This book, one of the handful of truly pathbreaking works in twentieth-century philosophical theology, presents Hartshorne's persuasive rehabilitation of Anselm's Ontological Argument, recast in neoclassical form as "the Modal Proof.".

Graham Priest presents an expanded edition of his exploration of the nature and limits of thought. Embracing contradiction and challenging traditional logic, he engages with issues across philosophical borders, from the historical to the modern, Eastern to Western, continental to analytic.

The authors investigated the ontological argument computationally. The premises and conclusion of the argument are represented in the syntax understood by the automated reasoning engine PROVER9. Using the logic of definite descriptions, the authors developed a valid representation of the argument that required three non-logical premises. PROVER9, however, discovered a simpler valid argument for God's existence from a single non-logical premise. Reducing the argument to one non-logical premise brings the investigation of the soundness of the argument into better focus. Also, (...) the simpler representation of the argument brings out clearly how the ontological argument constitutes an early example of a ?diagonal argument? and, moreover, one used to establish a positive conclusion rather than a paradox. (shrink)

Anselm of Canterbury, in his work Proslogion," originated the "ontological argument" for God's existence, famously arguing that "something than which nothing greater can be conceived," which he identifies with God, must actually exist, for otherwise something greater could indeed be conceived. Some commentators have claimed that although Anselm may not have been conscious of the fact, the Proslogion "as well as his Reply to Gaunilo" contains passages that constitute a second independent proof: a "modal ontological argument" that concerns the supposed (...) logical necessity of God's existence. Other commentators disagree, countering that the alleged second argument does not stand on its own but presupposes the conclusion of the first. Anselm's Other Argument "stakes an original claim in this debate, and takes it further. There is" a second a priori" argument in Anselm, A. D. Smith contends, but it is not the modal argument past scholars have identified. This second argument surfaces in a number of forms, though always turning on certain deep, interrelated metaphysical issues. It is this form of argument that in fact underlies several of the passages which have been misconstrued as statements of the modal argument. In a book that combines historical research with rigorous philosophical analysis, Smith discusses this argument in detail, finally defending a modification of it that is implicit in Anselm. This "other argument" bears a striking resemblance to one that Duns Scotus would later employ. (shrink)

In his essay Tracy Lupher (henceforth, TL) is concerned with Robert Kane's (1984) version of the modal ontological argument (MOA). As he correctly points out, Kane's argument is valid only if the accessibility relation between possible worlds is assumed to be symmetric. TL's remarks pave the way to thinking that the MOA is intended to establish the existence of a perfect being as a matter of logical necessity. Moreover, given TL's undisputed supposition (even shared by Kane) that S5 - in (...) which the accessibility relation is symmetric - captures the notion of logical necessity, the real issue becomes whether the premise of the MOA is true. Contrary to TL's main claim, the discussion thus shifts back from technical arguments for why the appropriate modal logic must have a symmetric accessibility relation to metaphysical, theological, or conceptual considerations about the notion of a perfect being itself. I argue that it is only due to such considerations that we even start to ponder the question of what modal logic is the appropriate one to choose. (shrink)

The structure of the second, Or so-Called modal version of anselm's ontological argument is discussed in relation to various systems of alethic modal logic. It is argued that there are three current problems standing in the way of acceptance of the argument, Each related to its modal structure, And each an analogue of a traditional objection to anselm's original argument. Two of these problems can probably be solved, But the third remains recalcitrant.

This note discusses P. Oppenheimer and E. Zalta's ?A Computationally-Discovered Simplification of the Ontological Argument? [this journal, 2011]. I try to explain why the simplification presented there was successful and comment on the technical aspects of the method they applied.

The authors investigated the ontological argument computationally. The premises and conclusion of the argument are represented in the syntax understood by the automated reasoning engine PROVER9. Using the logic of definite descriptions, the authors developed a valid representation of the argument that required three non-logical premises. PROVER9, however, discovered a simpler valid argument for God's existence from a single non-logical premise. Reducing the argument to one non-logical premise brings the investigation of the soundness of the argument into better focus. Also, (...) the simpler representation of the argument brings out clearly how the ontological argument constitutes an early example of a ‘diagonal argument’ and, moreover, one used to establish a positive conclusion rather than a paradox. (shrink)

In this paper, we discuss formal reconstructions of Anselm’s ontological argument. We first present a number of requirements that any successful reconstruction should meet. We then offer a detailed preparatory study of the basic concepts involved in Anselm’s argument. Next, we present our own reconstructions—one in modal logic and one in classical logic—and compare them with each other and with existing reconstructions from the reviewed literature. Finally, we try to show why and how one can gain a better understanding of (...) Anselm’s argument by using modern formal logic. In particular, we try to explain why formal reconstructions of the argument, despite its apparent simplicity, tend to become quite involved. (shrink)

Scholars were greatly indebted to Max Charlesworth for publishing in 1965 the Latin text of Anselm’s Proslogion, together with his own translation and commentary. The intense discussion this argument has received since then has, however, clarified a number of points about the logic of this argument. Its first premise is not a definition of God, and that identification is one of the conclusions of a three-stage argument. Also, the much-discussed issue of the relation of Chap. 3 to Chap. 2 has (...) now been clarified: that the premise with which Anselm begins Chap. 3 is entailed by the conclusion of Chap. 2. For that reason, substituting a description of anything other than God for Anselm’s formula, such as Gaunilo’s Lost Island, entails that that thing both can and could not be thought not to exist. So, no such substitution is legitimate. (shrink)

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)

This is a philosophical investigation of the nature of the limits of thought. Drawing on recent developments in the field of logic, Graham Priest shows that the description of such limits leads to contradiction, and argues that these contradictions are in fact veridical. Beginning with an analysis of the way in which these limits arise in pre-Kantian philosophy, Priest goes on to illustrate how the nature of these limits was theorised by Kant and Hegel. He offers new interpretations of Berkeley's (...) master argument for idealism and Kant on the antimonies. He explores the paradoxes of self reference, and provides a unified account of the structure of such paradoxes. The book concludes by tracing the theme of the limits of thought in modern philosophy of language, including discussions of the ideas of Wittgenstein and Derrida. (shrink)

This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: _An Introduction to Modal Logic_ and _A Companion to Modal Logic_. _A New Introduction to Modal Logic_ is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. The book takes (...) readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic. (shrink)