In this paper, I present what I call the symmetry conception of God within 1st order, extensional, non-well-founded set theory. The symmetry conception comes in two versions. According to the first, God is that unique being that is universally symmetrical with respect to set membership. According to the second, God is the universally symmetrical set of all sets that are universally symmetrical with respect to set membership. I present a number of theorems, most importantly that any universally symmetrical set is (...) identical to its essence, that show that the two symmetry conceptions intersect with some dominant theological conceptions of God. The theorems also show that both of the symmetry conceptions of God entail that God has a fractal like structure. (shrink)

Kurt Gödel made many affirmations of robust realism but also showed serious engagement with the idealist tradition, especially with Leibniz, Kant, and Husserl. The root of this apparently paradoxical attitude is his conviction of the power of reason. The paper explores the question of how Gödel read Kant. His argument that relativity theory supports the idea of the ideality of time is discussed critically, in particular attempting to explain the assertion that science can go beyond the appearances and ‘approach the (...) things’. Leibniz and post-Kantian idealism are discussed more briefly, the latter as documented in the correspondence with Gotthard Günther. (shrink)

This article is a reply to Michael Gettings' criticisms of a previous paper of mine on Godel's ontological argument. (All relevant bibliographical details may be found in the article.) I provide a patch to my previous -- faulty -- attempt to provide a parody of Godel's ontological argument on the model of Gaunilo's parody of Anselm's Proslogion 2 argument.

This paper discusses recent work on higher-order ontological arguments, including work on arguments due to Gödel, Maydole and Pruss. After setting out a range of these arguments, the paper seeks to highlight the principal difficulties that these kinds of arguments confront. One important aim of the paper is to cast light on Gödel's ontological argument by way of an examination of a range of related higher-order arguments.

The ontological argument in Anselm’s Proslogion II continues to generate a remarkable store of sophisticated commentary and criticism. However, in our opinion, much of this literature ignores or misrepresents the elegant simplicity of the original argument. The dialogue below seeks to restore that simplicity, with one important modification. Like the original, it retains the form of a reductio, which we think is essential to the argument’s great genius. However, it seeks to skirt the difficult question of whether 'exists' is a (...) genuine predicate by appealing instead to a distinction between having only mediated causal powers and having unmediated causal powers. Pegasus has no unmediated causal powers, but he has mediated causal powers through the thoughts, depictions, and literature in which he figures. This distinction allows us to argue about the existence of God without begging any questions. (shrink)

The Pinocchio paradox, devised by Veronique Eldridge-Smith in February 2001, is a counter-example to solutions to the Liar that restrict the use or definition of semantic predicates. Pinocchio’s nose grows if and only if what he is stating is false, and Pinocchio says ‘My nose is growing’. In this statement, ‘is growing’ has its normal meaning and is not a semantic predicate. If Pinocchio’s nose is growing it is because he is saying something false; otherwise, it is not growing. ‘Because’ (...) stands here for a non-semantic relation; it might be supposed to be causal or of some other nature, but it is not semantic. The paradox is discussed in relation to Tarski’s and Kripke’s theories of truth. Although the paradox is not necessarily a counter-example to a theory of a truth predicate, it is a problem for a theory of truth of the kind preserved by validity. (shrink)

Kurt Gödel’s version of the Ontological Proof derives rather than assumes the crucial Possibility Claim: the claim that it is possible that something God-like exists. Gödel’s derivation starts off with a proof of the Possible Instantiation of the Positive: the principle that, if a property is positive, it is possible that there exists something that has that property. I argue that Gödel’s proof of this principle relies on some implausible axiological assumptions but it can be patched so that it only (...) relies on plausible principles. But Gödel’s derivation of the Possibility Claim also needs a substantial axiological assumption, which is still open to doubt. (shrink)

Beschäftigung mit der Philosophie, selbst wenn keine positiven Ergebnisse herauskommen (sondern ich ratlos bleibe), ist auf jeden Fall wohltätig. Es hat die Wirkung (dass „die Farbe heller“), d.h., dass die Realität deutlicher als solche erscheint. – Kurt Gödel..