In his thesis Para uma Teoria Geral dos Homomorfismos (1944), the Portuguese mathematician José Sebastião e Silva constructed an abstract or generalized Galois theory, that is intimately linked to F. Klein’s Erlangen Program and that foreshadows some notions and results of today’s model theory; an analogous theory was independently worked out by M. Krasner in 1938. In this paper, we present a version of the theory making use of tools which were not at Silva’s disposal. At the same time, we (...) tried to keep in mind, so much as possible, the gist of his standpoint. (shrink)
On the one hand, non-reflexive logics are logics in which the principle of identity does not hold in general. On the other hand, quantum mechanics has difficulties regarding the interpretation of ‘particles’ and their identity, also known in the literature as ‘the problem of indistinguishable particles’. In this article, we will argue that non-reflexive logics can be a useful tool to account for such quantum indistinguishability. In particular, we will provide a particular non-reflexive logic that can help us to analyze (...) and discuss this problem. From a more general physical perspective, we will also analyze the limits imposed by the orthodox quantum formalism to consider the existence of indistinguishable particles in the first place, and argue that non-reflexive logics can also help us to think beyond the limits of classical identity. (shrink)
We first show that a theorem by Cartan that generalizes the Frobenius integrability theorem allows us (given certain conditions) to obtain noncurvature solutions for the differential Bianchi conditions and for higher-degree similar relations. We then prove that there is no algorithmic procedure to determine, for a reasonable restricted algebra of functions on spacetime, whether a given connection form satisfies the preceding conditions. A parallel result gives a version of Gödel's first incompleteness theorem within an (axiomatized) theory of gauge fields.
MEDIEVAL LOGICS LAMBERT MARIE DE RIJK (ed.), Die mittelalterlichen Traktate De mod0 opponendiet respondendi, Einleitung und Ausgabe der einschlagigen Texte. (Beitrage zur Geschichte der Philosophie und Theologie des Mittelalters, Neue Folge Band 17.) Miinster: Aschendorff, 1980. 379 pp. No price stated. THE SEVENTEENTH CENTURY MARTA FATTORI, Lessico del Novum Organum di Francesco Bacone. Rome: Edizioni dell'Ateneo 1980. Two volumes, il + 543, 520 pp. Lire 65.000. VIVIAN SALMON, The study of language in 17th century England. (Amsterdam Studies in the Theory (...) and History of Linguistic Science, Series 111: Studies in theHistory of Linguistics, Volume 17.) Amsterdam: John Benjamins B.V., 1979.x + 218 pp. Dfl. 65. Theoria cum Praxi. Zum Verhaltnis von Theorie und Praxis im 17. und 18. Jahrhundert. (Akten des 111. Internationalen Leibnizkongress, Hannover, 12. bis 17.November 1977, Band 111: Logik, Erkenntnistheorie, Wissenschaftstheorie, Metaphysik, Theologie.) Wiesbaden: Franz Steiner Verlag, 1980. vii + 269 pp. DM 48. CLASSICAL AND NON-CLASSICAL LOGICS MICHAEL CLARK, The place of syllogistic in logical theory. Nottingham: University of Nottingham Press, 1980. ix + 151 pp. £3.00. A.F. PARKER-RHODES, The theory of indistinguishables. Dordrecht, Boston and London: D. Reidel Publishing Company, 1981. xvii + 216 pp. Dfl.90.00/$39.50. NICHOLAS RESCHER and ROBERT BRANDOM, The logic of inconsistency. Oxford:Basil Blackwell, 1980. x + 174 pp. f 11.50. MISCELLANEOUS J. ZELENY, The logic of Marx. Translated from the German by T. Carver. Oxford: Basil Blackwell, 1980. xcii + 247 pp. £12.50. FELIX KAUFMANN, The infinite in mathematics. Edited by Brian McGuinness. Introduction by E. Nagel. Translation from the German by Paul Foulkes. Dordrecht: Reidel, 1978. xvii + 235 pp. Dfl 85/$39.50 (cloth); Dfl 45/$19.95 (paper). PAMELA MCCORDUCK, Machines who think. San Francisco: W.H. Freeman and Company, 1979. xiv + 275 pp. $14.95. J. MITTELSTRASS (ed.), Enzyklopadie Philosophie und Wissenschaftstheorie Bd. 1 : A-G. Mannheim, Wien, Ziirich: Bibliographisches Institut, 1980. 835 pp. DM 128. (shrink)
We propose a formalization of Meinong's theory of objects with the help of Hilbert's $\epsilon$-symbol and a paraconsistent logical system, with an eye towards its application in an axiomatization of the natural sciences.