Infinite Power and Finite Powers∗

The etymological meaning of ‘omnipotent’ is ‘all-powerful.’ Being all-powerful is usually understood as having all of the powers. The problem of analyzing omnipotence is then seen as the problem of determining over what class the quantifier ‘all’ in this assertion ranges. An omnipotent being would be one that has all of the powers; all of what powers? Attempts to answer this question have run into serious difficulties. Responding to these difficulties, Alexander Pruss and I recently proposed a way of analyzing omnipotence which makes no reference to the notion of power at all (Pearce and Pruss 2012). However, this raises an obvious worry: if our analysis is not related to the notion of power, then how can it count as an analysis of omnipotence, the property of being all-powerful, at all? In this paper, I propose to answer this question by appeal to a particular (non-mathematical) notion of infinity found in the tradition of philosophical theology. On the view I have in mind, the relation of the infinite to the finite is the relation of the universal or general to the particular. Thus to be infinitely powerful would be to have power in general, rather than having particular powers. Proponents of this understanding of infinity see the infinite as conceptually simpler than the finite: infinite concepts differ from finite concepts in that the latter have conceptual ingredients the former lack, namely, limitations. My aim here is to use this notion of the infinite as a model to understand the conceptual relationship between the Infinite Power of God and the finite powers of creatures. I begin by reviewing some of the difficulties involved in analyzing omnipotence. After this, I explain in more detail the notion of infinity with which I am working and the understanding of Infinite Power I wish to defend. The bulk of the paper is then taken up by a discussion of the various ways in which finite powers are limited, as compared to the Infinite Power of God. My hope is that this investigation will be of use to theologians and philosophers of religion by clarifying some of the puzzles about divine omnipotence as well as the nature of the infinite gulf between creature and creator. I also hope that it will be of interest to metaphysicians and philosophers of action, even those who are not theists, by showing how an idealized notion of Infinite Power, or of power simpliciter, can have considerable theoretical utility, regardless of whether one believes in an infinitely powerful being.