Corcoran, J. 2005. Counterexamples and proexamples. Bulletin of Symbolic Logic 11(2005) 460. -/- John Corcoran, Counterexamples and Proexamples. Philosophy, University at Buffalo, Buffalo, NY 14260-4150 E-mail: [email protected] Every perfect number that is not even is a counterexample for the universal proposition that every perfect number is even. Conversely, every counterexample for the proposition “every perfect number is even” is a perfect number that is not even. Every perfect number that is odd is a proexample for the existential proposition that some (...) perfect number is odd. Conversely, every proexample for the proposition “some perfect number is odd” is a perfect number that is odd. As trivial these remarks may seem, they can not be taken for granted, even in mathematical and logical texts designed to introduce their respective subjects. One well-reviewed book on counterexamples in analysis says that in order to demonstrate that a universal proposition is false it is necessary and sufficient to construct a counterexample. It is easy to see that it is not necessary to construct a counterexample to demonstrate that the proposition “every true proposition is known to be true” is false–necessity fails. Moreover the mere construction of an object that happens to be a counterexample does not by itself demonstrate that it is a counterexample–sufficiency fails. In order to demonstrate that a universal proposition is false it is neither necessary nor sufficient to construct a counterexample. Likewise, of course, in order to demonstrate that an existential proposition is true it is neither necessary nor sufficient to construct a proexample. This article defines the above relational concepts of counterexample and of proexample, it discusses their surprising history and philosophy, it gives many examples of uses of these and related concepts in the literature and it discusses some of the many errors that have been made as a result of overlooking the challenging subtlety of the proper use of these two basic and indispensable concepts. (shrink)

Thirty years ago, Alvin Plantinga gave a lecture called "Two Dozen (or so) Theistic Arguments," which served as an underground inspiration for two generations of scholars and students. In it, he proposed a number of novel and creative arguments for the existence of God which have yet to receive the attention they deserve. In Two Dozen (or so) Arguments for God, each of Plantinga's original suggestions, many of which he only briefly sketched, is developed in detail by a wide variety (...) of accomplished scholars. The authors look to metaphysics, epistemology, semantics, ethics, aesthetics, and beyond, finding evidence for God in almost every dimension of reality. Those arguments new to natural theology are more fully developed, and well-known arguments are given new life. Not only does this collection present ground-breaking research, but it lays the foundations for research projects for years to come."--Back cover. (shrink)

The first student-friendly introduction to the philosophical issues surrounding torture. It is a timely and useful contribution to a highly topical and on-going debate.

Although St Thomas Aquinas famously claimed that his Summa Theologiae was written for 'beginners', contemporary readers find it unusually difficult. Now, amid a surge of interest in virtue ethics J. Budziszewski clarifies and analyzes the text's challenging arguments about the moral, intellectual, and spiritual virtues, with a spotlight on the virtue of justice. In what might be the first contemporary commentary on Aquinas's virtue ethics, he juxtaposes the original text with paraphrase and detailed discussion, guiding us through its complex arguments (...) and classical rhetorical figures. Keeping an eye on contemporary philosophical issues, he contextualizes one of the greatest virtue theorists in history and brings Aquinas into the interdisciplinary debates of today. His brisk and clear style illuminates the most crucial of Aquinas' writings on moral character and guides us through the labyrinth of this difficult but pivotal work. (shrink)

J. Arthur Baird is the author of several important books in New Testament studies, his best known perhaps being his Audience Criticism and the Historical Jesus. At his untimely death, he left a nearly complete manuscript, now published here. In this timely and relevant manuscript, Baird offers first a critical introduction to the historical paradigm, pointing out its limitations in terms of tracing the paradigm of New Testament formation. He then traces this development himself, beginning with the starting point of (...) the Holy Word and noting its development through the context, theological interpretation, and application, to its manifestation in the apostles, schools and fathers. He concludes with comments on its current implications. This book represents the last and lasting final thoughts of a scholar who was very much devoted to the importance of the Holy Word. (shrink)

Celebrating the remarkable career of jurist Harold J. Berman, the essays in this volume demonstrate that Berman's contributions to Russian studies, international trade law, legal history, philosophy of law, and law and religion have firmly established him as part of the tradition of our greatest American jurists.

Upon first glance, readers might not think there is much new to be found in the most recent book from Wesley Wildman. After all, seven of the nine chapters contained between its covers began as essays previously published. However, this volume is also the sixth of six in his Religious Philosophy series, so clearly the author is making something of its contents. Indeed, there is much that is worthwhile to be found within. Taken together with the new material, this collection (...) of essays immediately reveals the depths of Wildman's pragmatic commitments. The chapters do not build upon one another like links in a chain or floors in a building from the foundation to the executive suites.... (shrink)

L'eschatologie a marqué la théologie chrétienne du XXe siècle. Initiateur en ce domaine, R. Bultmann entreprend une herméneutique « existentiale » et « démythologisante » de la prédication apocalyptique de Jésus, mise en lumière par J. Weiss et A. Schweitzer : en Jésus Dieu prononce la parole définitive qui m'appelle aujourd'hui à la décision de foi et à l'existence authentique. La théologie apprend ainsi à parler de Dieu avec sens en parlant de l'homme. Avec J. Moltmann, le futur est désenclavé (...) du présent où le laissait Bultmann, et l'eschatologie se fait résolument christologique en même temps qu'historique ; mais le passage de la Théologie de l’espérance au Dieu crucifié pose le problème redoutable du lien entre l’horizon de l’espérance et l'histoire abandonnée à la souffrance. Pour J. Moingt, la résurrection, fondement de la christologie, permet de relire la vie de Jésus comme l’histoire de Dieu menant avec les hommes depuis la création le combat eschatologique de la vie contre la mort.La pensée eschatologique s’élabore aussi dans la ligne des théologiens de l'histoire. O. Cullmann fait du Christ le centre de l’histoire du salut, entre un « déjà là » et un « pas encore ». Avec plus d’ambition mais aussi d’ambiguïté, W. Pannenberg situe la résurrection de Jésus, en tant qu’événement historique, au regard de l'histoire universelle dont elle anticipe la fin. La pensée eschatologique ne laisse pas de travailler également d’autres théologies, davantage marquées par les problématiques traditionnelles.Twentieth century Christian theology has been marked by eschatology. R. Bultmann, initiator in this field, underlook an “existential” and “demythologising” hermeneutic of the apocalyptic preaching of Jesus, which had been brought. to light by J. Weiss and A. Schweitzer : in Jesus God pronounces the definitive word that calls me to a decision of faith and authentic existence today. Theology thus learns to speak of God with meaning by speaking of man. With J. Moltmann, the future is freed from present, where Bultmann had left it, and eschatology became resolutely Christological at the same time as historical. But the passage from the Theology of Hope to the Crucified God poses the difficult problem of the connection between the horizon of hope and history left to suffering. For J. Moingt, the resurrection, foundation of Christology, permits a rereading of the life of Jesus as the history of God, who, from the time of creation, leads humanity in the eschatological combat of life against death.Eschatological thought also develops in the direction of theologies of history. O. Cullmann makes Christ the center of the history of salvation, between an “already here” and a “not yet”. With greater ambition but also ambiguity, W Pannenberg places the resurrection of Jesus as a historical event, in comparison with universal history, of which it anticipates the end. Eschatological thought does not fail to also influence others theologies, more marked by traditional problematics. (shrink)