The modal completeness proofs of Guaspari and Solovay (1979) for their systems R and R – are improved and the relationship between R and R – is clarified.

To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by Bernardi-Montagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical (Solovay-type) completeness theorem with respect to PA is obtained for LR.

To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by Bernardi-Montagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical completeness theorem with respect to PA is obtained for LR.

In this paper, we study IL(), the interpretability logic of . As is neither an essentially reflexive theory nor finitely axiomatizable, the two known arithmetical completeness results do not apply to : IL() is not or . IL() does, of course, contain all the principles known to be part of IL, the interpretability logic of the principles common to all reasonable arithmetical theories. In this paper, we take two arithmetical properties of and see what their consequences in the modal logic (...) IL() are. These properties are reflected in the so-called Beklemishev Principle , and Zambella’s Principle , neither of which is a part of IL. Both principles and their interrelation are submitted to a modal study. In particular, we prove a frame condition for . Moreover, we prove that follows from a restricted form of . Finally, we give an overview of the known relationships of IL() to important other interpretability principles. (shrink)

Semantic Automata Johan van Ben them. INTRODUCTION An attractive, but never very central idea in modern semantics has been to regard linguistic expressions ...

BackgroundIn the Canadian Alliance for Healthy Hearts and Minds (CAHHM) cohort, participants underwent magnetic resonance imaging (MRI) of the brain, heart, and abdomen, that generated incidental findings (IFs). The approach to managing these unexpected results remain a complex issue. Our objectives were to describe the CAHHM policy for the management of IFs, to understand the impact of disclosing IFs to healthy research participants, and to reflect on the ethical obligations of researchers in future MRI studies.MethodsBetween 2013 and 2019, 8252 participants (...) (mean age 58 ± 9 years, 54% women) were recruited with a follow-up questionnaire administered to 909 participants (40% response rate) at 1-year. The CAHHM policy followed a restricted approach, whereby routine feedback on IFs was not provided. Only IFs of severe structural abnormalities were reported.ResultsSevere structural abnormalities occurred in 8.3% (95% confidence interval 7.7–8.9%) of participants, with the highest proportions found in the brain (4.2%) and abdomen (3.1%). The majority of participants (97%) informed of an IF reported no change in quality of life, with 3% of participants reporting that the knowledge of an IF negatively impacted their quality of life. Furthermore, 50% reported increased stress in learning about an IF, and in 95%, the discovery of an IF did not adversely impact his/her life insurance policy. Most participants (90%) would enrol in the study again and perceived the MRI scan to be beneficial, regardless of whether they were informed of IFs. While the implications of a restricted approach to IF management was perceived to be mostly positive, a degree of diagnostic misconception was present amongst participants, indicating the importance of a more thorough consent process to support participant autonomy.ConclusionThe management of IFs from research MRI scans remain a challenging issue, as participants may experience stress and a reduced quality of life when IFs are disclosed. The restricted approach to IF management in CAHHM demonstrated a fair fulfillment of the overarching ethical principles of respect for autonomy, concern for wellbeing, and justice. The approach outlined in the CAHHM policy may serve as a framework for future research studies.Clinical trial registrationhttps://clinicaltrials.gov/ct2/show/nct02220582. (shrink)

We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

There appear to be a number of general things which can be said about forgiveness. If these are left sufficiently vague they seem to be applicable to all the situations in which the term is used.First, there can be no question of forgiveness unless an injury has been inflicted on somebody by a moral agent. There must be something to forgive; and the injury that is to be forgiven must be one for which a moral agent can be held responsible. (...) One cannot forgive a rock for falling on one's foot or a cougar for attacking one's child—even though a child might kick the rock and a father might shoot the cougar. (shrink)

The right to privacy is one of the rights most widely demanded today. Privacy has not always so been demanded. The reasons for the present concern for privacy are complex and obscure. They obviously relate both to the possibilities for very considerable enjoyment of privacy by the bulk of people living in affluent societies brought about by twentieth-century affluence, and to the development of very efficient methods of thoroughly and systematically invading this newly found privacy. However, interesting and important as (...) it is as a socio-philosophical inquiry, the concern of this paper is not with why privacy has come to be so highly prized, but rather with whether it is rightly prized, and if so, when and why. This means that my concern will be with what privacy is, what is its domain, whether there is a right to privacy, and, if so, whether it is an ultimate, basic, albeit, a prima facie right, or simply a conditional right. (shrink)

Many contemporary philosophers writing on punishment seek to show that much of the dispute between retributionists and utilitarians springs from a failure on the part of both parties to elucidate the concept of punishment. The writers are usually utilitarians who seek to show that what is true in the retributive theory is simply a point about the concept of punishment, and that for the rest, the morality of punishment is to be explained in terms of the utilitarian theory. Those who (...) attempt to destroy the retributive theory by reducing its element of truth to a mere conceptual point about the concept of punishment, seek to argue that the notion of being guilty of an offence is part of the concept of punishment. Against this kind of approach, I wish to consider whether a general theory of punishment is possible, and if so, what are its basic concepts—punishment, deserving of punishment, deserved, or justifiable punishment—and how they are to be elucidated. I shall be concerned to argue that much contemporary writing on punishment commits the Platonic fallacy of assuming that there is a single, core, paradigm use of ‘punishment’ which is to be found by elucidating the concept of legal punishment. (shrink)

Standard unary modal logic and binary modal logic, i.e. modal logic with one binary operator, are shown to be definitional extensions of one another when an additional axiom |$U$| is added to the basic axiomatization of the binary side. This is a strengthening of our previous results. It follows that all unary modal logics extending Classical Modal Logic, in other words all unary modal logics with a neighborhood semantics, can equivalently be seen as binary modal logics. This in particular applies (...) to standard modal logics, which can be given simple natural axiomatizations in binary form. We illustrate this in the logic K. We call such logics binary expansions of the unary modal logics. There are many more such binary expansions than the ones given by the axiom |$U$|⁠. We initiate an investigation of the properties of these expansions and in particular of the maximal binary expansions of a logic. Our results directly imply that all sub- and superintuitionistic logics with a standard modal companion also have binary modal companions. The latter also applies to the weak subintuitionistic logic WF of our previous papers. This logic doesn’t seem to have a unary modal companion. (shrink)

That mox means, or can mean, ‘soon,’ is an assertion which is made often and positively, in works of all sorts, from the ordinary dictionaries, such as Facciolati-Forcellini and Lewis and Short, and valuable writings on lexicography such as Merguet's lexicon to Cicero and Krebs-Schmalz' Antibarbarus, down to the latest little school book at which I have looked. As I had never been able to find a passage in which it clearly and unambiguously had that meaning, in any classical author, (...) I have thought it worth while to examine all the instances in a few good writers, with a view to finding out how they really do use it. (shrink)

The Gods and Typhon.—The story of how the gods took bestial shape to hide from the fury of Typhon is several times told in Hellenistic and Latin authors. There seems no room for doubt that it is an aetiological myth, intended to explain the cult of beasts in Egypt, and also, in one or two versions, the sacredness of fish in Syria. That in one form, that given by Antoninus Liberalis, it goes back to Nikandros is reasonably certain. The doubtful (...) point, to my mind, is whether it can be traced much further, and, in particular, whether it was known to Pindar, as is commonly assumed. The authority for supposing that he knew and referred to it is a single passage of Porphyry, de abstinentia III. 16 . It runs: Πίνδαρος δ ν προσοδίοις παντας τος θεος ποίησεν τε ύπ Τυνος διώκοντα οủκ νθρώποις όμοιωθέντας λλ τοις λοις ζοις έρασθέντα δ Πασιάης Δία γενέσθαι μν ταρον νν δ ετν και κύκνον. (shrink)

Not a little speculation has been expended on the Genius in ancient and modern times. I propose very briefly to recapitulate the known facts about him, examine the chief explanations, and give what I consider the true one.

The sumptuous edition of Herodas by Headlam-Knox, while it throws welcome light on many dark places, is perhaps hardly adequate in a few points where ancient religious ideas are involved. I venture, therefore, to offer the following suggestions: I. II and 66, μà τàς Моίρας. IV.30, πρòς Моιρέων. I. 32,μà τήν Αϊδεω Κούρην. I. 69, μà … τήν Φίλην δήμητρα.

No ancient has told us in any surviving writing when Iambulos lived. Lucian says no more than that he composed a work obviously fabulous but quite amusing; Diodoros of Sicily, the only other author to mention him at all, earns our gratitude by excerpting his romance, apparently under the impression that it was sober fact. Moderns are accordingly vague in dating him. It is obvious that he must be earlier than or contemporary with Diodoros, whose historical work mentions no date (...) later than 54 B.C, but his allusions to events of his own life indicate that he was old enough to take an intelligent interest in the world as early as about 60 B.C, and still alive as late as 21 B.C. Kroll contents himself with indicating that Iambulos is later than Megasthenes, which gives us a range of close on 250 years. I think, however, that we may reduce this very considerably and place Iambulos, if not in any definite year, at least within a period of less than a century. (shrink)

Reinhold Niebuhr, approaching the ethical field as a theologian rather than as a philosopher, has maintained that the Christian ethic is not single and indivisible, but that, on the contrary, it consists of what one might call an absolute ethic and a kind of interim ethic in which the notion of justice is prominent. Without commenting on Niebuhr's work I wish to put forward a view which, although more general than his, is perhaps not without a superficial resemblance to it.

Abstract.Growing interest in the origin of life, the physical foundations of biological theory, and the evolution of animal social systems has led to increasing efforts to understand the processes by which elements or living systems at one level of organizational complexity combine to form stable systems of higher order. J. Bronowski saw the need to extend or reformulate evolutionary theory to deal with the hierarchy problem and to account for the evolution of systems of “stratified stability.” The hierarchy problem has (...) become a matter of great interest also in nonequilibrium thermodynamic theory.An effort is made here to develop an abstract, phenomenological model, based on the laws of thermodynamics, to account for the origin and hierarchical evolution of living systems. It is argued that the principle of minimum entropy production, developed by I. Prigogine, applies generally to all thermodynamic systems and processes and is implicit in an extended and more complete formulation of the second law of thermodynamics. From this are derived a thermodynamic criterion and a principle of thermodynamic selection governing the formation of stable systems of “elements” of various levels of organization. Thermodynamic selection gives rise to the creation of “elements” having increasingly “open” characteristic structures which may combine spontaneously to form “social” or crystalline systems capable of growing and reproducing themselves through processes of fissioning or budding. Such simple, self‐reproducing systems are capable of evolving by natural selection, which is seen to be a special case of the more general process of thermodynamic selection. The principle of natural selection, thus formulated, has the character of a fundamental physical law. Self‐reproducing systems with suitably open hereditary programs may combine to form stable social systems, which may grow and reproduce as a unit. In this way self‐reproducing systems of increasing hierarchical order, size, and organizational complexity may evolve through processes of thermodynamic (natural) selection. Some implications of this open‐ended model and opportunities for testing its empirical and theoretical utility are explored. (shrink)