 18th century Hungarian mathematician and physicist. The paper shows the cultural-historical background of his work as well as the scientific-historical precedents of his life-work. The influence of the milieu of the University of Nagyszombat on his thinking is taken into account as well. Further, the paper sheds light on Makó´s interpretation of Leibniz and Ch. Wolff in his philosophical books and on his adaptation of advanced mathematics as the zenith of his career. Attention is paid (...) also to the methodology of his text-books and scientific and philosophical-historical lessons of his manuscripts. (shrink)

It is a central claim of György Márkus’s philosophy of culture that the Enlightenment project ended up in deep, apparently irresolvable antinomies. But, unlike the majority of ‘postmodern’ thinkers, Márkus insists that the commitments of the Enlightenment cannot and should not be given up. This tension between the failure of the Enlightenment to produce a society of free and equal persons, each leading their lives autonomously, drawing on the resources of rational high culture, and the impossibility and undesirability of the (...) abandonment of the commitments of the Enlightenment finds an expression in what Márkus calls ‘the antinomies of late modernity’. This paper offers an interpretation of Márkus’s conception; it identifies a certain ambiguity in Márkus’s use of the term ‘antinomies’, and suggests that Márkus’s ambition is compatible with maintaining the first two but is failed by the third one which should, therefore, be abandoned. (shrink)

This volume contains a collection of articles focusing on the philosophical and theological exchanges between Muslim and Christian intellectuals living in Baghdad during the classical period of Islamic history, when this city was a vibrant center of philosophical, scientific, and literary activity.

The paper deals with some of the contemporary theories of science which see the latter as an organized cognitive activity. On the background of the controversy concerning the nature of rationality and relativism the author underlines the contribution of the sociology of scientific knowledge, showing its role in reconceptualization of the dichotomy between internalism and externalism. His argumentation is in favor of the institutionalist conception of science as a subsystem of society. The problem of the reliability of knowledge is explained (...) in the context of the globalized science: for science to be cognitively successful it is necessary to optimize the institutional mechanisms producing consensus and working as the controlling and corrective mechanisms. (shrink)

The paper distinguishes two types of Platonist approach, namely the Traditional one and the Robust one. In relation to this distinction I am going to argue that if the ontology of mathematics is intended to be defended plausibly in a Platonist way then this cannot be done according to the Traditional version. This will draw our attention to the plausibility of the Robust version. The plausibility of the two versions of Platonism will be examined in relation to one of the (...) central problems of the philosophy of mathematics, namely the truth-proof problem. The surveying of the truth-proof problem will bring to the surface the prima facie plausibility of the Platonist approach, as well as the apparent accessibility problem of it. Focusing on the accessibility problem will help us to identify two conditions that have to be met by any particular access theory of Platonism. These will be the reducibility condition, and the matching one. The Traditional version will appear an insufficient philosophical theory in relation to the two former conditions. The insufficiency will be demonstrated in the area of the incompatible mathematical theories, namely in the area of Euclidean and hyperbolic geometries. It will turn out that Robust Platonism can escape the squeeze of these conditions, so can it save the original prima facie plausibility of the Platonist approach. (shrink)

Gene-technology was developed in the eighties and stimulated an overmuch heated social debate. Let's think such problems as cloning, transgenic organisms, Human Genom Project, DNA diagnostics and therapy, the geneticalisation of society etc. While the gene manipulation develops rapidly the necessary social control is missing. Regarding the social co-ordination of gene technology, the decision-makers still excessively trust in the institution of market and in the experts' competence.

Modem economics relied on the false presupposition that natural resources are free goods. It gave rise to exaggerated expectations on the side of economists concerning the possibilities of economic growth. I try to interpret the terms of natural resources, sustaining capacity, production from a human-ecological platform. The quantity of natural resources may vary within a large spectrum between absolute abundance and total exhaustion. The support capacity can be raised in different ways. Extensive growth is wrong while technological development is a (...) good way. So, certain technological-market processes aiming at extensive growth must be suppressed, processes that could increase effectivity and technical developments, which would draw new resources into production, should be supported. (shrink)

Die Thematisierung des modernen Verhältnisses zwischen Staat und Gesellschaft ist so ausgerichtet, dass sie von vornherein zu einer Privilegierung der Gesellschaft neigt. Die neuzeitliche sozialphilosophische Diskussion läuft auf eine Zurücknahme des Staates in die Gesellschaft hinaus. An die Stelle der staatlich bestimmten Gesellschaft tritt der gesellschaftlich bestimmte Staat. Die entscheidende Frage ist, wie kann die Gesellschaftlichkeit des Staates begründet werden. Der Staat ist nicht mehr selbstständig, schwebt nicht mehr über der sozialen Wirklichkeit, sondern muss selbst als sozial bestimmt verstanden werden. (...) Die grundsätzliche Frage der neuzeitlichen Sozialphilosophie ist daher: Wie ist der Staat überhaupt möglich? Diese Frage wird durch eine Theorie der Konstitution des Staates beantwortet. (shrink)