A Computationally-Discovered Simplification of the Ontological Argument (original) (raw)
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Reflections on the Logic of the Ontological Argument
2007
Our 1991 paper on the logic of the ontological argument contained an analysis of the structure of Anselm's argument for the existence of God. We showed that there is a valid argument for God's existence in Proslogion II. However, in that paper, we deliberately decided not to include a discussion and analysis of the soundness of the argument. In these afterthoughts, we shall take up this question. We plan to argue for the following:
2009
Ontological arguments are deductive arguments for the existence of God from general metaphysical principles and other assumptions about the nature or essence of God. There have been three very signifi cant developments in the history of ontological arguments. The fi rst is the ontological argument developed by St Anselm of Canterbury in the eleventh century. The second is the argument sketched by Descartes in the late seventeenth century and completed by Leibniz in the early eighteenth century. And the third development consists of the numerous ontological arguments of the twentieth century that explicitly utilize modal logic, particularly those of Malcolm, Hartshorne, Plantinga, and Godel. My chief aim in this chapter is to logically evaluate logical reconstructions of each of these six arguments. I shall also present and logically discuss two of my own explicitly modal ontological arguments. The logical evaluation of a logical reconstruction of an argument often requires that we e...
On the logic of the ontological argument
1991
Saint Anselm of Canterbury offered several arguments for the existence of God. We examine the famous ontological argument in Proslogium II. Many recent authors have interpreted this argument as a modal one.'But we believe that Jonathan Barnes has argued persuasively that Anselm's argument is not modal.
On the PROVER9 Ontological Argument [Philosophia]
Philosophia, 2015
Oppenheimer & Zalta have re-devised their non-modal version of the ontological argument, with the help of PROVER9, an impressive automated reasoning engine. The authors end up rejecting the new argument; however, the theist has a rejoinder worth considering. But after presenting this rejoinder, I highlight that the conceivability of the being does not imply its possibility. One lesson is that even non-modal ontological arguments must engage modal matters concerning God. Another lesson is that if PROVER9 derives a conclusion from fewer premises, the result is sometimes an inferior proof.
GIVING THE ONTOLOGICAL ARGUMENT ITS DUE
Philosophia, 2014
In this paper, I shall present and defend an ontological argument for the existence of God. The argument has two premises: (1) possibly, God exists, and (2) necessary existence is a perfection. I then defend, at length, arguments for both of these premises. Finally, I shall address common objections to ontological arguments, such as the Kantian slogan ('existence is not a real predicate'), and Gaunilo-style parodies, and argue that they do not succeed. I conclude that there is at least one extant ontological argument that is plausibly sound.
Recent Objections of Ontological Arguments
2020
This paper summarizes recent objections to modern versions of the ontological argument (OA) 1. I do not weigh one argument against another, nor offer counter-counter arguments to OAs. This paper only highlights some objections to OAs to synthesize the information in one place. Though there is some overlap between various arguments, each OA should be judged based on its own merits. Each argument has its nuances, operating presuppositions, and modes of logic used. Opponents of the OA argue that despite the many attempts to strengthen Anselm's original argument it can be shown that OAs fail to offer a theistic proof for God.
Reflections on the Logic of the Ontological Arrgument
2007
Our 1991 paper on the logic of the ontological argument contained an analysis of the structure of Anselm’s argument for the existence of God. We showed that there is a valid argument for God’s existence in Proslogion II. However, in that paper, we deliberately decided not to include a discussion and analysis of the soundness of the argument. In these afterthoughts, we shall take up this question. We plan to argue for the following: 1. Anselm’s argument for Premise 1 is not valid. This casts doubt on the truth of Premise 1 of the ontological argument. 2. If Premise 1 is revised so as to be clearly true, and the rest of the ontological argument is modified so as to preserve validity with the revised Premise 1, then the resulting argument is sound but doesn’t have the conclusion that Anselm wishes to establish. Our analysis in what follows appeals to the theory of abstract objects (Zalta 1983) and to the distinction between exemplifying and encoding a property fundamental to that theor...
Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning, 2020
An approach to universal (meta-)logical reasoning in classical higher-order logic is employed to explore and study simplifications of Kurt Gödel's modal ontological argument. Some argument premises are modified, others are dropped, modal collapse is avoided and validity is shown already in weak modal logics K and T. Key to the gained simplifications of Gödel's original theory is the exploitation of a link to the notions of filter and ultrafilter in topology. The paper illustrates how modern knowledge representation and reasoning technology for quantified non-classical logics can contribute new knowledge to other disciplines. The contributed material is also well suited to support teaching of non-trivial logic formalisms in classroom.
A Case Study On Computational Hermeneutics: E. J. Lowe's Modal Ontological Argument
FLAP, 2018
Computers may help us to better understand (not just verify) arguments. In this article we defend this claim by showcasing the application of a new, computer-assisted interpretive method to an exemplary natural-language argument with strong ties to metaphysics and religion: E. J. Lowe’s modern variant of St. Anselm’s ontological argument for the existence of God. Our new method, which we call computational hermeneutics, has been particularly conceived for use in interactive-automated proof assistants. It aims at shedding light on the meanings of words and sentences by framing their inferential role in a given argument. By employing automated theorem reasoning technology within interactive proof assistants, we are able to drastically reduce (by several orders of magnitude) the time needed to test the logical validity of an argument’s formalization. As a result, a new approach to logical analysis, inspired by Donald Davidson’s account of radical interpretation, has been enabled. In co...