This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The (...) volume includes 35 contributions. It is divided into nine parts: 1. Who Created the Concept of God; 2. Omniscience, Omnipotence, Timelessness and Spacelessness of God; 3. God and Perfect Goodness, Perfect Beauty, Perfect Freedom; 4. God, Fundamentality and Creation of All Else; 5. Simplicity and Ineffability of God; 6. God, Necessity and Abstract Objects; 7. God, Infinity, and Pascal's Wager; 8. God and (Meta-)Mathematics; and 9. God and Mind. (shrink)

Стаття присвячена онтологічному аргументу Курта Ґьоделя, його місцю в історії філософії і сучасних дебатах стосовно валідності онтологічного доказу. По-перше, ми аргументуємо що Ґьоделів аргумент є необхідним кроком в історії розвитку онтологічного аргументу. По-друге, ми показуємо, що Ґьоделів аргумент засновується на незадовільних аксіологічних принципах, проте може бути переформульований в термінах задовільних аксіологічних принципів. Також ми розглядаємо дебати щодо валідності Ґьоделевого аргументу між сучасним нео-ґаунілістом Ґремом Опі та захисником онтологічного аргументу Майклом Ґетінґсом. Ми доходимо висновку, що онтологічний аргумент Ґьоделя не вразливий до (...) ґаунілізму Опі. Нарешті, враховуючи той факт, що пародія Опі є, імовірно, найбільш досконалим аргументом ґаунілістського ґатунку в історії філософії, ми висновуємо, що ґаунілістська лінія аргументації, навіть якщо є успішною проти аргументу Ансельма, не працює проти аргументу Ґьоделя. (shrink)

Gödel's ontological argument is a formal argument for a being defined in terms of the concept of a positive property. I shall defend several versions of Gödel's argument, using weaker premises than Anderson's (1990) version, and avoiding Oppy's (1996 and 2000) parody refutations.

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)

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.

First, I suggest that it is possible to make some further improvements upon the Gödelian ontological arguments that Pruss develops. Then, I argue that it is possible to parody Pruss's Gödelian ontological arguments in a way that shows that they make no contribution towards 'lowering the probability of atheism and raising the probability of theism'. I conclude with some remarks about ways in which the arguments of this paper can be extended to apply to the whole family of Gödelian ontological (...) arguments. (shrink)

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 aim of this essay is twofold. First, it outlines the concept of ontological frame. Secondly, two models are distinguished on this structure. The first one is connected to Kant’s concept of possible object and the second one relates to Leibniz’s. Leibniz maintains that the source of possibility is the mere logical consistency of the notions involved, so that possibility coincides with analytical possibility. Kant, instead, argues that consistency is only a necessary component of possibility. According to Kant, something is (...) possible if there is a cause capable of bringing it into existence; to this end consistency alone is not sufficient. Thus, while the Leibnizian notion of consistency is at the root of the concept of analytical possibility, the Kantian notion of possibility is the source of real possibility. This difference plays an important role in the discussion of Gödel’s ontological proof, which can be formally interpreted on the ontological frame of the pure perfections. While this proof, under some emendation condition, is conclusive in the context of Leibniz’s ontological model, it is not so within the Kantian one. This issue will be the subject of the second part of the present essay. (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)

The article is devoted to Gödel's Ontological Argument, its place in the history of philosophy, and the current debate over the validity of Ontological Proof. First, we argue that Gödel's argument is a necessary step in the history of the development of Ontological Proof. Second, we show that Gödel's argument is based on implausible axiological principles, but can be appropriately reformulated in terms of plausible axiological principles. Also, we consider the debate over the validity of Gödel`s argument between contemporary neo-Gaunilist (...) Graham Oppy and the advocate of Gödel`s Ontological Proof Michael Gettings. We conclude that Gödel's Ontological Argument is immune to Oppy`s neo-Gaunilism. Finally, given the fact that Oppy`s parody is arguably the most fine-grained Gaunilo-style argument in the history of philosophy, we conclude that Gaunilist line of argumentation, even if successful in refuting Anselm`s Ontological Proof, does not work against Gödel's Ontological Argument. (shrink)

Latest version of my SEP entry on ontological arguments, which first appeared in 1996. General discussion of ontological arguments. Includes a brief historical overview, a taxonomy of different kinds of ontological arguments, a brief survey of objections to the different kinds of ontological arguments identified in the taxonomy, and more extended discussions of Anselm's ontological argument (Proslogion 2), Godel's ontological argument, and Plantinga's ontological argument.

This paper explores early Australasian philosophy in some detail. Two approaches have dominated Western philosophy in Australia: idealism and materialism. Idealism was prevalent between the 1880s and the 1930s, but dissipated thereafter. Idealism in Australia often reflected Kantian themes, but it also reflected the revival of interest in Hegel through the work of ‘absolute idealists’ such as T. H. Green, F. H. Bradley, and Henry Jones. A number of the early New Zealand philosophers were also educated in the idealist tradition (...) and were influential in their communities, but produced relatively little. In Australia, materialism gained prominence through the work of John Anderson, who arrived in Australia in 1927, and continues to be influential. John Anderson had been a student of Henry Jones, who might therefore be said to have influenced both main strands of Australian philosophical thought. (shrink)

Analytic theologians have proposed numerous “solutions” to the Logical Problem of the Trinity (LPT), mostly versions of Social Trinitarianism (ST) and Relative Identity Trinitarianism (RI). Both types of solution are controversial, but many hold out hope that further “Trinitarian theorizing” may yield some as yet unimagined, and somehow importantly different, solution to the LPT. I first give a precise definition of the LPT and of what would count as a solution to it. I then show how, though there are infinitely (...) many possible solutions, all solutions can be grouped together into a finite, exhaustive taxonomy, based precisely on those features which make them either controversial, heretical, or inconsistent. The taxonomy reveals why ST and RI have been the major proposed solutions, and also proves that there can be no importantly different, new solutions to the LPT. (shrink)

A metaphysical system engendered by a third order quantified modal logic S5 plus impredicative comprehension principles is used to isolate a third order predicate D, and by being able to impredicatively take a second order predicate G to hold of an individual just if the individual necessarily has all second order properties which are D we in Section 2 derive the thesis (40) that all properties are D or some individual is G. In Section 3 theorems 1 to 3 suggest (...) a sufficient kinship to Gödelian ontological arguments so as to think of thesis (40) in terms of divine property and Godly being; divine replaces positive with Gödel and others. Thesis (40), the sacred thesis, supports the ontological argument that God exists because some property is not divine. In Section 4 a fixed point analysis is used as diagnosis so that atheists may settle for the minimal fixed point. Theorem 3 shows it consistent to postulate theistic fixed points, and a monotheistic result follows if one assumes theism and that it is divine to be identical with a deity. Theorem 4 (the Monotheorem) states that if Gg and it is divine to be identical with g, then necessarily all objects which are G are identical with g. The impredicative origin of D suggests weakened Gaunilo-like objections that offer related theses for other second order properties and their associated diverse presumptive individual bearers. Nevertheless, in the last section we finesse these Gaunilo-like objections by adopting what we call an apathiatheistic opinion which suggest that the best concepts `God’ allow thorough indifference as to whether God exists or not. (shrink)