Can belief in God be rationally justified? Reviewing in detail traditional and modern arguments for and against the existence of God, Professor Plantinga concludes that they must all be judged unsuccessful. He then turns to the related philosophical problem of the existence of other minds, and defends the so-called analogical argument against current criticisms. He goes on to show, however, that although this argument affords us the best reasons we have for belief in other minds, it finally succumbs to the (...) same malady that afflicts the teleological argument of God. (shrink)

One of the cornerstones of western theology is the doctrine of divine omnipotence. God is traditionally conceived of as an omnipotent or all-powerful being. However, satisfactory analyses of omnipotence are notoriously elusive. In this paper, I first consider some simple attempts to analyze omnipotence, showing how each fails. I then consider two more sophisticated accounts of omnipotence. The first of these is presented by Edward Wierenga; the second by Thomas Flint and Alfred Freddoso. I argue that both of these accounts (...) fail. Finally, I propose and defend a novel account of omnipotence. (shrink)

Gödel has argued that we can cultivate the intuition or perception of abstractconcepts in mathematics and logic. Gödel's ideas about the intuition of conceptsare not incidental to his later philosophical thinking but are related to many otherthemes in his work, and especially to his reflections on the incompleteness theorems.I describe how some of Gödel's claims about the intuition of abstract concepts are related to other themes in his philosophy of mathematics. In most of this paper, however,I focus on a central (...) question that has been raised in the literature on Gödel: what kind of account could be given of the intuition of abstract concepts? I sketch an answer to this question that uses some ideas of a philosopher to whom Gödel also turned in this connection: Edmund Husserl. The answer depends on how we understand the conscious directedness toward objects and the meaning of the term abstract in the context of a theory of the intentionality of cognition. (shrink)

Gödel has argued that we can cultivate the intuition or ‘perception’ of abstractconcepts in mathematics and logic. Gödel's ideas about the intuition of conceptsare not incidental to his later philosophical thinking but are related to many otherthemes in his work, and especially to his reflections on the incompleteness theorems.I describe how some of Gödel's claims about the intuition of abstract concepts are related to other themes in his philosophy of mathematics. In most of this paper, however,I focus on a central (...) question that has been raised in the literature on Gödel: what kind of account could be given of the intuition of abstract concepts? I sketch an answer to this question that uses some ideas of a philosopher to whom Gödel also turned in this connection: Edmund Husserl. The answer depends on how we understand the conscious directedness toward ‘objects’ and the meaning of the term ‘abstract’ in the context of a theory of the intentionality of cognition. (shrink)

This paper provides examples in arithmetic of the account of rational intuition and evidence developed in my book After Gödel: Platonism and Rationalism in Mathematics and Logic . The paper supplements the book but can be read independently of it. It starts with some simple examples of problem-solving in arithmetic practice and proceeds to general phenomenological conditions that make such problem-solving possible. In proceeding from elementary ‘authentic’ parts of arithmetic to axiomatic formal arithmetic, the paper exhibits some elements of the (...) genetic analysis of arithmetic knowledge that is called for in Husserl’s philosophy. This issues in an elaboration on a number of Gödel’s remarks about the meaning of his incompleteness theorems for the notion of evidence in mathematics. (shrink)

Numerous examples have been offered that purportedly show that God cannot be omnipotent. I argue that a common response to such examples (i.e., that failure to do the impossible does not indicate a lack of power) does not preserve God’s omnipotence in the face of some of these examples. I consider another possible strategy for preserving God’s omnipotence in the face of these examples and find it wanting.

This book, one of the first full-length studies of the modalities to emerge from the debate to which Saul Kripke, David Lewis, Ruth Marcus, and others are contributing, is an exploration and defense of the notion of modality de re, the idea that objects have both essential and accidental properties. Plantinga develops his argument by means of the notion of possible worlds and ranges over such key problems as the nature of essence, transworld identity, negative existential propositions, and the existence (...) of unactual objects in other possible worlds. He also applies his logical theories to the elucidation of two problems in the philosophy of religion: the problem of evil and the ontological argument. (shrink)

Ternary exclusive or is the truth function that is true just in case exactly one of its three arguments is true. This is an interesting truth function, not definable in terms of the binary exclusive or alone, although the binary case is definable in terms of the ternary case. This article investigates the types of truth functions that can be defined by ternary exclusive or, and relates these findings to the seminal work of Emil Post.

This paper aims to show that Godel's ontological argument can be parodied in much the same kind of way in which Gaunilo parodied Anselm's Proslogion argument. The parody in this paper fails; there is a patch provided in "Reply to Gettings" (Analysis 60, 4, 2000, 363-7).

For any essential property God has, there is an ability He does not have. He is unable to bring about any state of affairs in which He does not have that property. Such inabilities seem to preclude omnipotence. After making trouble for the standard responses to this problem, I offer my own solution: God is not omnipotent. This may seem like a significant loss for the theist. But I show that it is not. The theist may abandon the doctrine that (...) God is omnipotent without scaling back the extent of His power and without denying that He has all perfections. (shrink)

An eleventh-century Greek text, in which a fourth-century patristic text is discussed, gives an outline of a solution to the Liar Paradox. The eleventh-century text is probably the first medieval treatment of the Liar. Long passages from both texts are translated in this article. The solution to the Liar Paradox, which they entail, is analysed and compared with the results of modern scholarship on several Latin solutions to this paradox. It is found to be a solution, which bears some analogies (...) to contemporary game semantics. Further, an overview of other Byzantine scholia on the Liar Paradox is provided. The findings and the originality of the discussed solution to the Liar Paradox suggest a change in the way in which Byzantine Logic is traditionally regarded in contemporary scholarship. (shrink)

It is fortunate for my purposes that English has the two words ‘almighty’ and ‘omnipotent’, and that apart from any stipulation by me the words have rather different associations and suggestions. ‘Almighty’ is the familiar word that comes in the creeds of the Church; ‘omnipotent’ is at home rather in formal theological discussions and controversies, e.g. about miracles and about the problem of evil. ‘Almighty’ derives by way of Latin ‘omnipotens’ from the Greek word ‘ pantokratōr ’; and both this (...) Greek word, like the more classical ‘ pankratēs ’, and ‘almighty’ itself suggest God's having power over all things. On the other hand the English word ‘omnipotent’ would ordinarily be taken to imply ability to do everything; the Latin word ‘omnipotens’ also predominantly has this meaning in Scholastic writers, even though in origin it is a Latinization of ‘ pantocratōr ’. So there already is a tendency to distinguish the two words; and in this paper I shall make the distinction a strict one. I shall use the word ‘almighty’ to express God's power over all things, and I shall take ‘omnipotence’ to mean ability to do everything. (shrink)

Semantic interpretations of both natural and formal languages are usually taken to involve the specification of a domain of entities with respect to which the sentences of the language are to be evaluated. A question that has received much attention of late is whether there is unrestricted quantification, quantification over a domain comprising absolutely everything there is. Is there a discourse or inquiry that has absolute generality? After framing the debate, this article provides an overview of the main arguments for (...) and against the possibility of unrestricted quantification, highlighting some of the broader implications of the debate. (shrink)

Analytic theology has sometimes been criticized as ahistorical. But what this means, and why it is problematic, have often been left unclear. This essay explicates and supports one way of making that charge while simultaneously showing this ahistoricity, although widespread within analytic theology, is not essential to it. Specifically, some analytic theologians treat problematic doctrines as metaphysical puzzles, constructing speculative accounts of phenomena such as the Trinity or Incarnation and taking the theoretical virtues of such accounts to be sufficient in (...) themselves to defend traditional doctrines with no need for additional, historical premises. But due to the different epistemic structures of metaphysical and theological puzzles, I argue that importing this methodology into philosophical theology results in invalid or question-begging arguments, and it is unclear how a virtue-centric methodology could be repaired without collapsing into a more historical methodology, which some of the best (but unfortunately not all) analytic theologians follow. (shrink)

Prima facie, relative identity looks like a perfect fit for the doctrine of the Trinity since it allows us to say that the Father, Son and Holy Spirit, each of which is a Trinitarian Person, are the same God but not the same Person. Nevertheless, relative identity solutions to logic puzzles concerning the doctrine of the Trinity have not, in recent years, been much pursued. Critics worry that relative identity accounts are unintuitive, uninformative or unintelligible. I suggest that the relative (...) identity account is worth a second look and argue that it provides a coherent account of the doctrine of the Trinity. (shrink)

It is difficult to reconcile claims about the Father's role as the progenitor of Trinitarian Persons with commitment to the equality of the persons, a problem that is especially acute for Social Trinitarians. I propose a metatheological account of the doctrine of the Trinity that facilitates the reconciliation of these two claims. On the proposed account, ‘Father’ is systematically ambiguous. Within economic contexts, those which characterize God's relation to the world, ‘Father’ refers to the First Person of the Trinity; within (...) theological contexts, which purport to describe intra-Trinitarian relations, it refers to the Trinity in toto-thus in holding that the Son and Holy Spirit proceed from the Father we affirm that the Trinity is the source and unifying principle of Trinitarian Persons. While this account is solves a nagging problem for Social Trinitarians it is theologically minimalist to the extent that it is compatible with both Social Trinitarianism and Latin Trinitarianism, and with heterodox Modalist and Tri-theist doctrines as well. Its only theological cost is incompatibility with the Filioque Clause, the doctrine that the Holy Spirit proceeds from both the Father and the Son—and arguably that may be a benefit. (shrink)

In this paper, I argue that the supposition of divine omnipotence entails a contradiction: omnipotence both must and must not be intrinsic to God. Hence, traditional theism must be rejected. To begin, I separate out some theoretical distinctions needed to inform the discussion. I then advance two different arguments for the conclusion that omnipotence must be intrinsic to God; these utilise the notions of essence and aseity. Next, I argue that some necessary conditions on being omnipotent are extrinsic, and that (...) this means omnipotence cannot be intrinsic to God. I consider three different ways of resolving this conflict, but contend that each is unsuccessful. Before concluding, I explain why the type of strategy used to resolve the traditional paradoxes of omnipotence cannot be successfully employed against the paradox presented here. (shrink)

"A Crossroad book." Translation of Grundkurs des Glaubens.

Not many years ago Carl Jung levelled the charge of “ crackpot psychology” against the philosophical writings of Hegel.1 There is, of course, an element of truth in Jung’s stricture; for one has only to read again the Phenomenology of Spirit in order to realize anew that the conceptual matrix of this work is an account of the self’s psycho-social development. Thus, both Hegel’s notion that the Other is a necessary condition of my selfidentity and his account of the master-slave (...) relationship draw upon psychological insights which become transformed into metaphysical utterances in the doctrine that the Logical Idea must pass over into Nature—that Nature, as other than Idea, is estranged Idea. Though Jung’s criticism is intended negatively, it serves positively to point up the interrelationship that has often (though not always) existed between philosophy and psychology—the former paying house calls (not sick calls) to the latter. In recent years psychology has returned the visit. A growing group of psychologists have turned to philosophy in order to borrow categories for interpreting various patterns of neurosis and psychosis. And here and there isolated voices have accused them of “ crackpot philosophy.” I am referring, of course, to the school of existential psychotherapy, which has by and large adopted Heidegger’s categories of being-in-the-world, facticity, thrownness, care, temporality, lived-space, authenticity, everydayness, project, freedom, anxiety, utensility, and being-unto-death as ready-made schemes for focusing neurotic and psychotic syndromes. Such reliance upon Heidegger’s existential analysis of human reality has tended to minimize the use of Sartre’s philosophy. (shrink)

Absolute identity seems at first sight to be presupposed in the branch of formal logic called identity theory. Classical identity theory may be obtained by adjoining a single schema to ordinary quantification theory.

The main subject of Cusanus’ investigations was the name of God. He claimed to have achieved the best possible one, Not-Other. Since Cusanus stressed that these two words do not mean the corresponding affirmative word, i.e. the same, they represent the failure of the double negation law and there￾fore belong to non-classical, and above all, intuitionist logic. Some of his books implicitly applied intuitionist reasoning and the corresponding organization of a theory which is governed by intuitionist logic. A comparison of (...) two of Cusanus’ short writings shows that throughout his life he substantially improved his use of this kind of logic and ultimately was able to reason consistently within such a logic and recognize some of its basic laws. One important idea developed by him was that of a proposition composed of a triple repetition of “not-other” expressing “the Tri-unity of concordance” i.e. the “best name for the Trinity”. I complete his application of intuitionist logic to theological subjects by charac￾terizing the inner relationships within the Trinity in such a way that there are no longer contradictions in the notion. Generally speaking, the notion of the Trin￾ity implies a translation from intuitionist to classical logic, to which Cusanus closely approximated. Moreover, I show that the main aspects of Christian rev￾elation, including Christ’s teachings, are represented both by this translation and by some doubly negated propositions of intuitionist logic. Hence, intuition￾ist logic was introduced into the history of Western theological thinking with Christian revelation, as only Cusanus partly recognized. Appendix 1 summa￾rizes a detailed analysis of Cusanus’ second short writing. Appendix 2 shows that the Athanasian creed regarding the Christian Trinity is a consistent se￾quence of intuitionist propositions provided that some verbal emendations are added, showing that ancient trinitarian thinking was also close to intuitionist reasoning. (shrink)

The doctrine of the Trinity is central to mainstream Christianity. But insofar as it posits “three persons” (Father, Son and Holy Spirit), who are “one God,” it appears as inconsistent as the claim that 1+1+1=1. -/- Much of the literature on “The Logical Problem of the Trinity,” as this has been called, attacks or defends Trinitarianism with little regard to the fourth century theological controversies and the late Hellenistic and early Medieval philosophical background in which it took shape. I argue (...) that this methodol- ogy, which I call “the Puzzle Approach,” produces obviously invalid arguments, and it is unclear how to repair it without collapsing into my preferred method- ology, “the Historical Approach,” which sees history as essential to the debate. I also discuss “mysterianism,” arguing that, successful or not, it has a different goal from the other approaches. I further argue that any solution from the His- torical Approach satisfies the concerns of the Puzzle Approach and mysterianism anyway. -/- I then examine the solution to the Logical Problem of the Trinity found in St. Gregory of Nyssa’s writings, both due to his place in the history of the doctrine, and his clarity in explicating what I call “the metaphysics of synergy.” I recast his solution in standard predicate logic and provide a formal proof of its consistency. I end by considering the possibilities for attacking the broader philosophical context of his defense and conclude that the prospects for doing so are dim. In any case, if there should turn out to be any problem with the doctrine of the Trinity at all, it will not be one of mere logical inconsistency in saying that “These Three are One.”. (shrink)

Review of Graham Oppy *Ontological Arguments and Belief in God* (CUP).