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 paper introduces the special issue on Logic and Philosophy of Religion of the journal Sophia: International Journal of Philosophy and Traditions (Springer). The issue contains the following articles: Logic and Philosophy of Religion, by Ricardo Sousa Silvestre and Jean-Yvez Béziau; The End of Eternity, by Jamie Carlin Watson; The Vagueness of the Muse—The Logic of Peirce’s Humble Argument for the Reality of God, by Cassiano Terra Rodrigues; Misunderstanding the Talk(s) of the Divine: Theodicy in the Wittgensteinian Tradition, by Ondřej (...) Beran; On the Concept of Theodicy, by Ricardo Sousa Silvestre; The Logical Problem of the Trinity and the Strong Theory of Relative Identity, by Daniel Molto; Thomas Aquinas on Logic, Being, and Power, and Contemporary Problems for Divine Omnipotence, by Errin D. Clark. -/- . (shrink)

We use a mechanized verification system, PVS, to examine the argument from Anselm’s Proslogion Chapter III, the so-called “Modal Ontological Argument.” We consider several published formalizations for the argument and show they are all essentially similar. Furthermore, we show that the argument is trivial once the modal axioms are taken into account. This work is an illustration of Computational Philiosophy and, in addition, shows how these methods can help detect and rectify errors in modal reasoning.

This paper attacks the modal ontological argument, as advocated by Plantinga among others. Whereas other criticisms in the literature reject one of its premises, the present line is that the argument is invalid. This becomes apparent once we run the argument assuming fictionalism about possible worlds. Broadly speaking, the problem is that if one defines “x” as something that exists, it does not follow that there is anything satisfying the definition. Yet unlike non-modal ontological arguments, the modal argument commits this (...) “existential fallacy” not in relation to the definition of ‘God’. Rather, it occurs in relation to the modal facts quantified over within a Kripkean modal logic. In brief, we can describe the modal facts by whichever logic we prefer—yet it does not follow that there are genuine modal facts, as opposed to mere facts-according-to-the-fiction. A broader consequence of the discussion is that the existential fallacy is an issue for many projects in “armchair metaphysics.”. (shrink)

Anselm’s original argument for the existence of God seems to pull in opposite directions. On the one hand, it is not easy to see what, if anything, is wrong with it; on the other, it seems incredible that the existence of a being like God could be proved entirely a priori. This paper presents a diagnosis of what seems to be wrong with Anselm’s original reasoning. The diagnosis is general enough to be of use elsewhere, and it is this: conceptual (...) possibilities are inferential dead-ends, not free inference tickets to prove any substantial claim. It remains to be seen if other versions of Anselm’s original insight, both contemporary and not, fall into the same conceptual possibility trap. (shrink)

O autor analisa a validade de uma certa variante do “argumento ontológico" deAnselmo, a saber, a versão lógico-modal de Charles Hartshorne. Ele investiga, primeiramente, a origem dos argumentos de Hartshorne, partindo de uma interpretação de Anselmo; em segundo lugar, o argumento lógico-modal é apresentado, junto com as suas pressuposições e implicações. Finalmente, o autor propõe uma avaliação da abordagem de Hartshorne.

Anselm’s ontological argument is an argument for the existence of God. This paper presents Iris Murdoch’s ontological argument for the existence of the Good. It discusses her interpretation of Anselm’s argument, her distinctive appropriation of it, as well as some of the merits of her version of the argument. In doing so, it also shows how the argument integrates some key Murdochian ideas: morality’s wide scope, the basicness of vision to morality, moral realism, and Platonism.

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.

There are several styles of ontological argument. Here are examples of the first style. God has all perfections. Existence is a perfection. ∴God exists. All perfect beings exist. God is a perfect being. ∴God exists. God couldn't be improved. A being that doesn't exist could be improved . ∴God exists.

The most famous objection to the ontological argument is given in Kant's dictum that existence is not a real predicate. But it is not obvious how this slogan is supposed to relate to the ontological argument. Some, most notably Alvin Plantinga, have even judged Kant's dictum to be totally irrelevant to Anselm's version of the ontological argument. In this paper I argue, against Plantinga and others, that Kant's claim is indeed relevant to Anselm's argument, in the straightforward sense that if (...) the claim is true, then Anselm's argument is unsound. (shrink)

Many versions of the ontological argument have two shortcomings: First, despite the arguments put forward, for example, by Hugh Chandler and Nathan Salmon, they assume that S5 is the correct modal logic for metaphysical modality. Second, despite the classical arguments put forward, for example, by David Hume and Immanuel Kant or the more recent arguments put forward, for example, by John Findlay and Richard Swinburne, they assume that necessary existence is possible. The aim of the paper is to develop an (...) alternative version of the ontological argument that, by an appeal to the logic of ‘actually’, avoids these two shortcomings. The version helps to leave aside unnecessary debates about the modal logic S5 or about the possibility of necessary existence and to focus on the actual challenge for the debate about the ontological argument: the challenge to evaluate the claim that it is possible that God exists. (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)

Having gained some idea of what MacIntosh logics there are, we conclude this paper with a remark about the totality of them. Let theterritory of a rule or condition be the class of all modal logics that have the rule or satisfy the condition. What is MacIntosh territory, the class of all normal logics with the MacIntosh rule, like? What is its structure?

This paper introduces a special issue on logic and philosophy of religion in this journal. After discussing the role played by logic in the philosophy of religion along with classical developments, we present the basic motivation for this special issue accompanied by an exposition of its content.

Chapter III of Anselm's Proslogion is quite naturally interpreted as presenting a second version of the ontological argument. In recent discussions it has been so interpreted by Charles Hartshorne and by Norman Malcolm. Other writers, however, have rejected this interpretation, maintaining that Anselm intended Chapter Ill, not as a second proof of God's existence, but only as a demonstration that the kind of existence which God has is necessary existence. Perhaps the latter writers are correct on this exegetical point, but (...) even so, it does not follow that there is anything improper about an inquiry into the character of the distinct, modal version of the ontological argument which can be derived from this passage. (shrink)