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)

The volume is a collection of papers on certain aspects of Indian history, historiography and culture. The papers are fundamental, insightful and path-breaking to some extent. Combining literary, archaeological, scientific and other perspectives, they cover a range of subjects stretching from ancient to modern India. The volume deals with the Greek historians, the Indian epic and Puranic tradition of historiography, colonial and cultural expansion of the Aryans, the early history of north-west India, society, trade and commerce in ancient India, economic, (...) political and cultural contacts of India with other parts of Asia in ancient and medieval periods, and the 1857 War of Independence in India. It takes up some very interesting and new subjects like role of Brahmanas in the anti-Alexander movement in north-west India and the concept of national integration in ancient India. It explores the sources of history of Uttar Pradesh and the antiquity of Ayodhya and historicity of Rama in an interesting study. The volume will be of immense use to historians and scholars of philosophy. (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)

In this first volume of original essays on rhetorical criticism to appear in many years, the authors stress active engagement in the critical process. Bearing in mind the complaint frequently leveled at rhetorical criticism—that method as method has taken precedence over understanding and appreciation—the editors encouraged innovation, and the contributors responded by moving beyond the merely theoretical to explore implications through implied criticism, participating in the activity rather than merely talking about it. Consequently, these essays avoid further lamentation over the (...) current state of the art and concentrate instead on constructive presentations. Not only do the essays add significantly to knowledge about rhetorical criticism, but they also serve liberal education by helping to bring understanding, discrimination, and appreciation to the entire process of human communication. (shrink)

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.

Plotinus (204/5–270 CE) was the first and greatest of Neoplatonic philosophers. His writings were edited by his disciple Porphyry, who published them sometime between 301 and 305 CE in six sets of nine treatises each (Enneads), with a biography of his master in which he also explains his editorial principles.

Discussions of forgiveness within Christian theology have tended to focus on the conditions in which forgiveness may be a moral or divine imperative for believers. With regard to Søren Kierkegaard’s theological ethics, this article explicates a radical perspective. For the Kierkegaardian Christian lover, no definitive relational break with the other (however objectionable) can occur. As Kierkegaard emphasizes in Works of Love, in a discourse which bears this sentiment as its title, “love abides.” Indeed, I illustrate how in three consecutive discourses (...) in Works of Love—“VI: Love Abideth,” “VII: Mercy, a Work of Love,” and “VIII: The Victory of the Reconciliation in Love”—Kierkegaard’s ethical vision is grounded in Christian love’s immutability. For Kierkegaard, if Christian love is present, then forgiveness is redundant, and unforgiveness is impossible. (shrink)