This article discusses the history of the concepts of potential infinity and actual infinity in the context of Christian theology, mathematical thinking and metaphysical reasoning. It shows that the structure of Ancient Greek rationality could not go beyond the concept of potential infinity, which is highlighted in Aristotle's metaphysics. The limitations of the metaphysical mind of ancient Greece were overcome through Christian theology and its concept of the infinite God, as formulated in Gregory of Nyssa's theology. That is how the (...) concept of actual infinity emerged. However, Gregory of Nyssa's understanding of human rationality went still further. He said that access to the infinity of God was to be found only in an asymptotic ascension, as expressed in apophatic theology, and this view endangered the rationality of theology. Deeply influenced by the apophatic tradition, Nicholas of Cusa avoided this danger by showing that infinity could be accessed by symbolic representation and asymptotic mathematical reasoning. Thus, he made an immense contribution in making infinity rationally accessible. This endeavor was finally realized by Georg Cantor. This rational accessibility revealed discernible structures of infinity, such as the continuum hypothesis, and the cardinal numbers. However, the probable logical inconsistency of Georg Cantor's all-encompassing Absolute Infinity points to an intuitive understanding of infinity that goes beyond its rational structures – as in apophatic theology. (shrink)

One historically significant model of God holds that God is a perfect being. Analytic philosophers of religion have typically understood this to mean that God is essentially unsurpassable in power, knowledge, goodness, and wisdom. Recently, however, several philosophers have argued that this is inconsistent with another common theistic position: the view that for any world that God can create, there is a better world that God could have created instead. The argument runs (roughly) as follows: if, no matter which world (...) God creates, there’s a better creatable one, then God’s action in creating a world is necessarily surpassable. And if God’s action in creating a world is necessarily surpassable, then God is necessarily surpassable. If this argument is sound, it reveals a serious flaw in an important model of God. In what follows, I set out this argument, and I then distinguish and evaluate four replies. (shrink)