In response to arguments against the existence of God, and in response to perceived conflicts between divine attributes, theists often face pressure to give up some pretheoretically attractive thesis about the divine attributes. One wonders: when does this unacceptably water down our concept of God, and when is it, as van Inwagen says, ‘permissible tinkering’ with the concept of God? A natural and widely deployed answer is that it is permissible tinkering iff it is does not violate the claim that (...) God is the greatest possible being. Call this the ’perfect being defense.’ In this paper I lay out some influential uses of the perfect being defense, and then argue that this strategy for defending theism fails. (shrink)

Patrick Grim has put forward a set theoretical argument purporting to prove that omniscience is an inconsistent concept and a model theoretical argument for the claim that we cannot even consistently define omniscience. The former relies on the fact that the class of all truths seems to be an inconsistent multiplicity (or a proper class, a class that is not a set); the latter is based on the difficulty of quantifying over classes that are not sets. We first address the (...) set theoretical argument and make explicit some ways in which it depends on mathematical Platonism. Then we sketch a non Platonistic account of inconsistent multiplicities, based on the notion of indefinite extensibility, and show how Grim’s set theoretical argument could fail to be conclusive in such a context. Finally, we confront Grim’s model theoretical argument suggesting a way to define a being as omniscient without quantifying over any inconsistent multiplicity. (shrink)

Cantor argued that absolute infinity is beyond mathematical comprehension. His arguments imply that the domain of mathematics cannot be grasped by mathematical means. We argue that this inability constitutes a foundational problem. For Cantor, however, the domain of mathematics does not belong to mathematics, but to theology. We thus discuss the theological significance of Cantor’s treatment of absolute infinity and show that it can be interpreted in terms of negative theology. Proceeding from this interpretation, we refer to the recent debate (...) on absolute generality and argue that the method of diagonalization constitutes a modern version of the vianegativa. On our reading, negative theology can evoke an attitude of humility with respect to the boundedness of the human condition. Along these lines, we think that the foundational problem of mathematics concerning its domain can be addressed through a methodological attitude of humility. (shrink)

Focusing on God's essential attributes of omnipotence, omniscience, being eternal and omnipresent, being a creator and sustainer, and being a person, I examine how far recent discussion has been able to provide for each of these divine attributes a consistent interpretation. I also consider briefly whether the attributes are compatible with each other.

The divine attributes of omniscience and omnipotence have faced objections to their very consistency. Such objections rely on reasoning parallel to semantic paradoxes such as the Liar or to set-theoretic paradoxes like Russell's paradox. With the advent of paraconsistent logics, dialetheism—the view that some contradictions are true—became a major player in the search for a solution to such paradoxes. This paper explores whether dialetheism, armed with the tools of paraconsistent logics, has the resources to respond to the objections levelled against (...) the divine attributes. (shrink)

RESUMO Este artigo é dedicado ao argumento contra o Requisito de Existência fornecido por Takashi Yagisawa. Argumentamos que o cerne do argumento de Yagisawa – a Forte Iterabilidade – não pode ser inferido pela ideia de contingente a priori (Kripke) e é incompatível com a ideia de @-transformação (Plantinga). Assim, essas ideias, contrariamente a Yagisawa, não podem servir de base metodológica da Forte Iterabilidade. Também argumentamos que a Forte Iterabilidade é incompatível com o Princípio Constitutivo. Finalmente, mostramos que o conceito (...) de propriedades indexadas pelo mundo (o argumento de Yagisawa se fa na ideia de propriedades indexadas pelo mundo) é inconsistente e, mesmo que o defensor da Forte Iterabilidade possa resistir a esta objeção, a Forte Iterabilidade deve ser abandonada. (shrink)