Sum rules are derived for the quantum wave functions of the Hadamard billiard in arbitrary dimensions. This billiard is a strongly chaotic (Anosov) system which consists of a point particle moving freely on a D-dimensional compact manifold (orbifold) of constant negative curvature. The sum rules express a general (two-point)correlation function of the quantum mechanical wave functions in terms of a sum over the orbits of the corresponding classical system. By taking the trace of the orbit sum rule or pre-trace formula, (...) one obtains the Selberg trace formula. The sum rules are applied in two dimensions to a compact Riemann surface of genus two, and in three dimensions to the only non-arithmetic tetrahedron existing in hyperbolic 3-space. It is shown that the quantum wave functions can be computed from classical orbits. Conversely, we demonstrate that the structure of classical orbits can be extracted from the quantum mechanical energy levels and wave functions (inverse quantum chaology). (shrink)

R. F. Atkinson; XIII*—Explanation in History, Proceedings of the Aristotelian Society, Volume 72, Issue 1, 1 June 1972, Pages 241–256, https://doi.org/10.1093/a.

R F Dearden; Freedom and the Development of Autonomy: a reply to Victor Quinn, Journal of Philosophy of Education, Volume 18, Issue 2, 30 May 2006, Pages 271–27.

Narrativist philosophy of history rejects all attempts to establish an epistemological link between the past and its historical representation. Two forms of narrativism should be distinguished. The first form attacks epistemology by stressing the autonomy of historical writing with regard to the past itself ; the second form does the same by de-contextualizing the elements of the past—the very idea of the past thus becomes problematic and epistemological queries can no longer even be formulated. The first form of narrativism is (...) synthetical, suggesting that the historian should construct broad panoramical views of the past ; the second, on the contrary, aims at a dispersive dissolution of the past. The article concentrates upon the dispersive form of narrativism. It is exemplified in Ginzburg's 'micro-storie'. The implication that these 'micro-storie' should not primarily be seen as historiography in the proper sense of the word but rather as a form of narrativist philosophy of history (expressing a theory of historical representation) is accepted wholeheartedly. It is shown that the 'micro-storie' come very close to Derrida's deconstructivist reading of texts. For in both cases we have to do with 'ruptures' announcing themselves in small, seemingly insignificant details. The conclusion of the article is that the synthetical and the dispersive forms of narrativism need each other and that we can give meaning to the concept of an objective historical reality only if we accept both of them. (shrink)

R F Dearden; Theory and Practice in Education, Journal of Philosophy of Education, Volume 14, Issue 1, 30 May 2006, Pages 17–29, https://doi.org/10.1111/j.1467-.

This paper proposes several concepts of efficient solutions for multicriteria decision problems under uncertainty. We show how alternative notions of efficiency may be grounded on different decision ‘contexts’, depending on what is known about the Decision Maker's (DM) preference structure and probabilistic anticipations. We define efficient sets arising naturally from polar decision contexts. We investigate these sets from the points of view of their relative inclusions and point out some particular subsets which may be especially relevant to some decision situations.

Historians rarely agree with Hayden White's account of their discipline. To a certain extent their dissatisfaction can be explained by the fact that historians customarily distrust historical theory and always tend to look at the historical theorist with the greatest suspicion. But historians find an extra argument for their dislike of White's ideas in his alleged cavalier disregard of how historical facts limit what the historian might wish to say about the past. And, admittedly, this criticism is not wholly unfounded.Nevertheless, (...) this essay attempts to show how misguided this traditional criticism of White actually is. For it is historians who too easily take the truth of their accounts of the past for granted, whereas White's theoretical writings can be shown to express a full awareness of the kind of problem encountered in the effort to tell the truth about historical reality. Hence, White's writings-rather than those by historians criticizing White-testify to the respect that we owe to historical reality itself. That this is how we should read White becomes clear if we consider his intellectual evolution as a whole rather than the individual books or essays that he wrote. (shrink)