It is argued that the preservation of truth by an inference relation is of little interest when premiss sets are contradictory. The notion of a level of coherence is introduced and the utility of modal logics in the semantic representation of sets of higher coherence levels is noted. It is shown that this representative role cannot be transferred to first order logic via frame theory since the modal formulae expressing coherence level restrictions are not first order definable. Finally, an inference (...) relation, calledyielding, is introduced which is intermediate between the coherence preservingforcing relation introduced elsewhere by the authors and the coherence destroying, inference relation of classical logic. (shrink)

This book is less about disjunction than about the English word ‘or’, and it is less for than against formal logicians—more exactly, against those who maintain that formal logic can be applied in certain ways to the evaluation of reasoning formulated in ordinary English. Nevertheless, there are many things to interest such of those persons who are willing to overlook the frequent animadversions directed against their kind in the book, and this review will concentrate on them.

I am idebted to members of the Wellington Logic Seminar for useful discussions of work of which this essay forms part, in particular to M. J. Cresswell for comments in the earlier stages of the investigation and to R. I. Goldblatt who suggested the definition ofB infD supu and made numerous other suggestions.

In this paper we investigate nonnormal modal systems in the vicinity of the Lewis system S1. It might be claimed that Lewis's modal systems are the starting point of modern modal logics. However, our interests in the Lewis systems and their relatives are not historical. They possess certain syntactical features and their frames certain structural properties that are of interest to us. Our starting point is not S1, but a weaker logic S1$^0$. We extend it to S1$^0$D, which can be (...) considered as a deontic counterpart of the alethic S1. Soundness and completeness of these systems are then demonstrated within a prenormal idiom. We conclude with some philosophical remarks on the interpretation of our deontic logic. (shrink)

In [3] I argued for a particular kind of semantics for subjunctive conditionals. The arguments were based upon some linguistic considerations of the general character of what we mean when we say such and such. I urged that a semantics for subjunctive conditionals ought to provide a distinct representation of the subjunctive mood of a sentence, and should take seriously the fact that subjunctive conditionals admit distinctions of tense. The envisaged semantics took the subjunctive conditional to be about occasions, and (...) the central problem discussed was, accordingly, how to represent what must count as the same occasion in spite of whatever changes were required to make the antecedent of the conditional true. (shrink)

This paper is an experiment in Leibnizian analysis. The reader will recall that Leibniz considered all true sentences to be analytically so. The difference, on his account, between necessary and contingent truths is that sentences reporting the former are finitely analytic; those reporting the latter require infinite analysis of which God alone is capable. On such a view at least two competing conceptions of entailment emerge. According to one, a sentence entails another when the set of atomic requirements for the (...) first is included in the corresponding set for the other; according to the other conception, every atomic requirement of the entailed sentence is underwritten by an atomic constituent of the entailing one. The former conception is classical on the twentieth century understanding of the term; the latter is the one we explore here. Now if we restrict ourselves to the formal language of the propositional calculus, every sentence has a finite analysis into its conjunctive normal form. Semantically, then, every sentence of that language can be represented as a simple hypergraph, H, on the powerset of a universe of states. Entailment of the sort we wish to study can be represented as a known relation, subsumption between hypergraphs. Since the lattice of hypergraphs thus ordered is a DeMorgan lattice, the logic of entailment thus understood is the familiar system, FDE of first-degree entailment. We observe that, extensionalized, the relation of subsumption is itself a DeMorgan Lattice ordered by higher-order subsumption. Thus the semantic idiom that hypergraph-theory affords reveals a hierarchy of lattices capable of representing entailments of every finite degree. (shrink)

I argue that the conjunctive distribution of permissibility over or, which is a puzzling feature of free-choice permission is just one instance of a more general class of conjunctive occurrences of the word, and that these conjunctive uses are more directly explicable by the consideration that or is a descendant of oper than by reference to the disjunctive occurrences which logicalist prejudices may tempt us to regard as semantically more fundamental. I offer an account of how the disjunctive uses of (...) or may have come about through an intermediate discourse-adverbial use of or, drawing a parallel with but, which, etymologically, is disjunctive rather than conjunctive and whose conjunctive uses seem to represent just such a discourse-adverbial application. (shrink)

An epistemic logic is built up on the basis of an analysis of two skeptical arguments. the method used is to first construct an inference relation appropriate to epistemic contexts and introduce "a knows that..." as an operator giving rise to sentences closed with respect to this new concept of inference. soundness and completeness proofs are provided using auxiliary three-valued valuations.

In this paper we investigate nonnormal modal systems in the vicinity of the Lewis system S1. It might be claimed that Lewis's modal systems (S1, S2, S3, S4, and S5) are the starting point of modern modal logics. However, our interests in the Lewis systems and their relatives are not (merely) historical. They possess certain syntactical features and their frames certain structural properties that are of interest to us. Our starting point is not S1, but a weaker logic S1 (S1 (...) without the schema [T]). We extend it to S1D, which can be considered as a deontic counterpart of the alethic S1. Soundness and completeness of these systems are then demonstrated within a prenormal idiom. We conclude with some philosophical remarks on the interpretation of our deontic logic. (shrink)

In human languages, a palindrome reads the same forward as backward (e.g., ‘madam’). In regulatory DNA, a palindrome is an inverted sequence repeat that allows a transcription factor to bind as a homodimer or as a heterodimer with another type of transcription factor. Regulatory palindromes are typically imperfect, that is, the repeated sequences differ in at least one base pair, but the functional significance of this asymmetry remains poorly understood. Here, we review the use of imperfect palindromes in Drosophila photoreceptor (...) differentiation and mammalian steroid receptor signaling. Moreover, we discuss mechanistic explanations for the predominance of imperfect palindromes over perfect palindromes in these two gene regulatory contexts. Lastly, we propose to elucidate whether specific imperfectly palindromic variants have specific regulatory functions in steroid receptor signaling and whether such variants can help predict transcriptional outcomes as well as the response of individual patients to drug treatments. (shrink)

GENERALIZED RECUBION THEORY II © North-Holland Publishing Company (1978) MONOTONE QUANTIFIERS AND ADMISSIBLE SETS Ion Barwise University of Wisconsin ...

Do the rich descriptions and narrative shapings of literature provide a valuable resource for readers, writers, philosophers, and everyday people to imagine and confront the ultimate questions of life? Do the human activities of storytelling and complex moral decision-making have a deep connection? What are the moral responsibilities of the artist, critic, and reader? What can religious perspectives—from Catholic to Protestant to Mormon—contribute to literary criticism? Thirty well known contributors reflect on these questions, including iterary theorists Marshall Gregory, James Phelan, (...) and Wayne Booth; philosophers Martha Nussbaum, Richard Hart, and Nina Rosenstand; and authors John Updike, Charles Johnson, Flannery O'Connor, and Bernard Malamud. Divided into four sections, with introductory matter and questions for discussion, this accessible anthology represents the most crucial work today exploring the interdisciplinary connections between literature, religion and philosophy. (shrink)

Volume 1: A-B -- Volume 2: C-E -- Volume 3: F-I -- Volume 4: J-O -- Volume 5: P-R -- Volume 6: S-X.

J. Krishnamurti (1895-1986) was thought by many to be a modern-day equivalent of the Buddha. In fact, he was once even considered to be the second coming of Christ. While many think it wonderful to live and work in close proximity with such a person, it's difficult to understand the depth of what this means and how challenging this might be. In Knocking at the Open Door, author R.E. Mark Lee provides an ordinary person view of what being close-up and (...) working together with such a man means, how it challenges one at every turn, and how it causes one to question ceaselessly, even more deeply than one ordinarily would. Lee offers an insightful, candid, and heartfelt narrative that reveals various unknown facets of the eminent world teacher J. Krishnamurti and highlights his distinctive vision for education worldwide. This comprehensive volume brings alive the practical and everyday interactions Lee had with Krishnamurti during a twenty-year period in India and the United Sates. Knocking at the Open Door shares a clear and honest account that demonstrates the challenges of working with Krishnamurti in running a school that is true to the teaching and yet able to function in the reality of modern parental, student, and educational establishment expectations. (shrink)

One point fairly frequently argued by moral philosophers is the capacity of the various forms of Utilitarianism to handle the concept of a right. I want to show that any plausible moral theory must employ a concept of a right that does not allow of Utilitarian analysis. One requirement of any plausible moral code is that it allow us to live together peacefully; in that sense, at least, morality has its home in communities. Somebody might form their own purely personal (...) 'ethical' code according to which she would devote her life to private pleasure or the production of great art or whatever, but that sort of ethical code is of no concern to me here: what concerns me is the sort of ethical code put up as a candidate for regulating the life of a community. One necessary condition of our living together peacefully in communities is that we recognise the concept of a right (whether or not we have one word for that concept) which does not allow of Utilitarian treatment. We need that concept of a right, or something that is definitive in disputes, because of our need for a conventional decision-procedure. (shrink)