INTRODUCTION MATHEMATICAL logic differs from the traditional formal logic so markedly in method, and so far surpasses it in power and subtlety, ...

This is a wide-ranging 2004 book about arguments for and against beliefs in God. The arguments for the belief are analysed in the first six chapters and include ontological arguments from Anselm to Gödel, the cosmological arguments of Aquinas and Leibniz, and arguments from evidence for design and miracles. The next two chapters consider arguments against belief. The last chapter examines Pascalian arguments for and against belief in God. There are discussions of Cantorian problems for omniscience, of challenges to divine (...) omnipotence, and of the compatibility of everlasting complete knowledge of the world with free-will. There are appendices that present formal proofs in a system for quantified modal logic, a theory of possible worlds, notes on Cantorian set theory, and remarks concerning non-standard hyperreal numbers. This book will be a valuable resource for philosophers of religion and theologians and will interest logicians and mathematicians as well. (shrink)

Sets of contingent objects, perhaps, are as contingent as their members; but properties, propositions, numbers and states of affairs, it seems, are objects whose non-existence is quite impossible. If so, however, how are they related to God? Suppose God has a nature: a property he has essentially that includes each property essential to him. Does God have a nature? And if he does, is there a conflict between God's sovereignty and his having a nature? How is God related to such (...) abstract objects as properties and propositions? These are the questions I want to explore. - Introduction. (shrink)

This is the first single-volume edition and translation of Frege's philosophical writings to include his seminal papers as well as substantial selections from ...

A deep and precise introduction to the philosophy of religion that is also remarkably clear and insightful. The author has a conversation with the student and uses concrete examples to explain often abstract concepts and issues.

The doctrine of divine simplicity, according to which God is devoid of physical or metaphysical complexity, is widely believed to be incoherent. I argue that although two prominent recent attempts to defend it fail, it can be defended against the charge of obvious incoherence. The defense rests on the isolation and rejection of a crucial assumption, namely, that no property is an individual. I argue that there is nothing in our ordinary concepts of property and individual to warrant the assumption, (...) and that once the assumption is rejected, the way is clear to viewing the divine attributes as self-exemplifying properties whose self-exemplification entails their identity with an individual. (shrink)

The doctrine of God’s absolute simplicity denies the possibility of real distinctions in God. It is, e.g., impossible that God have any kind of parts or any intrinsic accidental properties, or that there be real distinctions among God’s essential properties or between any of them and God himself. After showing that some of the counter-intuitive implications of the doctrine can readily be made sense of, the authors identify the apparent incompatibility of God’s simplicity and God’s free choice as a special (...) difficulty and associate it with two others: the apparent incompatibilities between essential omnipotence and essential goodness, and between perfect goodness and moral goodness. Since all three of these difficulties are associated with a certain understanding of the nature of God’s will, the authors base their resolution of them on an account of will in general and of God’s will in particular, drawing on Aquinas’s theory of will.Taking creation as their paradigm of divine free choice, the authors develop a solution of the principal incompatibility based on three claims: God’s acts of choice are both free and conditionally necessitated; the difference between absolutely and conditionallynecessitated acts of will is not a real distinction in God; and the conditional necessity of God’s acts of will is compatible with contingency in the objects of those acts. The heart of their solution consists in their attempt to make sense of and support those claims.The authors extend their solution to cover the two associated apparent incompatibilities as well.The article concludes with observations on the importance of the doctrine of God’s absolute simplicity for resolving problems in religious morality and in the cosmological argument. (shrink)

One of the most difficult and perplexing tenets of classical theism is the doctrine of divine simplicity. Broadly put, this is generally understood to be the thesis that God is altogether without any proper parts, composition, or metaphysical complexity whatsoever. For a good deal more than a millennium, veritable armies of philosophical theologians – Jewish, Christian and Islamic – proclaimed the truth and importance of divine simplicity. Yet in our own time, the doctrine has enjoyed no such support. Among many (...) otherwise orthodox theists, those who do not just disregard it completely explicitly deny it. However, in a couple of recent articles, William E. Mann has attempted to expound the idea of divine simplicity anew and to defend it against a number of criticisms. He even has gone so far as to hint at reaffirming its importance, suggesting that the doctrine may have a significant amount of explanatory power and other theoretical virtue as part of an overall account of the nature of God, by either entailing or in other ways providing for much else that traditional theists have wanted to say about God. In this paper, I want to take a close look at Mann's formulation of the doctrine and at a general supporting theory he adumbrates in his attempt to render more plausible, or at least more defensible, various of its elements and implications. As Mann has made what is arguably the best attempt to defend the doctrine in recent years, I think that such an examination is important and will repay our efforts. (shrink)

One of the most difficult and perplexing tenets of classical theism is the doctrine of divine simplicity. Broadly put, this is generally understood to be the thesis that God is altogether without any proper parts, composition, or metaphysical complexity whatsoever. For a good deal more than a millennium, veritable armies of philosophical theologians – Jewish, Christian and Islamic – proclaimed the truth and importance of divine simplicity. Yet in our own time, the doctrine has enjoyed no such support. Among many (...) otherwise orthodox theists, those who do not just disregard it completely explicitly deny it. However, in a couple of recent articles, William E. Mann has attempted to expound the idea of divine simplicity anew and to defend it against a number of criticisms. He even has gone so far as to hint at reaffirming its importance, suggesting that the doctrine may have a significant amount of explanatory power and other theoretical virtue as part of an overall account of the nature of God, by either entailing or in other ways providing for much else that traditional theists have wanted to say about God. In this paper, I want to take a close look at Mann's formulation of the doctrine and at a general supporting theory he adumbrates in his attempt to render more plausible, or at least more defensible, various of its elements and implications. As Mann has made what is arguably the best attempt to defend the doctrine in recent years, I think that such an examination is important and will repay our efforts. (shrink)

The doctrine of divine simplicity, the doctrine that God has no physical or metaphysical complexity whatsoever, is not a doctrine designed to induce immediate philosophical acquiescence. There are severe questions about its coherence. And even if those questions can be answered satisfactorily in favour of the doctrine, there remains the question why anyone should accept it. Thomas V. Morris raises both sorts of questions about a version of the doctrine which I have put forward. In the following pages I shall (...) respond to what I take to be the most serious of Morris's objections. I shall argue that the doctrine survives Morris's onslaught, but that one observation of his points it in a direction I had hitherto not taken seriously. The bulk of Morris's paper raises questions of the first sort; perforce the bulk of my paper will also. I shall offer, at the end, a reason for thinking that neither of us is yet in a position to pronounce categorically on the second question. My remarks in this paper constitute an interim report on how I think things presently stand with divine simplicity. (shrink)

In The City of God, XI, 10, St Augustine claims that the divine nature is simple because ‘it is what it has’ (quod habet hoc est). We may take this as a slogan for the Doctrine of Divine Simplicity (DDS), a doctrine which finds its way into orthodox medieval Christian theological speculation. Like the doctrine of God's timeless eternality, the DDS has seemed obvious and pious to many, and incoherent, misguided, and repugnant to others. Unlike the doctrine of God's timeless (...) eternality, the DDS has received very little critical attention. The DDS did not originate with Augustine, but I am not primarily concerned with its pedigree. Nor am I concerned to ask how the doctrine interacts with trinitarian speculation. I will have my hands full as it is. In Section I of this paper I shall provide a rough characterization of the DDS, indicate its complexity, and focus on a particular aspect of the doctrine which will exercise us in the remainder of the paper, namely, the thesis that the divine attributes are all identical with each other and with God. In section n I shall discuss Alvin Plantinga's recent objections to Aquinas' version of the DDS. I shall then offer a more detailed presentation of what I take to be Aquinas' version (section III), and recast it in terms of a theory of attributes which is significantly different from Plantinga's (section IV). Although the recasting of the doctrine will enable me to rebut Plantinga's objections (section v), it by no means solves all the problems of the DDS. In section vi I shall discuss the chief lingering problem facing a defender of the DDS. (shrink)

In The City of God , XI, 10, St Augustine claims that the divine nature is simple because ‘it is what it has’ . We may take this as a slogan for the Doctrine of Divine Simplicity , a doctrine which finds its way into orthodox medieval Christian theological speculation. Like the doctrine of God's timeless eternality, the DDS has seemed obvious and pious to many, and incoherent, misguided, and repugnant to others. Unlike the doctrine of God's timeless eternality, the (...) DDS has received very little critical attention. The DDS did not originate with Augustine, but I am not primarily concerned with its pedigree. Nor am I concerned to ask how the doctrine interacts with trinitarian speculation. I will have my hands full as it is. In Section I of this paper I shall provide a rough characterization of the DDS, indicate its complexity, and focus on a particular aspect of the doctrine which will exercise us in the remainder of the paper, namely, the thesis that the divine attributes are all identical with each other and with God. In section n I shall discuss Alvin Plantinga's recent objections to Aquinas' version of the DDS. I shall then offer a more detailed presentation of what I take to be Aquinas' version , and recast it in terms of a theory of attributes which is significantly different from Plantinga's . Although the recasting of the doctrine will enable me to rebut Plantinga's objections , it by no means solves all the problems of the DDS. In section vi I shall discuss the chief lingering problem facing a defender of the DDS. (shrink)

Before Duns Scotus, most philosophers agreed that God is identical with His necessary intrinsic attributes--omnipotence, omniscience, etc. This Identity Thesis was a component of widely held doctrines of divine simplicity, which stated that God exemplifies no metaphysical distinctions, including that between subject and attribute. The Identity Thesis seems to render God an attribute, an abstract object. This paper shows that the Identity Thesis follows from a basic theistic belief and does not render God abstract. If also discusses how one might (...) move from the Identity Thesis to the full doctrine of divine simplicity and shows that the Identity Thesis generates a new ontological argument. (shrink)

Die theoretische Logik, auch mathematische oder symbolische Logik genannt, ist eine Ausdehnung der fonnalen Methode der Mathematik auf das Gebiet der Logik. Sie wendet fUr die Logik eine ahnliche Fonnel­ sprache an, wie sie zum Ausdruck mathematischer Beziehungen schon seit langem gebrauchlich ist. In der Mathematik wurde es heute als eine Utopie gelten, wollte man beim Aufbau einer mathematischen Disziplin sich nur der gewohnlichen Sprache bedienen. Die groBen Fortschritte, die in der Mathematik seit der Antike gemacht worden sind, sind zum (...) wesentlichen Teil mit dadurch bedingt, daB es gelang, einen brauchbaren und leistungsfahigen Fonnalismus zu finden. - Was durch die Formel­ sprache in der Mathematik erreicht wird, das solI auch in der theoretischen Logik durch diese erzielt werden, namlich eine exakte, wissenschaftliche Behandlung ihres Gegenstandes. Die logischen Sachverhalte, die zwischen Urteilen, Begriffen usw. bestehen, finden ihre Darstellung durch Formeln, deren Interpretation frei ist von den Unklarheiten, die beim sprachlichen Ausdruck leicht auftreten konnen. Der Dbergang zu logischen Folgerungen, wie er durch das SchlieBen geschieht, wird in seine letzten Elemente zerlegt und erscheint als fonnale Umgestaltung der Ausgangsfonneln nach gewissen Regeln, die den Rechenregeln in der Algebra analog sind; das logische Denken findet sein Abbild in einem LogikkalkUl. Dieser Kalkiil macht die erfolgreiche Inangriffnahme von Problemen moglich, bei denen das rein inhaltliche Denken prinzipiell versagt. Zu diesen gehort z. B. (shrink)

Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Ja?kowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks?the standard conduits of (...) the method to a generation of philosophers?with an eye to determining what the ?essential characteristics? of natural deduction are. (shrink)