Simple finite axiomatizations are given for versions of the modal logics K and K4 with non-contingency (or contingency) as the sole modal primitive. This answers two questions of I. L. Humberstone.

Montague, Prior, von Wright and others drew attention to resemblances between modal operators and quantifiers. In this paper we show that classical quantifiers can, in fact, be regarded as S5-like operators in a purely propositional modal logic. This logic is axiomatized and some interesting fragments of it are investigated.

Applications of game theory to moral philosophy are impededby foundational issues and troublesome examples. In the first part of this paper,questions are raised about the appropriate game-theoretical frameworks for applications to moralphilosophy and about the proper interpretations of the theoretical devices employed inthese frameworks. In the second part, five examples that should be of particular interest to thoseinterested in the connections between ethics and game theory are delineated and discussed. Thefirst example comprises games in which there is an outcome unanimously (...) preferred to the``solution'' of the game, appropriately defined. The second comprises games whose solution callsfor different players to employ different strategies. The third comprises games whosesolution calls for players to adopt mixed strategies. The fourth comprises games whose solutionrequires players to cycle among a variety of strategies. The fifth comprises games whose solutionrequires players to discriminate in morally inappropriate ways. (shrink)

The semantics of tense has received a great deal of attention in the contemporary linguistics, philosophy and logic literatures. This is probably due partly to a renewed appreciation for the fact that issues involving tense touch on certain issues of philosophical importance (viz., determinism, causality, and the nature of events, of time and of change). It may also be due partly to neglect. Tense was noticeably omitted from the theories of meaning advanced in previous generations. In the writings of both (...) Russell and Frege there is the suggestion that tense would be absent altogether from an ideal or scientifically adequate language. (Tense was not the only blemish of natural language to be removed, of course, but tense is a more serious omission than, say, pronouns because it is present in every sentence of the language.) Finally, in recent years there has been a greater recognition of the important role that all of the so-called “indexical” expressions must play in an explanation of mental states and human behavior. Tense is no exception. Knowing that our friend died is cause for mourning, knowing that he dies is just another confirmation of a familiar syllogism. (shrink)

The prisoner 's dilemma game has acquired large literatures in several disciplines. It is surprising, therefore, that a good definition of the game is hard to find. Typically an author relates a story about captured criminals or military rivals, provides a particular payoff matrix and asserts that the PD is characterized, or illustrated, by that matrix. In the few cases in which characterizing conditions are given, the conditions, and the motivations for them, do not always agree with each other or (...) with the paradigm examples elsewhere. In this paper we describe several varieties of PD's. In particular, we suggest there are two distinctions among PD's with philosophical significance, the pure/impure and the utilitarian/nonutilitarian distinctions. In the first section, we explain and characterize the two distinctions. In the second, we discuss an issue of moral philosophy that illustrates the significance of the former. (shrink)

A notable early result of David Makinson establishes that every monotone modal logic can be extended to LI, LV, or LF, and every antitone logic can be extended to LN, LV, or LF, where LI, LN, LV, and LF are logics axiomatized, respectively, by the schemas □α↔α, □α↔¬α, □α↔⊤, and □α↔⊥. We investigate logics that are both monotone and antitone (hereafter amphitone). There are exactly three: LV, LF, and the minimum amphitone logic AM axiomatized by the schema □α→□β. These logics, (...) along with LI, LN, and a wider class of “extensional” logics, bear close affinities to classical propositional logic. Characterizing those affinities reveals differences among several accounts of equivalence between logics. Some results about amphitone logics do not carry over when logics are construed as consequence or generalized (“multiple-conclusion”) consequence relations on languages that may lack some or all of the nonmodal connectives. We close by discussing these divergences and conditions under which our results do carry over. (shrink)

The system obtained by adding full propositional quantification to S5 is known to be decidable, while that obtained by doing so for T is known to be recursively intertranslatable with full second-order logic. Recently it was shown that the system with two S5 operators and full propositional quantification is also recursively intertranslatable with second-order logic. This note establishes that the map assigning [1][2]p to \squarep provides a validity and satisfaction preserving translation between the T system and the double S5 system, (...) thus providing an easier proof of the recent result. (shrink)

Peter Abelard (1079–1142 ce) was the most wide‐ranging philosopher of the twelfth century. He quickly established himself as a leading teacher of logic in and near Paris shortly after 1100. After his affair with Heloise, and his subsequent castration, Abelard became a monk, but he returned to teaching in the Paris schools until 1140, when his work was condemned by a Church Council at Sens. His logical writings were based around discussion of the “Old Logic”: Porphyry's Isagoge, aristotle'S Categories and (...) On Interpretation and boethius'S textbook on topical inference. They comprise a freestanding Dialectica (“Logic”; probably c.1116), a set of commentaries (known as the Logica [Ingredientibus], c. 1119) and a later (c. 1125) commentary on the Isagoge (Logica Nostrorum Petititoni Sociorum or Glossulae). In a work Abelard called his Theologia, issued in three main versions (between 1120 and c.1134), he attempted a logical analysis of trinitarian relations and explored the philosophical problems surrounding God's claims to omnipotence and omniscience. The Collationes (“Debates,” also known as “Dialogue between a Christian, a Philosopher and a Jew”; probably c.1130) present a rational investigation into the nature of the highest good, in which the Christian and the Philosopher (who seems to be modeled on a philosopher of pagan antiquity) are remarkably in agreement. The unfinished Scito teipsum (“Know thyself,” also known as the “Ethics”; c.1138) analyses moral action. (shrink)

In this tribute to Steven T. Katz on the occasion of his seventieth birthday, Michael Zank and Ingrid Anderson present sixteen original essays written by senior and junior scholars in comparative religion, philosophy of religion, modern Judaism, and theology after the Holocaust, fields of inquiry where Steven Katz made major contributions over the course of his distinguished scholarly career. The authors of this volume, specialists in Jewish history, especially the modern experience, and Jewish thought from the Bible to (...) Buber, offer theoretical and practical observations on the value of the particular. Contributions range from Tim Knepper's reevaluation of the ineffability discourse to the particulars of the Settlement Cookbook, examined by Nora Rubel as an American classic. (shrink)

Each of our theories of mental representation provides some insight into how the mind works. However, these insights often seem incompatible, as the debates between symbolic, dynamical, emergentist, sub-symbolic, and grounded approaches to cognition attest. Mental representations—whatever they are—must share many features with each of our theories of representation, and yet there are few hypotheses about how a synthesis could be possible. Here, I develop a theory of the underpinnings of symbolic cognition that shows how sub-symbolic dynamics may give rise (...) to higher-level cognitive representations of structures, systems of knowledge, and algorithmic processes. This theory implements a version of conceptual role semantics by positing an internal universal representation language in which learners may create mental models to capture dynamics they observe in the world. The theory formalizes one account of how truly novel conceptual content may arise, allowing us to explain how even elementary logical and computational operations may be learned from a more primitive basis. I provide an implementation that learns to represent a variety of structures, including logic, number, kinship trees, regular languages, context-free languages, domains of theories like magnetism, dominance hierarchies, list structures, quantification, and computational primitives like repetition, reversal, and recursion. This account is based on simple discrete dynamical processes that could be implemented in a variety of different physical or biological systems. In particular, I describe how the required dynamics can be directly implemented in a connectionist framework. The resulting theory provides an “assembly language” for cognition, where high-level theories of symbolic computation can be implemented in simple dynamics that themselves could be encoded in biologically plausible systems. (shrink)

History is not the record of humanity’s progress through otherwise empty time. It is rather to be conceived messianically, i.e., in terms of God’s eschatological promises and the interruptive capacity of dangerous memories of human suffering. This insight is contained in both the historical philosophy of Walter Benjamin and the political theology of Johann Baptist Metz. Metz’s theological categories also contribute an understanding of messianic history that avoids the dualism of Benjamin’s description of history in both messianic and materialist terms.

Esse artigo foi originalmente publicado como capítulo do livro Mysticism and Philosophical Analysis, organizado por Steven T. Katz e publicado pela Oxford University Press em 1978. O texto trata de questões epistemológicas da mística e problematiza uma série de concepções dessa temática, tendo por principal objetivo marcar uma maneira de abordar os dados fornecidos pelos místicos, concentrando-se especialmente na tentativa de defender a concepção de que assim como as ideias são mediadas por contextos culturais, sociais e religiosos, as experiências (...) místicas são vivenciadas, ou como prefere dizer o autor, interpretadas, de formas diferenciadas de acordo com esses mesmos contextos. (shrink)

We consider measurements, described by a positive-operator-valued measure (POVM), whose outcome probabilities determine an arbitrary pure state of a D-dimensional quantum system. We call such a measurement a pure-state informationally complete (PS I-complete) POVM. We show that a measurement with 2D−1 outcomes cannot be PS I-complete, and then we construct a POVM with 2D outcomes that suffices, thus showing that a minimal PS I-complete POVM has 2D outcomes. We also consider PS I-complete POVMs that have only rank-one POVM elements and (...) construct an example with 3D−2 outcomes, which is a generalization of the tetrahedral measurement for a qubit. The question of the minimal number of elements in a rank-one PS I-complete POVM is left open. (shrink)

This collection of essays was created as a tribute to Dr. Irving Greenberg, a truly major figure in the American Jewish community for the past forty years. The authors who have contributed to this volume are a testimony to Dr. Greenberg's repercussive presence and theological contribution.

Husik, I. An anonymous medieval Christian critic of Maimonides.--Neuburger, C. Das Wesen des Gesetzes in der Philosophie des Maimonides.--Neubauer, J. Zum ursprünglichen Titel von Maimunis Buch der Gebote und seiner Geschichte.--Teicher, J. Studi su Maimonide.--Wolfson, H. Maimonides and Halevi.--Diesendruck, Z. Die Telelogie bei Maimonides.--Heinemann, I. Maimuni und die arabischen Einheitslehrer.--Strauss, L. Quelques remarques sur la science politique de Maimonide et de Fârâbî.--Teicher, J. Observations critiques sur l'interprétation traditionelle de la doctrine des attributs négatifs chez Maimonide.--Altmann, A. Das Verhältnis Maimunis zur (...) jüdischen Mystik.--Shmiedl, A. Die Auferstehungslehre in der jüdischen Religionsphilosophie des Mittelalters.--Rawidowicz, S. Knowledge of God.--Strauss, L. Der Ort der Vorsehungslehre nach der Ansight Maimunis.--Strauss, L. Maimunis Lehre von der Prophetie und ihre Quellen. (shrink)

A collection of articles, some of which appeared previously. Partial contents:.

Rau, D. Die Ethik R. Saadjas.--Neumark, D. Saadya's philosophy.-- Vajda, G. Saadia Gaon et l'amour courtois.--Diesendruck, Z. Saadya's formulation of the time-argument for creation.--Altmann, A. Saadya's conception of the law.-- Vajda, G. Saʻadyā commentateur du "Livre of la création."-- Vajda, G. Études sur Saadia.--Harkavy, A. Fragments of anti-Karaite writings of Saadiah in the Imperial Public Library at St. Petersburg.--Eisler, M. Vorlesungen über die jüdischen Philosophen des Mittelalters.

Absolute linguistic universals are often justified by cross-linguistic analysis: If all observed languages exhibit a property, the property is taken to be a likely universal, perhaps specified in the cognitive or linguistic systems of language learners and users. In many cases, these patterns are then taken to motivate linguistic theory. Here, we show that cross-linguistic analysis will very rarely be able to statistically justify absolute, inviolable patterns in language. We formalize two statistical methods—frequentist and Bayesian—and show that in both it (...) is possible to find strict linguistic universals, but that the numbers of independent languages necessary to do so is generally unachievable. This suggests that methods other than typological statistics are necessary to establish absolute properties of human language, and thus that many of the purported universals in linguistics have not received sufficient empirical justification. (shrink)

This research is an extension of Walker Information’s (Business Ethics: Ethical Decision Making and Cases, pp. 235–255, 1999) study on employees’ job attitudes that was conducted exclusively in the United States. Walker Information found that the reputation of the organization, fairness at work, care, and concern for employees, trust in employees, and resources available at work were important factors in an employee’s decision to remain with his or her company. Our sample includes 713 students from seven countries: Canada, Colombia, Ecuador, (...) Hong Kong, Ireland, South Africa, and the United States. When analyzing the entire sample, our data indicate that both social desirability response bias and gender were significant; however, this was not the case when the data are analyzed by country. On an individual country basis, our data suggest that the generally accepted premise that women are more ethically conscious than men was only true for the samples from the United States and Canada. The data also indicate that, while social desirability response bias was significant for the four factors suggesting ethical components for the sample from the United States, this finding was not universal. (shrink)

The capacity to generate recursive sequences is a marker of rich, algorithmic cognition, and perhaps unique to humans. Yet, the precise processes driving recursive sequence generation remain mysterious. We investigated three potential cognitive mechanisms underlying recursive pattern processing: hierarchical reasoning, ordinal reasoning, and associative chaining. We developed a Bayesian mixture model to quantify the extent to which these three cognitive mechanisms contribute to adult humans’ performance in a sequence generation task. We further tested whether recursive rule discovery depends upon relational (...) information, either perceptual or semantic. We found that the presence of relational information facilitates hierarchical reasoning and drives the generation of recursive sequences across novel depths of center embedding. In the absence of relational information, the use of ordinal reasoning predominates. Our results suggest that hierarchical reasoning is an important cognitive mechanism underlying recursive pattern processing and can be deployed across embedding depths and relational domains. (shrink)