If S is a finite set, let |S| be the cardinality of S. We show that if $m \in \omega, A \subseteq \omega, B \subseteq \omega$ , and |{i: 1 ≤ i ≤ 2 m & x i ∈ A}| can be computed by an algorithm which, for all x 1 ,...,x 2 m , makes at most m queries to B, then A is recursive in the halting set K. If m = 1, we show that A is recursive.

If and the function is partial recursive, it is easily seen that A is recursive. In this paper, we weaken this hypothesis in various ways (and similarly for ``min'' in place of ``max'') and investigate what effect this has on the complexity of A. We discover a sharp contrast between retraceable and co-retraceable sets, and we characterize sets which are the union of a recursive set and a co-r.e., retraceable set. Most of our proofs are noneffective. Several open questions are (...) raised. (shrink)

To be intrinsically valuable means to be valuable for its own sake. Moral philosophy is often ethically anthropocentric, meaning that it locates intrinsic value within humans. This paper rejects ethical anthropocentrism and asks, in what ways might nonhumans be intrinsically valuable? The paper answers this question with a wide-ranging survey of theories of nonhuman intrinsic value. The survey includes both moral subjects and moral objects, and both natural and artificial nonhumans. Literatures from environmental ethics, philosophy of technology, philosophy of art, (...) moral psychology, and related fields are reviewed, and gaps in these literatures are identified. Although the gaps are significant and much work remains to be done, the survey nonetheless demonstrates that those who reject ethical anthropocentrism have considerable resources available to develop their moral views. Given the many very high-stakes issues involving both natural and artificial nonhumans, and the sensitivity of these issues to how nonhumans are intrinsically valued, this is a vital project to pursue. (shrink)

An ω-set is a subset of the recursive ordinals whose complement with respect to the recursive ordinals is unbounded and has order type ω. This concept has proved fruitful in the study of sets in relation to metarecursion theory. We prove that the metadegrees of the sets coincide with those of the meta-r.e. ω-sets. We then show that, given any set, a metacomplete set can be found which is weakly metarecursive in it. It then follows that weak relative metarecursiveness is (...) not a transitive relation on the sets, extending a result of G. Driscoll [2, Theorem 3.1]. Coincidentally, we discuss the notions of total and complete regularity. Finally, we solve Post's problem for the transitive closure of weak relative metarecursiveness. We recommend the reader look at pp. 324–328 of the fundamental article [6] of Kreisel and Sacks before proceeding. He will find there a proof of the following very basic fact: a subset of the integers is iff it is metarecursively enumerable (metafinite). (shrink)

A Cantor singleton is the unique nonrecursive member of some $\Pi^0_1$ class. In this paper we investigate the relationships between the following three notions: Cantor singletons, Cantor-Bendixson rank, and recursive join. Among other results, we show that the rank of $A\oplus B$ is at most the natural sum of the ranks of $A$ and $B$ , and that, if $B$ has the same rank as $A\o plus B$ , then $A$ is recursive in $B$.

Reading Certainty offers incisive historical analysis of the foundational questions of the Christian tradition: how are we to read scripture, and how can we know we are saved? This collection of essays honors the work and thought Susan E. Schreiner by exploring the import of these questions across a wide range of time periods. With contributions from renowned scholars and from Schreiner's students from her more than three decades of teaching, each of the contributions highlights the nexus of certainty, perception, (...) authority, and exegesis that has defined her scholarly work. Intellectual historians, early modernists, and scholars of Christianity will all appreciate this testament to Schreiner's influence. Contributors include: Vincent Evener, Bruce Gordon, Ralph Keen, Mark Lambert, Kevin J. Madigan, Richard A. Muller, Willemien Otten, Daniel Owings, Elizabeth Palmer, Karen Park, Barbara Pitkin, Ronald K. Rittgers, William Schweiker, Jonathan Strom, and Matthew Vanderpoel. (shrink)

Diversity is an important ethical concept, but it is almost exclusively studied within two domains: biodiversity and diversity of sociological attributes such as race and gender. We provide a general study of the intrinsic value of diversity. We survey prior literature on the intrinsic value of biodiversity and sociological diversity in search of insights relevant to the intrinsic value of all types of diversity. We then present three thought experiments designed to clarify intuitions about the intrinsic value of small amounts (...) of diversity, large amounts of diversity, and diversity as compared to other intrinsic values. We find that many types of diversity are intrinsically valuable at both small and large amounts, but that diversity may be a weak intrinsic value in comparison to others. Noting that diversity can be defined in many ways, we propose that, for purposes of moral evaluation, diversity should be defined to include both a diversity of individual elements within a group and a diversity of the overall patterns or structures of the group. Some of our findings about the intrinsic value of diversity are tentative, indicating that moral intuitions about diversity are sometimes ambiguous and would benefit from further study. (shrink)

Since around 2012, there has been a ‘deep learning revolution’ in artificial intelligence (AI) that has brought AI to the forefront of many sectors of human activity. As new AI technology has sprea...

A case is made for supposing that the total probability accounted for in a decision analysis is less than unity. This is done by constructing a measure on the set of all codes for computable functions in such a way that the measure of every effectively accountable subset is bounded by a number <1. The consistency of these measures with the Savage axioms for rational preference is established. Implications for applied decision theory are outlined.

Recent work in AI ethics often calls for AI to advance human values and interests. The concept of “AI for people” is one notable example. Though commendable in some respects, this work falls short by excluding the moral significance of nonhumans. This paper calls for a shift in AI ethics to more inclusive paradigms such as “AI for the world” and “AI for the universe”. The paper outlines the case for more inclusive paradigms and presents implications for moral philosophy and (...) computer science work on AI ethics. (shrink)

We introduce the notion of "semi-r.e." for subsets of ω, a generalization of "semirecursive" and of "r.e.", and the notion of "weakly semirecursive", a generalization of "semi-r.e.". We show that A is weakly semirecursive iff, for any n numbers x 1 ,...,x n , knowing how many of these numbers belong to A is equivalent to knowing which of these numbers belong to A. It is shown that there exist weakly semirecursive sets that are neither semi-r.e. nor co-semi-r.e. On the (...) other hand, we exhibit nonzero Turing degrees in which every weakly semirecursive set is semirecursive. We characterize the notion "A is weakly semirecursive and recursive in K" in terms of recursive approximations to A. We also show that if a finite Boolean combination of r.e. sets is semirecursive then it must be r.e. or co-r.e. Several open questions are raised. (shrink)

We find the idea that infant crying arises from thermoregulation more consistent with a coregulatory account of its evolutionary history than it is with the informational account advocated in the target article.

_God Owes Us Nothing_ reflects on the centuries-long debate in Christianity: how do we reconcile the existence of evil in the world with the goodness of an omnipotent God, and how does God's omnipotence relate to people's responsibility for their own salvation or damnation. Leszek Kolakowski approaches this paradox as both an exercise in theology and in revisionist Christian history based on philosophical analysis. Kolakowski's unorthodox interpretation of the history of modern Christianity provokes renewed discussion about the historical, intellectual, and (...) cultural omnipotence of neo-Augustinianism. "Several books a year wrestle with that hoary conundrum, but few so dazzlingly as the Polish philosopher's latest."—Carlin Romano, _Washington Post Book World_ "Kolakowski's fascinating book and its debatable thesis raise intriguing historical and theological questions well worth pursuing."—Stephen J. Duffy, _Theological Studies_ "Kolakowski's elegant meditation is a masterpiece of cultural and religious criticism."—Henry Carrigan, _Cleveland Plain Dealer_. (shrink)

Neither employer expectations of loyalty, nor good treatment of employees by employers, nor employee appreciation of employers, nor the duty of nonmaleficence, nor the intention to be loyal, nor the duty not to act disloyally provide a basis for a moral or ethical duty of employee loyalty. However, in addition to the law, a pledge to be loyal can obligate one to be loyal. But if the specific content of such a pledge is unstated, the conduct required by the pledge (...) may be indefinite. Moreover, the content and implications of loyalty are fluid, varying from context to context. Consequently, there is only a limited basis for the thesis that employees owe loyalty to their employers. (shrink)

How do we judge whether an action is morally right or wrong? If an action is wrong, what reason does that give us not to do it? Why should we give such reasons priority over our other concerns and values? In this book, T. M. Scanlon offers new answers to these questions, as they apply to the central part of morality that concerns what we owe to each other. According to his contractualist view, thinking about right and wrong is thinking (...) about what we do in terms that could be justified to others and that they could not reasonably reject. He shows how the special authority of conclusions about right and wrong arises from the value of being related to others in this way, and he shows how familiar moral ideas such as fairness and responsibility can be understood through their role in this process of mutual justification and criticism. Scanlon bases his contractualism on a broader account of reasons, value, and individual well-being that challenges standard views about these crucial notions. He argues that desires do not provide us with reasons, that states of affairs are not the primary bearers of value, and that well-being is not as important for rational decision-making as it is commonly held to be. Scanlon is a pluralist about both moral and non-moral values. He argues that, taking this plurality of values into account, contractualism allows for most of the variability in moral requirements that relativists have claimed, while still accounting for the full force of our judgments of right and wrong. (shrink)

The suffering of war refugees is often regarded as a wrong-less harm. Although war refugees have been made worse off in severe ways, they have not been wronged, because no one intentionally caused their suffering. In military parlance, war refugees are collateral damage. As such, nothing is owed to them as a matter of justice, because their suffering is not the result of intentional wrongdoing; rather, it is the regrettable and unintended result of necessary and proportionate wartime actions. So, while (...) the warring national or extra-national groups might help war refugees, such aid is regarded as humanitarian, not as justice.I challenge the view that war refugees are harmed but not wronged when those harms directly result from necessary and proportionate wartime actions. War refugees are innocent bystanders, and so are an exception to the principle that permits defense by any necessary and proportionate means. Just as an individual may not kill or seriously harm an innocent bystander to save herself, so too national or extra-national groups may not create refugees to win a war. If such groups do create war refugees during the legitimate pursuit of military goals, they have wronged those refugees, and so owe them recompense. (shrink)

Criticism of H.L.A. Hart's account of how the movements of a person during the performance of an act that is done by mistake or owing to ignorance are not uncontrolled or involuntary. movements.

Who are refugees? Who, if anyone, is responsible for protecting them? What forms should this protection take? In a world of people fleeing from civil wars, state failure, and environmental disasters, these are ethically and politically pressing questions. In this book, David Owen reveals how the contemporary politics of refuge is structured by two rival historical pictures of refugees. In reconstructing this history, he advocates an understanding of refugeehood that moves us beyond our current impasse by distinguishing between what is (...) owed to refugees in general and what is owed to different types of refugee. He provides an account of refugee protection and the forms of international cooperation required to implement it that is responsive to the claims of both refugees and states. At a time when refugee protection is once again prominent on the international agenda, this book offers a guide to understanding the challenges this topic raises and shows why addressing it matters for all of us. (shrink)

Organizational citizenship behavior (OCB) has been widely recognized as a contributor to improving organizational performance and wealth creation. The purpose of this article is to briefly summarize the motives of many employees who exercise OCB and to identify the ethical duties owed by organizational leaders to the highly committed employees with whom they work. After reviewing the nature of OCB and the psychological contracts made with highly committed employees, we then use Hosmer’s framework of ten ethical perspectives to identify how (...) OCB is viewed from each of those ethical viewpoints. We offer six propositions about OCB that relate to building employee commitment and trust. (shrink)

This essay criticises ‘modest’ one‐child policies, which would impose sanctions upon parents who create multiple children. Specifically, this article considers what the state owes individuals who would be born (illegally) beneath restrictive procreative policies and argues that such policies would fail to show due respect to second‐ or third‐born individuals created beneath them. First, I argue that modest procreative restrictions (like sanctions) are likely to generate only modest compliance. I then suggest it is reasonable to think a one‐child policy fails (...) to demonstrate due respect to existing second and third children. I argue that such a policy generates an undue burden on any second or third children who would be born beneath them, before concluding by considering whether the state might be able to avoid effectively reinscribing ‘bastardy’ into its law by locating responsibility for the effects of such a policy entirely on the parents, rather than on children. (shrink)

It is, if not a happy accident, then surely a pleasing peripety that despite Pascal's intention to complete an Apology for the Christian Religion, the fragmentary character of his Pensées should, by its very incompleteness, so well have served his purpose, as the vitality of the torso he left us attests. Yet there is ample evidence in the Pensées themselves that the book's orderless order captures both the rhetorical problem Pascal confronted and the solution he envisaged. More broadly stated, the (...) literary form of the work, such as it is, mirrors its substance, namely, the fragmentary character of the created whole and the human part of that whole. In short, the last thing Pascal wished to do was to make things easy for his reader, and in this respect the Pensées he left us serve his intentions admirably. While Kolakowski's study of "Pascal's religion" ultimately denies that the rigors of Pascal's argument are compatible with human happiness or reason, God Owes Us Nothing does honor Pascal's purpose by refusing to ease our way by making things simple. (shrink)

This paper is about an overlooked aspect—the cognitive or epistemic aspect—of the moral demand we place on one another to be treated well. We care not only how people act towards us and what they say of us, but also what they believe of us. That we can feel hurt by what others believe of us suggests both that beliefs can wrong and that there is something we epistemically owe to each other. This proposal, however, surprises many theorists who claim (...) it lacks both intuitive and theoretical support. This paper argues that the proposal has intuitive support and is not at odds with much contemporary theorizing about what we owe to each other. (shrink)

Liberal nationalists have been trying to argue that a suitably sanitized version of nationalism—namely, one that respects and embodies liberal values—is not only morally defensible, but also of great moral value, especially on grounds liberals should find very appealing. Although there are plausible aspects to the idea and some compelling arguments are offered in defense of this position, one area still proves to be a point of considerable vulnerability for this project and that is the issue of what, according to (...) the liberal nationalists, we owe both members of our nation, our co-nationals, and what we owe those who are not members of our nation. It is here that we see the project still has some distance to go if a version of liberal nationalism is, indeed, to be morally defensible. In this paper I examine leading liberal nationalist accounts of our obligations to co-nationals and non-nationals. I argue that liberal nationalists have not yet given us an adequate account of our obligations to non-nationals for a number of reasons. For instance, on the issue of the priority we may give co-nationals' interests over non-nationals', the theorists' view show significant tension, they seem to be confused about what their positions entail, the views are unhelpful, ad hoc, or the positions are quite unclear. Liberal nationalists also have a misleading impression that their positions better capture the relation between personal identity and duty, but this turns out to be false. Other defects with their specific projects are highlighted. I go on to offer a more promising method for determining our obligations to non-nationals. Rather than this alternative precluding any scope for nationalism, it actually makes clearer to us how there might be some defensible space for nationalism once our obligations to put in place appropriate institutions and sets of rules have been fulfilled. (shrink)

We argue that in contemporary business organizations, in which fundamental purpose is construed to be increased value—especially in ‘participative’ organizations, in which non–hierarchal interaction (for example, work teams) is the norm; and in ‘adaptive’ organizations, in which unpredictable change is the rule—a process of values covenanting will be much more valueable than just espoused values or even values covenants. We propose such a process model for organizational values covenanting and argue that such covenanting reflects an anthropomorphism of the human character (...) development process, validated in terms of the theory of viable systems. (shrink)