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 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)

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)

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)

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)

Central to Buber's philosophy of I-Thou is his understanding of the related notions of dialogue and revelation and his espousal of a non-propositional account of revelation framed in the language and structure of personal dialogical encounter. The consequent re-interpretation of revelation in this form has been widely influential in contemporary theological circles, especially among those theologians and philosophers of religion broadly known as existentialists. However, the wide dissemination and influence of this position does not guarantee its validity. This paper will (...) try to show that the dialogical account of revelation, at least in the form given it by Buber, is logically and philosophically deficient, being based on a set of misleading analogies between inter-human and Divine-human relations. (shrink)

Ethics and mysticism, we are regularly instructed, are if not antithetical, then certainly, at the very least, unrelated. This common wisdom is predicated on a specific understanding of morality and a flawed, though widespread, conception of mysticism and mystical traditions. It is yet another distorted and distorting manifestation of the still more universal misapprehension that mystics are essentially arch-individualists, ‘Lone Rangers’ of the spirit, whose sole intention is to escape the religious environments that spawned them in order to find personal (...) liberation or salvation. Accordingly, mystics are portrayed as rebels and heretics, antinomians and spiritual revolutionaries, if not also underminers of existing social and religious structures. But this characterization, despite its popularity, needs revision. In this essay it is not possible to argue all the detailed reasons why this construal is simply incorrect, but, as a shorthand summary of a much larger, more complex interpretative reconstruction, I would call attention to the fact that mystics share not only the metaphysical problematic, the metaphysical diagnosis of existence, as this is conceptualized within their particular traditions, but also view its overcoming or deconstruction in ways consistent with the teachings of their ‘faith’mmunities. They are, that is to say, fully situated in the ontological, theological, and social contexts of their traditions. Essentially, they share the Weltanschauung of their inherited circumstance and seek to realize, experience, the ‘solutions’ proposed by their tradition. (shrink)

Having considered the role of ethics in Indian mystical teachings in a previous, related, essay I would like to consider the same question in its western religious contexts in the present paper, beginning with the Christian mystical tradition. As is the case with Asian traditions charges of moral unconcern are widely directed at Christian mystics, but they are false. Christian mystics are not indifferent to morality nor do they disconnect morality from an intrinsic relationship to their mystical quest. Augustine would (...) already teach that the story of Leah and Rachel was an instructive allegory in which the active life represented by Leah was intrinsic to the contemplative life represented by Rachel while Gregory the Great would unambiguously assert: ‘We ascend to the heights of contemplation by the steps of the active life’, defining the active life as: ‘to dispense to all what they need and to provide those entrusted to us with the means of subsistence’. These representative early samples of the salience of ethical behaviour to the life of contemplation could be multiplied at great length, and almost without exception in the teaching of the major Christian mystics. This historical exegetical exercise, however, is in the present circumstances, both out of place and I hope unnecessary. Instead, the more general, more enigmatic, more repercussive, issues raised by the place and significance of morality within the Christian mystical tradition need attending to. (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)

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

"[Of] the 12 well-crafted essays in this volume...the most useful are those dealing with the Holocaust." —Choice "Especially recommended for college-level students of Jewish history and culture." —The Bookwatch This is a critical exploration of the most repercussive topics in modern Jewish history and thought. A sequel to Katz's National Jewish Book Award-winning study, Post-Holocaust Dialogues, this book identifies the main issues in the contemporary Jewish intellectual universe and outlines a larger, more synthetic understanding of contemporary Jewish existence.

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.

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)