Panel: THE CONCEPT OF GOD IN THE INTERPLAY OF THE INFINITE AND THE FINITE



980.4 - ONLY GOD KNOWS WHAT, BUT HOW MUCH IS THAT?

AUTHORS:
Klimbacher J. (Departments of Philosophy and Physics, University of Vienna ~ Vienna ~ Austria)
Text:
Among the many properties attributed to God omniscience and omnipotence are often mentioned. Thus, the answer to the question how many things God knows or can do is an infinite amount. For a long time, this answer was satisfying. But with the development of higher infinites in modern mathematics this answer can get more precise. The goal of this paper is to give a reason to choose Cantor's Absolute Infinity Ω instead of just assuming it. At first glance, it may seem that all propositional knowledge or descriptions of (possible) actions might be translated into numbers and fit into the reals. However, using God's omniscience and omnipotence, any large cardinal mathematicians might introduce can be reached quantitatively by God. God might even know or be able to do more than that. Therefore, I take the largest cardinal available to us to be the lower bound of the number of things God knows or can do. This sets us up for the Absolute Infinity Ω. It lies in the nature of Ω to be somewhat mysterious as it cannot be distinguished from the large cardinals. All properties of Ω are shared with the other large cardinals, but parts of it can be found out. The similarities are pointed out by Robert John Russell in his article "God and Infinity: Theological Insights from Cantor's Mathematics" from 2011, but he works only with the similarities. If we see God's knowledge as a subset of God, then Russell's link between God and Ω strengthens further because no superset could be smaller than its subset.