All the papers of the present collection implicitly or explicitly grapple with the elaborated questions concerning the infinity of God. There are two parts: The papers of the first part mainly deal with historical appreciations of the concept of infinity and the various assessments of its capacity to function as a categorematic or syncategorematic attribute of God. The first part is opened by Franz Krainer and his paper The Concept of Infinity in Ancient Greek Thought . Krainer provides a brief analysis of the variety of concepts of qualitative and quantitative infinity found in ancient Greek thought reaching from Plato to Gregory of Nyssa. Although in this period the term "infinity" often has more than one meaning, sometimes even within the work of a single philosopher, Krainer argues that at least two contrary conceptions of God''s infinity can be identified: infinity as expressing divine indeterminacy or perfection. On both these account, however, there is a subtle agreement that God''s qualitative infinity is strongly related to God''s incomprehensibility. Therefore, according to Krainer, the concept of an infinite God in ancient Greek thought naturally led to the development and support of negative theology on which it is disputable whether the infinity of God allows us to formulate any intelligible statement about God at all. In his paper Infinity in Augustine''s theology , Adam Drozdek provides an analysis of Augustine''s stance on the infinity of God.

Although Augustine at first thought about God as an infinite corporeal being, he later became convinced that God had to be understood in an incorporeal manner. Drozdek argues that although in this respect Augustine struggled both with problems concerning quantitative notions of infinity related to infinite space and time, and with the possibility of infinite divine knowledge - for which every infinite quantity, according to Augustine, is finite and thus comprehensible - he never explicitly developed an account of divine infinity as such. Instead, Augustine stressed that God''s essence lies in his immutability and eternity, both of which indicate that God is beyond infinity and finitude. William Carroll''s paper, Aquinas on Creation and the Analogy of Infinity , argues that for Thomas there is a close connection between the concept of creation and the concept of the infinity of God: Whereas creatures are identified as creatures by the reception of being, and thus are always in certain respects finite, unreceived being is the hallmark of God the Creator. To show that for Thomas unreceived being is absolutely infinite and fully determined, Carroll analyses what Thomas says about divine infinity in "In I Sent", "Summa contra Gentiles" and "Summa theologiae", all of which deal with the concept of God as subsistent being. Carroll, then, concludes that for Thomas divine infinity is a natural consequence of his concept of creation, and can be known, at least in an analogical way, by reason alone. In her Spinoza and Leibniz on the Absolute and its Infinity - A Case Study , Christina Schneider analyses the entailments of different concepts of infinity for the concept of the Absolute and its relation to the world. To do so, she compares Spinoza''s and Leibniz''s conceptions of the infinity of God.

Based on the assumption that divine infinity, formally, is used to express a divine perfection, Schneider distinguishes between two concepts of divine infinity as a perfection: on the first meaning, divine infinity is understood to exclude negation, whereas on the second meaning divine infinity refers to the highest degree of an attribute, as found, for instance, in God''s omniscience and omnipotence. Spinoza, according to Schneider, operates with the first concept of divine infinity and Leibniz with the second. Once this is clarified, she spells out some problems for Leibniz''s attempts to avoid Spinozism: To escape Spinozism, Leibniz both conceived God to be completely independent of His creatures and introduced the concept of monads. However, since monads are not intellectually accessible by God, Schneider identifies a crucial problem: either the concept of God''s omniscience has to be modified to include a kind of Spinozistic omnisubjectivity or God cannot be omniscient - the latter of which is not consistent with Leibniz''s concept of divine infinity. Ruben Schneider''s paper, What does Kant really say about God? , deals with Kant''s account of the existence and essence of God understood as the infinite being which is the ground of the world order. In contrast to traditional interpretations on which Kant rejects every attempt to construe a metaphysical theory of God, Schneider argues in a first step that God firmly presupposed the existence of God, but argued against philosophical attempts to grasp divine attributes as they are in themselves. In a second step, Schneider investigates Kant''s concept of infinite divine reason and spells out some possible consequences of Kantian philosophy: It seems that Kant''s philosophy is at least open to a panentheistic interpretation on which the difference between God and the created world is within God and the finite mind of creatures is participating in the absolute spirit of God. In Infinity and Spirit: How Hegel Integrates Science and Religion, and Nature and the Supernatural , Robert M.

Wallace shows how Hegel employs his conception of infinity in order to try to integrate science and religion as well as both the natural and the supernatural realm of being. He first argues that Hegel''s concept of true infinity should be understood as ''the finite''s own going beyond its finitude''. He then spells out how based on this notion of the ascent of finitude science, religion, ethics, art, and philosophy can all be understood as metaphysically necessary aspects of a single self-determining reality that is properly referred to as the divine being. Everything that constitutes this ultimate reality is part of an ascent above its initial opinions and appetites and frees the individual of determination by things that are not itself. Thus it enables a true self-determination of reality. Christian Tapp''s paper Bolzano''s Concept of Divine Infinity argues that infinity is central to each of the three areas in which Bolzano had expertise: mathematics, philosophy, and theology. He concentrates on Bolzano''s analysis of the infinity of God and shows that on Bolzano''s view the concept of quantitative infinity is best understood as follows: A series is quantitatively infinite if and only if it has no last term and every finite series can be mapped one-one onto a part of it. According to Tapp, on Bolzano''s view this concept of quantitative infinity is more basic than all other concepts of infinity.

Therefore, even qualitative concepts of the infinity of God have to be related in one way or the other to the elaborated quantitative concept of infinity. Tapp ends by identifying further tasks that must be dealt with to fully specify an adequate conception of divine infinity. (excerpted from introduction).