We introduce a linear analogue of Läuchli's semantics for intuitionistic logic. In fact, our result is a strengthening of Läuchli's work to the level of proofs, rather than provability. This is obtained by considering continuous actions of the additive group of integers on a category of topological vector spaces. The semantics, based on functorial polymorphism, consists of dinatural transformations which are equivariant with respect to all such actions. Such dinatural transformations are called uniform. To any sequent in Multiplicative Linear Logic (...) , we associate a vector space of“diadditive” uniform transformations. We then show that this space is generated by denotations of cut-free proofs of the sequent in the theory MLL + MIX. Thus we obtain a full completeness theorem in the sense of Abramsky and Jagadeesan, although our result differs from theirs in the use of dinatural transformations.As corollaries, we show that these dinatural transformations compose, and obtain a conservativity result: diadditive dinatural transformations which are uniform with respect to actions of the additive group of integers are also uniform with respect to the actions of arbitrary cocommutative Hopf algebras. Finally, we discuss several possible extensions of this work to noncommutative logic.It is well known that the intuitionistic version of Läuchli's semantics is a special case of the theory of logical relations, due to Plotkin and Statman. Thus, our work can also be viewed as a first step towards developing a theory of logical relations for linear logic and concurrency. (shrink)

This paper discusses lower bounds for proof length, especially as measured by number of steps (inferences). We give the first publicly known proof of Gödel's claim that there is superrecursive (in fact. unbounded) proof speedup of (i + 1)st-order arithmetic over ith-order arithmetic, where arithmetic is formalized in Hilbert-style calculi with + and · as function symbols or with the language of PRA. The same results are established for any weakly schematic formalization of higher-order logic: this allows all tautologies as (...) axioms and allows all generalizations of axioms as axioms. Our first proof of Gödel's claim is based on self-referential sentences: we give a second proof that avoids the use of self-reference based loosely on a method of Statman. (shrink)

The geometric system of deduction called N-Graphs was introduced by de Oliveira in 2001. The proofs in this system are represented by means of digraphs and, while its derivations are mostly based on Gentzen's sequent calculus, the system gets its inspiration from geometrically based systems, such as the Kneales' tables of development, Statman's proofs-as-graphs, Buss' logical flow graphs, and Girard's proof-nets. Given that all these geometric systems appeal to the classical symmetry between premises and conclusions, providing an intuitionistic version of (...) any of these is an interesting exercise in extending the range of applicability of the geometric system in question. In this article we produce an intuitionistic version of N-Graphs, based on Maehara's LJ' system, as described by Takeuti. Recall that LJ' has multiple conclusions in all but the essential intuitionistic rules, e.g., implication right and negation right. We show soundness and completeness of our intuitionistic N-Graphs with respect to LJ'. We also discuss how we expect to extend this work to a version of N-Graphs corresponding to the intuitionistic logic system FIL (Full Intuitionistic Logic) of de Paiva and Pereira and sketch future developments. (shrink)

The central question in contemporary ethics is whether virtue can replace duty as the primary notion in ethical theory. The subject of intense contemporary debate in ethical theory, virtue ethics is currently enjoying an increase in interest. This is the first book to focus directly on the subject. It provides a clear, systematic introduction to the area and houses under one cover a collection of the central articles published on the debate over the past decade. The essays encompass a wide (...) range ofaspects: the difference between virtue ethics and traditional duty ethics; present arguments for and against virtue ethics; the practical implications of virtue ethics and the Aristotelian and Kantian attitudes to virtue ethics. (shrink)

Moral dilemmas set a challenge for ethical theory. They are situations where agents seem to be under an obligation both to do, and to refrain from doing, a specific act. Are such situations possible? What is their exact nature? These are the questions that _Moral Dilemmas_ tries to answer. The book argues that moral theories should not allow for the possibility of irresolvable dilemmas, for situations in which no right answer exists. To this end, arguments seeking to prove the existence (...) of irresolvable dilemmas, especially the argument from the incommensurability of values, are discussed at length and refuted. The book shows that though on the normative level dilemmas are resolved, they typically involve a high moral cost for which there is no adequate compensation. This moral cost is the source of the regret and pain suffered by agents in moral dilemmas. Thus, moral dilemmas do not point to any inconsistency in our moral reasoning or theory, but to a problematic aspect of the human condition; at times (probably less often than is usually believed), human beings are justified, and even required, to dirty their hands by behaving in ways that in ordinary situations would be strictly forbidden and condemned. (shrink)

_Religion and Morality_ seeks to answer two fundamental questions regarding the relation between religion and morality. The first is the puzzle posed by Socrates, the so-called '_Euthyphro_ dilemma', which asks: is morality valuable by virtue of its intrinsic importance and worth, or is morality valuable because, and only because, God approves it and commands us to follow its dictates? The second question is raised by Kierkegaard in _Fear and Trembling_. He asks: Is a conflict between religion and morality possible? Does (...) God ever demand that we neglect our moral commitments? The discussion on these questions is divided into three parts. In the first two parts, we discuss the idea that morality depends on religion. The authors distinguish two types of dependence: strong dependence, according to which the very existence, or validity, of moral obligations depends on God's command, and weak dependence, according to which though morality itself is independent of God, God (or belief in God) is necessary to enable human beings to know their moral duties and to carry them out. The authors reject the strong dependence thesis, as well as most versions of the weak dependence. The third part of the book discusses different versions of the view that religion might conflict with morality. The authors reject this view, and show that very few religious thinkers would follow it all the way through to its ultimate consequences. The book has implications for the philosophy of religion, in its emphasis on the centrality of the moral element in religion, and for moral philosophy, in its highlighting, among other things, of the nature of moral judgments. (shrink)

Розкрито сутність поняття «рейтинг». Доведено значущість рейтингової оцінки для суб’єктів фінансового ринку, зокрема для страхових компаній, потенційних страхувальників, інвесторів та кредиторів.

Proponents of corporate environmental responsibility argue that corporations shortchange shareholders by investing too little in environmental responsibility. They claim that corporations can improve their financial performance by increasing their investment in environmental responsibility. Opponents of corporate social responsibility argue that corporations shortchange shareholders by investing too much in environmental responsibility. They claim that corporations can improve their financial performance by reducing their investment in environmental responsibility. Yet, others claim that corporations serve their shareholders well by investing just enough in social (...) responsibility, not too little and not too much. If so, corporations increase their investment in environmental responsibility when an increase improves financial performance and reduce their investment in environmental responsibility when a decrease improves financial performance. Our evidence is consistent with this last claim. We find that the behavior of corporations is consistent with the claim that they act in the interest of shareholders, increasing or decreasing their investment in environmental responsibility as necessary to improve their financial performance. (shrink)

We consider three problems concerning alpha conversion of closed terms (combinators). (1) Given a combinator M find the an alpha convert of M with a smallest number of distinct variables. (2) Given two alpha convertible combinators M and N find a shortest alpha conversion of M to N. (3) Given two alpha convertible combinators M and N find an alpha conversion of M to N which uses the smallest number of variables possible along the way. We obtain the following results. (...) (1) There is a polynomial time algorithm for solving problem (1). It is reducible to vertex coloring of chordal graphs. (2) Problem (2) is co-NP complete (in recognition form). The general feedback vertex set problem for digraphs is reducible to problem (2). (3) At most one variable besides those occurring in both M and N is necessary. This appears to be the folklore but the proof is not familiar. A polynomial time algorithm for the alpha conversion of M to N using at most one extra variable is given. There is a tradeoff between solutions to problem (2) and problem (3) which we do not fully understand. (shrink)

Yitzhak Benbaji and Daniel Statman present a new theory on the ethics of war which shows that wars can be morally justified at both the ad bellum level and the in bello level.

"Williams's masterful translation satisfies (at last!) a long-standing need. There are lots of good translations of Augustine's great work, but until now we have been forced to choose between those that strive to replicate in English something of the majesty and beauty of Augustine's Latin style and those that opt instead to convey the careful precision of his philosophical terminology and argumentation. Finally, Williams has succeeded in capturing both sides of Augustine's mind in a richly evocative, impeccably reliable, elegantly readable (...) presentation of one of the most impressive achievements in Western thought--Augustine's Confessions." --Scott MacDonald, Professor of Philosophy and Norma K. Regan Professor in Christian Studies, Cornell University. (shrink)

Some luck, in a decision of Gauguin's kind, is extrinsic to his project, some intrinsic; both are necessary for success, and hence for actual justification, but only the latter relates to un- justification. If we now broaden the range of cases slightly, ...

Pascal’s wager faces serious criticisms and is generally considered unconvincing. We argue that it can make a comeback powered by an unlikely ally: postmodernism. If one denies the existence of objective facts (e.g. about God or His relation to the world), then various non-theological considerations should come to the fore when considering the rationality of religious commitment and the choice of education for one’s children. In fact, we shall argue that, if one genuinely cares about one’s children, then – in (...) many Western countries – one cannot consistently be both secular and post-modernist. (shrink)

The topic of standing to blame has recently received a lot of attention. Until now, however, it has focused mainly on the blamer's perspective, investigating what it means to say of blamers that they lose standing to blame and why it is that they lose this standing under specified conditions. The present paper focuses on the perspective of the blamees and tries to explain why they are allowed to disregard standingless, more specifically hypocritical, blame. According to the solution proposed by (...) the paper, while hypocritical blamers present themselves as caring about justice or about the moral or material good of the blamees—and they themselves half‐believe this presentation—their real motivation in blaming is less respectable. It is this problematic motivation that explains why blamees are permitted to disregard hypocritical blame. Ill‐motivated blame is often unreliable, and readiness to even consider it often involves a compromise on the self‐respect of the blamees. (shrink)

This book offers a critical introduction to the work of American philosopher D. G. Leahy (1937-2014). Leahy's fundamental thinking can be characterized as an absolute creativity in which all creating is 'live' -- a happening occurring now that manifests a supersaturated polyontological actuality that is essentially created by the logic that characterizes it. Leahy leaves behind the categorial presuppositions of modern thought, eclipsing both Cartesian and Hegelian subjectivities and introducing instead an essentially new form of thinking founded in a nondual (...) logic of creation. The new thinking delineates the absolute unicity of existence as a creative interactivity beyond all traditional dichotomies (such as one vs. many, unity vs. plurality, identity vs. change): a fully "digitized" actuality that is nothing but newness, which inherently implies nothing but change. Through this new form of thinking, change itself is revealed to be the very essence of reality and mind. Any reader looking for a quantum leap beyond the thrall of modern and postmodern fixations is invited to hear and apprehend this new thinking that refuses to be conditioned by paradigms, categories, species, genera, walls, bridges, boundaries, or abstractions: an essentially free thinking that embodies creative novelty itself. (shrink)

That an intimate connection exists between the notion of human dignity and the notion of humiliation seems to be a commonplace among philosophers, who tend to assume that humiliation should be explained in terms of (violation of) human dignity. I believe, however, that this assumption leads to an understanding of humiliation that is too "philosophical" and too detached from psychological reality. The purpose of the paper is to modify the above connection and to offer a more "down to earth" account (...) of humiliation that does not depend on metaphysical or axiological questions concerning the unique dignity enjoyed by all human beings qua human beings. The paper argues for a subjective-psychological notion of self-respect in the explication of humiliation, instead of an objective-normative one. To be humiliated means to suffer an actual threat to or fall in one's self-respect. (shrink)

The paper discusses a neglected condition for justified self-defense, namely, 'The Success Condition [SC].' According to SC, otherwise immoral acts can be justified under the right to self-defense only if they actually achieve the intended defense from the perceived threat. If they don't, they are almost always excused, but not morally justified. I show that SC leads to a troubling puzzle because victims who estimate they cannot prevent the attack against them would be morally required to surrender. I try to (...) solve the puzzle by relying on what I call 'The Honor Solution.' Even if defensive acts fail to protect the victim's body, property, or life, they are successful in protecting her honor, thus they do ultimately meet the success condition. (shrink)

The paper discusses a neglected condition for justified self-defense, namely, 'The Success Condition [SC].' According to SC, otherwise immoral acts can be justified under the right to self-defense only if they actually achieve the intended defense from the perceived threat. If they don't, they are almost always excused, but not morally justified. I show that SC leads to a troubling puzzle because victims who estimate they cannot prevent the attack against them would be morally required to surrender. I try to (...) solve the puzzle by relying on what I call 'The Honor Solution.' Even if defensive acts fail to protect the victim's body, property, or life, they are successful in protecting her honor, thus they do ultimately meet the success condition. (shrink)

R.I.G Hughes offers the first detailed and accessible analysis of the Hilbert-space models used in quantum theory and explains why they are so successful.

Hypocrites are generally regarded as morally-corrupt, cynical egoists who consciously and deliberately deceive others in order to further their own interests. The purpose of my essay is to present a different view. I argue that hypocrisy typically involves or leads to self-deception and, therefore, that real hypocrites are hard to find. One reason for this merging of hypocrisy into self-deception is that a consistent and conscious deception of society is self-defeating from the point of view of egoistical hypocrites. The best (...) way for them to achieve their ends would be to believe in the deception, thereby not only deceiving others but also themselves. If my thesis is sound, we ought to be more cautious in ascribing hypocrisy to people, and less harsh in our attitude toward hypocrites. (shrink)

The paper offers a theory of cruelty that includes the following claims: First, cruelty is best understood as a disposition to take delight in the very infliction of suffering on others. Thus understood, cruelty is the same phenomenon as that studied and operationalized by psychologists in the last decade or so under the heading of everyday sadism. Second, for people to be cruel, they need not have proper understanding of the moral standing of their victims. Third, ascriptions of cruelty do (...) not depend on judgments regarding the moral wrongness of the assumed cruel act. Fourth, since cruelty is primarily a property of agents rather than of actions, and since actions are not always a reliable indication of cruelty, identifying cruelty is a more challenging task than usually thought. (shrink)

A recent empirical study has argued that experts in the ethics or the law of war cannot reach reasonable convergence on dilemmas regarding the number of civilian casualties who may be killed as a side effect of attacks on legitimate military targets. This article explores the philosophical implications of that study. We argue that the wide disagreement between experts on what in bello proportionality means in practice casts serious doubt on their ability to provide practical real-life guidance. We then suggest (...) viewing in bello proportionality through the prism of virtue ethics. (shrink)

Christopher New recently argued for the seemingly paradoxical idea that there is no moral reason not to punish someone before she commits her crime (‘prepunishment’), provided that we can be sure that she will, in fact, commit the crime in the future. I argue that the air of paradox dissolves if we understand the possibility of prepunishment as relying on an anti‐moral‐luck position. However, New does not draw the full conclusions from such a position, which would allow prepunishment even prior (...) to the formation of a wrongful intention, on the basis of the idea that bad character is enough to entail blameworthiness. I conclude by examining a legal system which seems to use the idea of prepunishment, i.e. the Talmudic idea that we might punish a child who has not yet sinned in order to save him from sinning in the future. (shrink)

According to a widespread view, the same constraints that limit the use of otherwise immoral measures in individual self-defense apply to collective self-defense too. I try to show that this view has radical implications at the level of jus in bello, implications which have not been fully appreciated. In particular, if the necessity condition must be satisfied in all cases of killing in war, then most fighting would turn out to be unjust. One way to avoid this result is to (...) adopt a contractualist view of killing in war, a view which interprets the necessity condition in a way that is more permissive with regard to killing combatants in war. At least in this respect, a contractualist view of killing in war has an advantage over other candidates in explaining how wars might be fought justly. (shrink)

In this paper we consider the problem of the existence of a λ-theory T such that:–T is recursive enumerable;–the ω-rule holds in T .We solve affirmatively this problem.Some related questions are also discussed.

One motivation for adopting a justice-based view of the right to self-defense is that it seems to solve the puzzle of how a victim may kill her attacker even when doing so is not predicted to protect her from the threat imposed upon her. The paper shows (a) that this view leads to unacceptable results and (b) that its solution to cases of futile self-defense is unsatisfactory. This failure makes the interest-based theory of self-defense look more attractive, both in the (...) context of futile self-defense and in general. To understand how a victim might use force in this context, one need only point to some interest of hers that is threatened, and the best candidate for such interest in cases of futile self-defense is her honor. (shrink)

abstract Assume that some group, A, is under a serious threat from some other group, B. The only way group A can defend itself is by using lethal force against group B, but the standard conditions for using force in self‐defence are not met. Ought group A to avoid the use of force even if this means yielding to an aggressive, evil power? Most people would resist this conclusion, yet given the violation of essential conditions for self‐defence, this resistance is (...) hard to justify. The aim of this paper is to point to an interesting yet unnoticed move made by some philosophers to find a way out of this problem, a move which relies on construing the situation at hand as a tragic dilemma. I show the attractiveness of this solution and argue that in the end it fails. (shrink)

The purpose of this paper is to explore the relation between the right to self-defense against an innocent attacker and the notion of moral luck. It argues that those who accept the existence of such a right rely on the assumption that mere agency makes a significant moral difference – which is precisely the assumption that underlies the view held by believers in moral luck. Those who believe in the right to self-defense against innocent attackers are thus committed to the (...) idea of moral luck much more than they usually acknowledge. The paper also argues that the arguments offered in support of moral luck, in particular the one based on the relation between agency and self-identity, might help to shed light on the rather puzzling above right. (shrink)

Given the religious appeal of divine command theories of morality (DCM), and given that these theories are found in both Christianity and Islam, we could expect DCM to be represented in Judaism, too. In this essay, however, we show that hardly any echoes of support for this thesis can be found in Jewish texts. We analyze texts that appear to support DCM and show they do not. We then present a number of sources clearly opposed to DCM. Finally, we offer (...) a theory to explain the absence of DCM in Judaism, claiming that the rational character of "Halakha", as well as the moral and rational character of God, does not provide suitable ground for the growth of DCM theses. (shrink)

The purpose of this paper is to provide a philosophical defense for targeted killings in the wars against terror. The paper argues that if one accepts the moral legitimacy of the large-scale killing of combatants in conventional wars, one cannot object - on moral grounds - to the targeted killing of terrorists in wars against terror. If one rejects this legitimacy, one must object to all killing in war, targeted and non-targeted alike, and thus not support the view, which is (...) criticized here, that targeted killings are particularly disturbing from a moral point of view. (shrink)

In light of the enormous suffering brought about by war, war might be justified only if the benefit it yields is significant enough, namely, a clear and durable victory over the enemy. The logic of this argument leads to a Clausewitz-style war of “annihilation.” I argue that the best way to justify the ending of war short of such annihilation is by relying on a contractarian view of jus ex bello. I conclude by exploring the implications of this view to (...) warfare in which no effective social contract is in place. (shrink)

Cartesian closed categories (CCCs) have played and continue to play an important role in the study of the semantics of programming languages. An axiomatization of the isomorphisms which hold in all Cartesian closed categories discovered independently by Soloviev and Bruce, Di Cosmo and Longo leads to seven equalities. We show that the unification problem for this theory is undecidable, thus settling an open question. We also show that an important subcase, namely unification modulo the linear isomorphisms, is NP-complete. Furthermore, the (...) problem of matching in CCCs is NP-complete when the subject term is irreducible. CCC-matching and unification form the basis for an elegant and practical solution to the problem of retrieving functions from a library indexed by types investigated by Rittri. It also has potential applications to the problem of polymorphic type inference and polymorphic higher-order unification, which in turn is relevant to theorem proving and logic programming. (shrink)