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)

The work of 6th century Indian logician Dharmakirti is explored in detail in series of twelve articles analyzing deviant logic, subject failure, andther important aspects of the Indo-Tibetan Buddhist logical tradition.riginal.

This Handbook documents the main trends in current research between logic and language, including its broader influence in computer science, linguistic theory and cognitive science. The history of the combined study of Logic and Linguistics goes back a long way, at least to the work of the scholastic philosophers in the Middle Ages. At the beginning of this century, the subject was revitalized through the pioneering efforts of Gottlob Frege, Bertrand Russell, and Polish philosophical logicians such as Kazimierz Ajdukiewicz. Around (...) 1970, the landmark achievements of Richard Montague established a junction between state-of-the-art mathematical logic and generative linguistic theory. Over the subsequent decades, this enterprise of Montague Grammar has flourished and diversified into a number of research programs with empirical and theoretical substance. This appears to be the first Handbook to bring logic-language interface to the fore. Both aspects of the interaction between logic and language are demonstrated in the book i.e. firstly, how logical systems are designed and modified in response to linguistic needs and secondly, how mathematical theory arises in this process and how it affects subsequent linguistic theory. The Handbook presents concise, impartial accounts of the topics covered. Where possible, an author and a commentator have cooperated to ensure the proper breadth and technical content of the papers. The Handbook is self-contained, and individual articles are of the highest quality. (shrink)

The first main result isolates some conditions which fail for the class of graphs and hold for the class of Abelian p-groups, the class of Abelian torsion groups, and the special class of "rank-homogeneous" trees. We consider these conditions as a possible definition of what it means for a class of structures to have "Ulm type". The result says that there can be no Turing computable embedding of a class not of Ulm type into one of Ulm type. We apply (...) this result to show that there is no Turing computable embedding of the class of graphs into the class of "rank-homogeneous" trees. The second main result says that there is a Turing computable embedding of the class of rank-homogeneous trees into the class of torsion-free Abelian groups. The third main result says that there is a "rank-preserving" Turing computable embedding of the class of rank-homogeneous trees into the class of Boolean algebras. Using this result, we show that there is a computable Boolean algebra of Scott rank ${\mathrm{\omega }}_{1}^{\mathrm{C}\mathrm{K}}$. (shrink)

In an article published in 2009 titled "How Do Mādhyamikas Think?" I tried to go some distance with Yasuo Deguchi, Jay Garfield, and Graham Priest (henceforth "DGP") in reading certain Buddhist texts as dialetheist.1 The dialetheism that I saw as plausible for the Prajñāpāramitā-sūtras and Nāgārjuna was not the full-blown robust variety of DGP (i.e., acceptance of the truth of some statement of the form p & ¬p) but a non-adjunctive variety, acceptance of p and acceptance of ¬p. In short, (...) the adjunctive move to p & ¬p is blocked.In the article, I focused on texts like the Vajracchedikā Prajñāpāramitā-sūtra ("Diamond Cutter Suūtra") with its famous "signature formulae" along the lines of "x does not exist / x is not .. (shrink)

The paper looks at how Tsong kha pa, mKhas grub, and Go rams pa understood the third and fourth lemmas in the tetralemma, “both A and B” and “neither A nor B,” respectively.

PAPERS IN LOGIC AND ETHICS by A. N. Prior. Duckworth, 1976. 233 pp. £8.95.THE DOCTRINE OF PROPOSITIONS AND TERMS by A. N. Prior. Duckworth, 1976. 143 pp. £5.95.

Let it be granted that Buddhism has, e.g., in its logical literature, detailed canons and explicit rules of right reason that, amongst other things, ban inconsistency as irrational. This is the normative dimension of how people should think according to many major Buddhist authors. But do important Buddhist writers ever recognize any interesting or substantive role for inconsistency and forms of irrationality in their account of how people actually do think and act? The article takes as its point of departure (...) a recurring theme in the writings of the 8th Century Indian Buddhist thinker, Śāntideva, who subjects his own behaviour and thought to minute scrutiny in argumentation with himself, only to be puzzled at his own seemingly irrational persistence in ways of thinking that he knows to be wrong and actions that he knows to be worse courses. The Buddhist’s situation is profitably comparable to issues of akrasia, weakness of the will, that are taken up by Plato, Aristotle and many modern philosophers, including notably Donald Davidson and David Wiggins. (shrink)

The first solid bit of argumentation you get in Plato's Phaedo goes something like this: Whatever comes to be, comes to be from its opposite . If at a certain time t a given thing a begins to be F , before that time t it must have been non- F . Wherever a pair of predicates, F and G , are genuine contradictories; where, that is, they stand to each other in the same relation as F stands in to (...) non- F ; it is necessarily true that if a began to be F at t before then a was G . The only trouble comes from the difficulty of finding substitutes for F and G that people will allow to be genuine contradictories. It the butter began to be soft at four o'clock, we may suggest, before four it was hard. A tiresome opponent will retort that there is a state in which butter cannot properly be called either hard or soft. We try again: If Ann began to be asleep at eight, before eight she was awake; if my shirt became dirty on Tuesday, before Tuesday it was clean; if Bonzo died last week, before last week he was alive. And when the advocate of the borderline state reminds us of the various twilight areas of consciousness or cleanliness, we are reduced to legislation: “asleep” shall henceforth apply to every mental state short of complete wakefulness, “alive” to every condition of the body before the onset of putrefaction, “clean” to every shirt incapable of producing a certain measurable discoloration in the water in which it is washed. “Let F and G be contradictories”, we still guardedly maintain: “then if a comes to be F at time t , before time t a was G ”. (shrink)