By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

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)

This book is a unique contribution to the philosophy of religion. It offers a comprehensive discussion of one of the most famous arguments for the existence of God: the ontological argument. The author provides and analyses a critical taxonomy of those versions of the argument that have been advanced in recent philosophical literature, as well as of those historically important versions found in the work of St Anselm, Descartes, Leibniz, Hegel and others. A central thesis of the book is that (...) ontological arguments have no value in the debate between theists and atheists. There is a detailed review of the literature on the topic (separated from the main body of the text) and a very substantial bibliography, making this volume an indispensable resource for philosophers of religion and others interested in religious studies. (shrink)

In this paper, the authors show that there is a reading of St. Anselm's ontological argument in Proslogium II that is logically valid (the premises entail the conclusion). This reading takes Anselm's use of the definite description "that than which nothing greater can be conceived" seriously. Consider a first-order language and logic in which definite descriptions are genuine terms, and in which the quantified sentence "there is an x such that..." does not imply "x exists". Then, using an ordinary logic (...) of descriptions and a connected greater-than relation, God's existence logically follows from the claims: (a) there is a conceivable thing than which nothing greater is conceivable, and (b) if <em>x</em> doesn't exist, something greater than x can be conceived. To deny the conclusion, one must deny one of the premises. However, the argument involves no modal inferences and, interestingly, Descartes' ontological argument can be derived from it. (shrink)

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).

This chapter contains sections titled: The Validity of Anselm's Ontological Argument The Truth of the Anselmian Premises On Whether Anselm's Ontological Argument Begs the Question On Parodies The Validity of the Ontological Argument of Descartes and Leibniz On the Truth of the Descartes–Leibniz Premises Critiques of the Descartes–Leibniz Ontological Argument Ontological Arguments of the Twentieth Century Gödel's Ontological Argument On Whether Gödel's Argument is Sound The Modal Perfection Argument The Temporal‐Contingency Argument Conclusion References Appendix 1. Logic Matters Appendix 2. Formal (...) Proofs of Some Modal Arguments. (shrink)

We describe a KB Gödelian ontological system, and some other weak systems, in a fully formal way using theory of types and natural deduction, and present a completeness proof in its main and specific parts. We technically and philosophically analyze and comment on the systems (mainly with respect to the relativism of values) and include a sketch of some connected aspects of Gödel's relation to Kant.

The taste of this particular chunk of fresh pineapple, the one which I am just now eating, is scrumptious. That taste is something the chunk has in common with other such chunks, like the one I had a few seconds ago and the one I will have in a few seconds time. The taste of this pineapple chunk is thus a feature, a property, which this and various other chunks of pineapple share. Now, intuitively at least, no purely mathematical entity, (...) like a function, is scrumptious. Hence a property, like the taste of this chunk of pineapple, cannot be any such function. This kind of argument, if sound, would cut a wide swathe through the field of metaphysics. All those theories which attempt to reduce onto logically suspicious types of entities to mathematical entities would fall to the blade. This could well help to reduce the impact of contemporary philosophy on the world's dwindling forests. I save contemporary metaphysics by explaining where the argument goes wrong. (shrink)

In positive theories, we have an axiom scheme of comprehension for positive formulas. We study here the “generalized positive” theory GPK∞+. Natural models of this theory are hyperuniverses. The author has shown in [2] that GPK∞+ interprets the Kelley Morse class theory. Here we prove that GPK∞+ + ACWF and the Kelley-Morse class theory with the axiom of global choice and the axiom “On is ramifiable” are mutually interpretable. This shows that GPK∞+ + ACWF is a “strong” theory since “On (...) is ramifiable” implies the existence of a proper class of inaccessible cardinals. (shrink)

This was an attempt to show what is wrong with Anselm’s ‘Ontological Argument’ for the existence of God. My present view is that Peter Millican has given us a similar, but much better line of attack in his “The One Fatal Flaw….” Paper.

Arguments are given against the thesis that properties and propositional functions are identical. The first shows that the familiar extensional treatment of propositional functions -- that, for all x, if f(x) = g(x), then f = g -- must be abandoned. Second, given the usual assumptions of propositional-function semantics, various propositional functions (e.g., constant functions) are shown not to be properties. Third, novel examples are given to show that, if properties were identified with propositional functions, crucial fine-grained intensional distinctions would (...) be lost. (shrink)

Kurt Gödel’s version of the ontological argument was shown by J. Howard Sobel to be defective, but some plausible modifications in the argument result in a version which is immune to Sobel’s objection. A definition is suggested which permits the proof of some of Godel’s axioms.

Empiricism and the Problem of Metaphysics develops and defends an empiricist solution to the problem of metaphysics, then examines the implications of such a solution for skeptical arguments and the is-ought gap. At the heart of the solution is an empirically verifiable empiricist view of the a priori.

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

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