Logic and Computation is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is a computer program for reasoning about computation. It combines methods of mathematical logic with domain theory, the basis of the denotational approach to specifying the meaning of statements in a programming language. This book consists of two parts. Part I outlines the mathematical preliminaries: elementary logic and domain theory. They are explained at an intuitive level, giving references (...) to more advanced reading. Part II provides enough detail to serve as a reference manual for Cambridge LCF. It will also be a useful guide for implementors of other programs based on the LCF approach. (shrink)

Ackermann’s function can be expressed using an iterative algorithm, which essentially takes the form of a term rewriting system. Although the termination of this algorithm is far from obvious, its equivalence to the traditional recursive formulation—and therefore its totality—has a simple proof in Isabelle/HOL. This is a small example of formalising mathematics using a proof assistant, with a focus on the treatment of difficult recursions.

We present an embedding of quantified multimodal logics into simple type theory and prove its soundness and completeness. A correspondence between QKπ models for quantified multimodal logics and Henkin models is established and exploited. Our embedding supports the application of off-the-shelf higher-order theorem provers for reasoning within and about quantified multimodal logics. Moreover, it provides a starting point for further logic embeddings and their combinations in simple type theory.

The tendency to reciprocate – to return good for good and evil for evil – is a potent force in human life, and the concept of reciprocity is closely connected to fundamental notions of ‘justice’, ‘obligation’ or ‘duty’, ‘gratitude’ and ‘equality’. In _Reciprocity_, first published in 1986,_ _Lawrence Becker presents a sustained argument about reciprocity, beginning with the strategy for developing a moral theory of the virtues. He considers the concept of reciprocity in detail, contending that it is a basic (...) virtue that provides the basis for parental authority, obligations to future generations, and obedience to law. Throughout the first two parts of the book, Becker intersperses short pieces of his own narrative fiction to enrich reflection on the philosophical arguments. The final part is devoted to extensive bibliographical essays, ranging over anthropology, psychology, political theory and law, as well as the relevant ethics and political philosophy. (shrink)

A philosophical essay under this title faces severe rhetorical challenges. New accounts of the good life regularly and rapidly turn out to be variations of old ones, subject to a predictable range of decisive objections. Attempts to meet those objections with improved accounts regularly and rapidly lead to a familiar impasse — that while a life of contemplation, or epicurean contentment, or stoic indifference, or religious ecstasy, or creative rebellion, or self-actualization, or many another thing might count as a good (...) life, none of them can plausibly be identified with the good life, or the best life. Given the long history of that impasse, it seems futile to offer yet another candidate for the genus “good life” as if that candidate might be new, or philosophically defensible. And given the weariness, irony, and self-deprecation expected of a philosopher in such an impasse, it is difficult for any substantive proposal on this topic to avoid seeming pretentious. (shrink)

_Property Rights: Philosophic Foundations,_ first published in 1977, comprehensively examines the general justifications for systems of private property rights, and discusses with great clarity the major arguments as to the rights and responsibilities of property ownership. In particular, the arguments that hold that there are natural rights derived from first occupancy, labour, utility, liberty and virtue are considered, as are the standard anti-property arguments based on disutility, virtue and inequality, and the belief that justice in distribution must take precedence over (...) private ownership. Lawrence Becker goes on to contend that there are four sound lines of argument for private property that, together with what is sound in the anti-property arguments, must be co-ordinated to form the foundations of a new theory. He therefore expounds a concise but sophisticated theory of property that is relevant to the modern world, and concludes by indicating some of the implications of his theory. (shrink)

The question addressed by this book is what, if anything, stoic ethics would be like today if stoicism had had a continuous history to the present day as a plausible and coherent set of philosophical commitments and methods. The book answers that question by arguing that most of the ancient doctrines of Stoic ethics remain defensible today, at least when ancient Stoicism's cosmological commitments are replaced by modern scientific ones.

Philosopher Lawrence Becker applies modern knowledge and psychology to the ancient stoic ethic system. In keeping with the ancients, Becker argues that virtue, not happiness, is the proper end of all activity. Moreover, he rejects the popular caricature of the stoic as a grave and emotionally detached figure, proposing instead, that stoic discipline is the very foundation not only of strength, but also of joy.

What would stoic ethics be like today if stoicism had survived as a systematic approach to ethical theory, if it had coped successfully with the challenges of modern philosophy and experimental science? A New Stoicism proposes an answer to that question, offered from within the stoic tradition but without the metaphysical and psychological assumptions that modern philosophy and science have abandoned. Lawrence Becker argues that a secular version of the stoic ethical project, based on contemporary cosmology and developmental psychology, (...) provides the basis for a sophisticated form of ethical naturalism, in which virtually all the hard doctrines of the ancient Stoics can be clearly restated and defended. Becker argues, in keeping with the ancients, that virtue is one thing, not many; that it, and not happiness, is the proper end of all activity; that it alone is good, all other things being merely rank-ordered relative to each other for the sake of the good; and that virtue is sufficient for happiness. Moreover, he rejects the popular caricature of the stoic as a grave figure, emotionally detached and capable mainly of endurance, resignation, and coping with pain. To the contrary, he holds that while stoic sages are able to endure the extremes of human suffering, they do not have to sacrifice joy to have that ability, and he seeks to turn our attention from the familiar, therapeutic part of stoic moral training to a reconsideration of its theoretical foundations. (shrink)

The editors, working with a team of 325 renowned authorities in the field of ethics, have revised, expanded, and updated this classic encyclopedia. Along with the addition of 150 new entries, all of the original articles have been newly peer-reviewed and revised, bibliographies have been updated throughout, and the overall design of the work has been enhanced for easier access to cross-references and other reference features. New entries include * Aristotelian Ethics * Avicenna * Bad Faith * Beneficence * Categorical (...) and Hypothetical Imperatives * Cheating * Civil Liberty * Conventions * Dirty hands * Evolution * Fiduciary Relationships * Gay ethics * Genetic Engineering * Holocaust * Journalism * Killing/Letting Die * Moral Imagination * Narrative Ethics * Political correctness * Population Ethics * Public and 0rivate Morality * Racism, concepts of * and many more. (shrink)

This symposium paper for the APA analyzes Locke's labor theory of property acquisition as a formal argument – or set of alternative arguments – and shows how several of them are indeed sound, if appropriately limited by what amounts to a social welfare proviso. That proviso is, however, strong enough to limit the acquisition of private property in a significant way. The argument here anticipates fuller and more decisive ones in later work by the same author.

When philosophers speak of the inconclusiveness of arguments for the existence of God, they often do so as if they were talking about a matter of principle—as if it were in principle impossible to prove God's existence, that every proof was in principle inconclusive. Of course, rebutals of the cosmological, ontological, and teleological arguments are usually designed to show that these types of arguments are in principle inconclusive. But one supposes that religious experience arguments are not all in such difficulties. (...) That is, one supposes, for example, that an encounter with the deity would provide a proof of his existence which is at least as conclusive as proofs for the existence of an ‘external world’. And thus it would be false to maintain in an unqualified way that ‘Reason cannot prove the existence of God’. The most one would be able to say would be that at present , or in terms of the currently available evidence, no one can prove God's existence. Further, whether or not sufficient evidence has ever been available in the past would be seen as an historical question— a matter of contingencies, not logical possibilities. (shrink)

This book argues for adopting a new account of the circumstances of justice ("the habilitation framework") for philosophical theories of basic justice. It proposes a concept of basic health as a metric for such theories, and healthy agency as a target for them. It does not, however, propose a specific distributive rule or set of distributive principles. Nor does it propose a specific type of theory to pursue (e.g., utilitarian, contractarian, etc.). The book is thus meant to be largely theory-independent (...) respect to standard normative theories. (shrink)

The editors, working with a team of 325 renowned authorities in the field of ethics, have revised, expanded, and updated this classic encyclopedia. Along with the addition of 150 new entries, all of the original articles have been newly peer-reviewed and revised, bibliographies have been updated throughout, and the overall design of the work has been enhanced for easier access to cross-references and other reference features. New entries include * Aristotelian Ethics * Avicenna * Bad Faith * Beneficence * Categorical (...) (...). (shrink)

The editors, working with a team of 325 renowned authorities in the field of ethics, have revised, expanded and updated this classic encyclopedia. Along with the addition of 150 new entries, all of the original articles have been newly peer-reviewed and revised, bibliographies have been updated throughout, and the overall design of the work has been enhanced for easier access to cross-references and other reference features. New entries include * Cheating * Dirty hands * Gay ethics * Holocaust * Journalism (...) * Political correctness * and many more. (shrink)