This book translates into English ten influential articles and extracts from books about Homer written in German over the past fifty years. The work of prestigious scholars such as Wolfgang Schadenwaldt, Karl Reinhardt, and Hermann Fraenkel are represented. These key works, which cover such topics as similes, the end of the Odyssey, the adventures of Odysseus, the meeting of Hector and Andromache, ring-composition, the Telemachy, and Homeric social life will now become easily accessible for the first time to teachers (...) and scholars in the English-speaking world. An accompanying introduction develops the arguments in the light of contemporary scholarly concerns. (shrink)

When is an ideal of a ring radical or prime? By examining its generators, one may in many cases definably and uniformly test the ideal’s properties. We seek to establish such definable formulas in rings of p-adic power series, such as $\mathbb Q_{p}\langle X\rangle $, $\mathbb Z_{p}\langle X\rangle $, and related rings of power series over more general valuation rings and their fraction fields. We obtain a definable, uniform test for radicality, and, in the one-dimensional case, for primality. This (...) builds upon the techniques stemming from the proof of the quantifier elimination results for the analytic theory of the p-adic integers by Denef and van den Dries, and the linear algebra methods of Hermann and Seidenberg.prepared by Madeline G. Barnicle.E-mail: [email protected]: https://escholarship.org/uc/item/6t02q9s4. (shrink)

Reflecting Alan Robinson's fundamental contribution to computational logic, this book brings together seminal papers in inference, equality theories, and logic programming. It is an exceptional collection that ranges from surveys of major areas to new results in more specialized topics. Alan Robinson is currently the University Professor at Syracuse University. Jean-Louis Lassez is a Research Scientist at the IBM Thomas J. Watson Research Center. Gordon Plotkin is Professor of Computer Science at the University of Edinburgh. Contents: Inference. Subsumption, A Sometimes (...) Undervalued Procedure, Larry Wos, Ross Overbeek, and Ewing Lusk. The Markgraf Karl Refutation Procedure, Hans Jurgen Ohlbach and Jorg H. Siekmann. Modal Logic Should Say More than it Does, Melvin Fitting. Interactive Proof Presentation, W. W. Bledsoe. Intelligent Backtracking Revisited, Maurice Bruynooghe. A Science of Reasoning, Alan Bundy. Inductive Inference of Theories from Facts, Ehud Y. Shapiro. Equality. Solving Equations in Abstract Algebras: A Rule-based Survey of Unification, Jean-Pierre Jouannaud and Claude Kirchner. Disunification: A Survey, Hubert Comon. A Case Study of the Completion Procedure: Proving Ring Commutativity Problems, Deepak Kapur and Hantao Zhang. Computations in Regular Rewriting Systems I and II, Girard Huet and JeanJacques Levy. Unification and ML Type Reconstruction, Paris Kanellakis, Harry Mairson, and John Mitchell. Automatic Dimensional Analysis, Mitchell Wand. Logic Programming. Logic Programming Schemes and Their Implementations, Keith Clark. A Near-Horn Prolog for Compilation, Donald Loveland and David Reed. Unfold/Fold Transformations of Logic Programs, P. A. Gardner and J. C. Shepherdson. An Algebraic Representation of Logic Program Computations, Andrea Corradini and Ugo Montanari. Theory of Disjunctive Logic Programs, Jack Minker, Arcot Rajasekar, and Jorge Lobo. Bottom-Up Evaluation of Logic Programs, Jeffrey Naughton and Raghu Ramakrishnan. Absys, the First Logic Programming Language: A View of the Inevitability of Logic Programming, E. W. Elcock. (shrink)

ABSTRACT: René Descartes' Cogito is an example of a paradigmatic thought experiment, herald of both subjectivism and new science in Europe's Modern Age, that seems to have escaped the attention of thought experiment philosophers. On deep analysis, the Cogito appears as universal instantiation. The Cogito has strong rhetorical effects for it narratively generalizes from I to all human kind, and its historical and philosophical success can be explained from its concise enthymematic structure that rings true in many possible senses. We (...) consider it a preeminent example of a thought experiment as it states the power of thinking as its very contents. From Descartes' methodology of doubt we can conclude that, e.g., on a Wittgensteinian interpretation, the Cogito is a logical thought experiment rather than a psychological one. RESUMO: O Cogito de René Descartes é um exemplo de experimento mental paradigmático, precursor tanto do subjetivismo quanto da nova ciência, na Idade Moderna europeia, o qual parece ter escapado à atenção dos filósofos que estudaram o experimento mental. Na análise profunda, o Cogito aparece como uma instanciação universal. O Cogito tem fortes efeitos retóricos por si mesmo, generalizando narrativamente desde o eu para toda a espécie humana, e seu sucesso histórico e filosófico pode ser explicado por sua estrutura entimemática concisa, que soa através de muitos sentidos possíveis. Consideramos que é um exemplo proeminente de um experimento mental, na medida em que afirma o poder de pensar como seus próprios conteúdos. A partir da metodologia da dúvida de Descartes, podemos concluir que, em uma interpretação wittgensteiniana, o Cogito é um experimento mental mais lógico que psicológico. (shrink)

We say that a ring admits elimination of quantifiers, if in the language of rings, {0, 1, +, ·}, the complete theory of R admits elimination of quantifiers. Theorem 1. Let D be a division ring. Then D admits elimination of quantifiers if and only if D is an algebraically closed or finite field. A ring is prime if it satisfies the sentence: ∀ x ∀ y ∃ z (x = 0 ∨ y = 0 ∨ xzy (...) ≠ 0). Theorem 2. If R is a prime ring with an infinite center and R admits elimination of quantifiers, then R is an algebraically closed field. Let A be the class of finite fields. Let B be the class of 2 × 2 matrix rings over a field with a prime number of elements. Let C be the class of rings of the form $GF(p^n) \bigoplus GF(p^k)$ such that either n = k or g.c.d. (n, k) = 1. Let D be the set of ordered pairs (f, Q) where Q is a finite set of primes and f: Q → A ∪ B ∪ C such that the characteristic of the ring f(q) is q. Finally, let E be the class of rings of the form $\bigoplus_{q \in Q}f(q)$ for some (f, Q) in D. Theorem 3. Let R be a finite ring without nonzero trivial ideals. Then R admits elimination of quantifiers if and only if R belongs to E. Theorem 4. Let R be a ring with the descending chain condition of left ideals and without nonzero trivial ideals. Then R admits elimination of quantifiers if and only if R is an algebraically closed field or R belongs to E. In contrast to Theorems 2 and 4, we have Theorem 5. If R is an atomless p-ring, then R is finite, commutative, has no nonzero trivial ideals and admits elimination of quantifiers, but is not prime and does not have the descending chain condition. We also generalize Theorems 1, 2 and 4 to alternative rings. (shrink)

Among the most outstanding discoveries of the last century is one that is not quite as momentous as the theory of relativity or cybernetics. It may even still be enigmatic. It has no one single author, it is not expressed in a single formula, conception, or invention. Nonetheless it is worth all the others combined.

This chapter contains sections titled: The Tractatus and rules of logical syntax From logical syntax to philosophical grammar Rules and rule‐formulations Philosophy and grammar The scope of grammar Some morals.

Despite traditionally being characterised as a melancholy thinker with a propensity to dwell on existential anxiety, sin and despair, scholarly interest in the place of love in Søren Kierkegaard’s ethical thought is currently gaining significant traction. In particular, Kierkegaard’s Works of Love (1847) has increasingly come under the academic spotlight as a text with potentially rich and previously underappreciated insights for Christian ethics. This article aims to contribute to this ongoing illumination, by highlighting the moral psychology and theological anthropology of (...) Kierkegaard’s Christian lover in discourses II–V of Works of Love’s second series. In doing this, I aim to put forward an overarching ethical framework which can be seen to structure these moral deliberations. (shrink)

The writings of English poet and mystic Thomas Traherne (1626–1674) remain a relatively underexplored reservoir. Traherne's technological context includes the invention of the telescope (1608) as well as the microscope (c. 1590). As will become evident in this article, Traherne's expositions on creation display an imagination that is adept at placing itself behind both types of lenses. This article focuses on Traherne's treatment of two types of insects—the fly and the ant—in order to extrapolate some of the insights that can (...) be gleaned from Traherne's writings for the ontological status of all nonhuman animals. (shrink)

At the end of the prayer with which he begins Works of Love (1847), Søren Kierkegaard notes that while ‘works of love’ might normally be viewed as a subset of worthwhile human endeavours or ‘works’, from heaven's perspective no work can be pleasing unless it is a work of love. From this arises the question—which Kierkegaard himself moves swiftly to address—of what distinguishes a work of ‘love’ from other, non-loving works? In this article, and with particular reference to Jacob Boehme (...) (1575–1624), I highlight how Kierkegaard's answer to this question draws upon the theological tradition that Bernard McGinn has called ‘the mysticism of the ground’. (shrink)

G. P. Meredith; XIII—Words as Instruments, Proceedings of the Aristotelian Society, Volume 62, Issue 1, 1 June 1962, Pages 241–260, https://doi.org/10.1093/aris.