The Infinity of God

New Perspectives in Theology and Philosophy

Benedikt Paul Göcke, Christian Tapp, Benedikt Paul Göcke, Christian Tapp

• Publisher: University of Notre Dame Press
• Year: 2018
• Print ISBN: 9780268104139
• eBook ISBN: 9780268104160
• Topic: Philosophy
• Subtopic: Theology

Two questions regarding contemporary theological and philosophical studies are often overlooked: "Is God infinite or finite?" and, "What does it mean to say that God is infinite?" In The Infinity of God, Benedikt Paul Göcke and Christian Tapp bring together prominent scholars to discuss God's infinitude from philosophical and theological perspectives. Each contributor deals with a particular aspect of the infinity of God, employing the methods of analytic theology and analytic philosophy. The essays in the first section examine historical issues from a systematic point of view. The contributors focus on the Cappadocian Fathers, Thomas Aquinas, Leibniz, Kant, Hegel, Bolzano, and Cantor. The second section deals with particular issues concerning the relation between God's infinity and both the finitude of the world and the classical attributes of God: eternity, simplicity, omnipresence, omnipotence, omniscience, and moral perfection. There are some books that deal with the notion of infinity in mathematics and in general philosophy, but no single text brings together the best analytic philosophers and theologians tackling the various aspects of the infinity of God and the correlated problems. This book will interest students and scholars in philosophy of religion, theology, and metaphysics.

Contributors: Benedikt Paul Göcke, Christian Tapp, Franz Krainer, Adam Drosdek, William E. Carroll, Christina Schneider, Ruben Schneider, Robert M. Wallace, Bruce A. Hedman, Bernhard Lang, Richard Swinburne, Kenneth L. Pearce, William Hasker, Paul Helm, Brian Leftow, Ken Perszyk, Thomas Schärtl, and Philip Clayton.

CHAPTER 1

Introduction

The Infinity of God

BENEDIKT PAUL GÖCKE AND CHRISTIAN TAPP

In analytic philosophy of religion, the existence of God and the classical divine attributes of omniscience, omnipotence, and moral perfection have received extensive treatment over the last few decades. The infinity of God, in contrast, has received comparatively little scholarly attention.¹ There is no single edited volume dealing exclusively with the infinity of God.² To rectify, we have brought together philosophers and theologians to grapple exclusively with the infinity of God from historical and systematic points of view. Since our authors come from different philosophical and theological backgrounds, we hope to provide a fruitful stimulus to discussion of the infinity of God. In this introduction, we briefly clarify the question(s) at stake in the volume.

THE INFINITY OF GOD?

Whoever asserts that “God is infinite” brings together two of the most complicated terms of the humanities and the natural sciences. The statement needs clarification in at least three ways.

The “God” Problem. It is not clear which concept the term “God” expresses. “God” is used in different senses in different philosophical and theological contexts. And so it is unclear whether these uses are intended to refer to the same being or not, or whether they refer to a single entity.³ In order to understand the question of whether God is infinite we have to clarify, at least roughly, which concept of God we have in mind throughout our volume.

The “Infinity” Problem. It is not clear which concept the term “infinity” expresses.⁴ In different sciences, it is deployed to articulate concepts that are not always obviously related to each other. But in mathematics the infinite is dealt with almost everywhere, such as in the conception of real numbers as infinite sets of natural numbers. In the philosophy of mathematics, there is an inquiry into the nature of transfinite sets and if there is an actually infinite set of numbers.⁵ Answers to these questions cover positions as diverse as mathematical platonism, according to which there is an infinite realm of mind-independent mathematical entities, and intuitionism, which entails that mathematical objects are mind-dependent entities and therefore unlikely to be infinite. On the other hand, in physics and the philosophy of physics, based on the various mathematical concepts of infinity, questions concerning the infinitely large and the infinitesimally small are discussed. It is asked whether space is of infinite extension and whether there is a limit to spatial divisibility. Singularities that appear in the mathematical description of physical processes are called “infinities.”

In contrast, most theologians and philosophers do not think of infinity primarily in terms of quantity but as a unique quality of the Divine or the Absolute, a quality not directly connected with number and measurement.⁶

The Relation Problem. There are at least three ways of understanding the statement that God is infinite. First, that God is infinite is an abbreviated way of referring to features of God, and nothing in addition to those features: we can sum up whatever is true of God by saying that God is infinite. Second, saying that God is infinite means that infinity is an independent feature of God in addition to other features He might have, that is, whatever else is true of God, that He is infinite is a further qualification of God. Third, that God is infinite means that certain features of God are themselves infinite: there is at least one divine attribute that is itself infinite.⁷

Since, in the first way of understanding, the statement that God is infinite is just a façon de parler that adds no further content to the analysis of the divine attributes, we bracket this way of speaking of the infinity of God. Two options remain: the statement that God is infinite refers to a feature additional to other attributes of God, or it entails that at least one of the divine attributes is itself infinite.

Since, in the first case the infinity of God is considered to stand on its own, but, in the second case it needs to be qualified by some divine attribute that is putatively infinite, we call the first account the categorematic approach to the infinity of God and the second the syncategorematic approach.⁸ Infinity is treated in a different way in each case, but the categorematic and the syncategorematic approaches are not mutually exclusive. It is not inconsistent, prima facie, to argue that the infinity of God is both an extra feature of God and a feature of at least one of His attributes.

CONCEPTS OF GOD

Depending on one’s philosophical and theological commitments, the term “God” is deployed to articulate different concepts. We would probably obtain as many concepts of God as the number of philosophers and theologians we asked. For the sake of clarity, we provisionally use “God” with a minimal determination that allows us to unify positions as diverse as classical theism, panentheism, process theology, and open theism.

To do so, we distinguish a theological from a philosophical use of the term “God.” From a theological point of view, “God” denotes the deity mentioned in the holy scriptures of a particular monotheistic religion.⁹ Because the focus in this volume is on the Christian understanding of God, in its theological use, “God” refers to the deity mentioned in the Bible. Even though throughout the books of the Bible the concept of God is subject to development and thus to change, we assume theologians agree that there is a minimal set of necessary features any concept of God based on the Bible must entail to be adequate. Such a minimal theological consensus at least includes that God is the loving creator of all that is, and He wants us to be saved.¹⁰

What philosophers of religion primarily have in mind when they deploy the term “God” is neither scripture nor revelation, but either the ultimate source of everything or the ultimate goal of everything. Although these philosophers often criticize theological concepts of God for inconsistency, they are mainly interested in the question whether any theological concept of God corresponds to a philosophical concept of the ultimate source or goal that is based not on revelation and faith, but on reason alone. They ask: Can reason confirm that the theological concept of God is an adequate concept of the ultimate source or goal of everything?

Based on a combination of the theological and the philosophical uses of “God,” we suggest the following minimal account of “God”:

God (def.): deity that has the essential features of the God of the Bible and is the ultimate source and goal of existence, insofar as such a source or goal is available to purely philosophical argument.

Based on this understanding, whether God is infinite turns out to be the following question:

Q1: Is the deity mentioned in the Bible, specified by the minimal theological consensus, and rationally accessed as the ultimate source or goal of everything, infinite, and, if so, in what sense?

THE CATEGOREMATIC APPROACH TO THE INFINITY OF GOD

We will briefly analyze categorematic notions of infinity here before we turn to syncategorematic notions of infinity in the next section.

The problem with the categorematic understanding of infinity is that even when intended to express an independent and additional quality, “infinite” is used in ways that express mutually exclusive concepts. Historically and systematically, popular interpretations of infinity used to refer to a genuine property of an entity that include the notions of to be boundless, to be unlimited, and to lack finitude.¹¹

We can exclude boundlessness and unlimitedness because the predicates “being without bound” and “being without limit” need to be qualified by stating the respect in which something is without bound or limit. For instance, something can be “without spatial limit” or “without temporal bound.” However, since the intelligibility of spatial and temporal infinity depends on a possible measure by spatial or temporal units, spatial and temporal infinity belong to the class of syncategorematic notions of infinity and do not specify anything categorematic. This leaves us with the negation of finitude as a possible criterion of categorematic infinity.

Infinity as the denial of finitude can either be understood in a negative or in a positive way. In Plato’s thought, paradigmatically representing the mind of classical Greece, infinity as the denial of finitude is expressed by apeiron, “absolute formlessness” and “absolute ontological underdetermination.” Being finite consists in possessing a certain form of ontological determination. Since anything that lacks form eo ipso is inaccessible to the mind and is of the lowest ontological status, being infinite for Plato is a very bad thing indeed—whatever is infinite is without form and therefore lacks intelligibility.¹²

Gregory of Nyssa as influenced by Neoplatonism saw things in a different light. Paradigmatically representing early Christian orthodoxy, he thought of infinity as expressing total superabundance and the fullness of being.¹³ Since in our volume here God is understood philosophically as the ultimate source or goal of everything, we can exclude the Platonic interpretation of categorematic infinity and adopt that of Gregory of Nyssa. On the categorematic concept of infinity, whether God is infinite therefore turns out to be expressed in the following question:

Q2: Does the deity mentioned in the Bible, specified by the minimal theological consensus, and rationally accessed as the ultimate source or goal of everything, possess total superabundance and the fullness of being?

SYNCATEGOREMATIC APPROACHES TO THE INFINITY OF GOD

On the syncategorematic approach, the infinity of God is not a quality in addition to other divine attributes but consists in the infinity of at least one divine attribute. The difficulty here is that there is more than one way of understanding the syncategorematic infinity of a divine attribute. There are two relevant directions we can take. First, “syncategorematic infinity” can be used to refer to a quantity. Second, it can be used to express the mode of givenness of a particular attribute.

The first way of understanding syncategorematic infinity is, again, open to two interpretations, depending on the concept of quantity we have in mind. “Quantity” can refer to an extension or to an intension, that is, to the size of the class of objects having the respective property or to the degree to which an object has that property.¹⁴ (This is the sense of “intension” that the Scholastics had in mind when they considered the intensio of a property. It is not to be confused with the Fregean concept of intension, which is the sense a certain predicate expresses.)

If we understand quantity as extensional quantity, then we obtain a notion of quantitative infinity on which the extension of a property is putatively infinite. Since an infinite extension can either be understood to be an infinite continuum or to be an infinite extension of discrete units, there are two further ways of spelling out quantitative extensional infinity: (1) that a property F is infinite according to its extensional quantity means either that there are infinitely many Fs (an infinite multitude) or that there is an infinite continuum of F (an infinite magnitude).¹⁵ For example, one might take divine omniscience to entail infinite knowledge, in the sense that God knows infinitely many true propositions. Or, (2) one might take divine omnipotence to entail infinite power, in the sense that what God can do has no limits in space or time.

If we understand quantity not in an extensional way but according to its intensio, then we obtain a different notion of syncategorematic quantitative infinity. Whereas the extensional account is concerned with infinitely many Fs or infinitely much of F, this account of syncategorematic infinity is concerned with the degree to which a property is realized in an object. The classical example is “infinite whiteness” (if there were such), which, in the extensional sense, means infinitely many white things, or an infinitely extended white surface, and, in the intensional sense, means unlimited or infinite degree of whiteness (the brightness or, in terms of physics, the capacity to reflect all colors of the visible spectrum). “Mary is infinitely wise” cannot mean that Mary’s wisdom extends to infinitely many or infinitely large entities, but means that the degree of her wisdom is unlimited. Some philosophers take omnipotence to entail infinite power in the sense of God’s power not being limited to any degree.

Finally, we can understand syncategorematic infinity as referring to the mode of givenness of a certain property. What does it mean to say that the mode of givenness of a property is infinite? Could the mode of givenness of some property F be infinite? This is the most puzzling of the notions discussed in this introduction, but there are some uses in which it seems clearly to make sense. For instance, some philosophers take God’s omnipresence to presuppose presence in a mode quite different from the presence of physical objects in space, which can be said to be present at a place by being contained by it. “Presence” applies to God—if it does at all—in a sense that requires dropping the element of limitation by containment.

Since to exemplify a property F in an infinite mode means to possess this property irrespective of any limitations of the exemplifying entity (as in the case of presence), the infinity of the mode of givenness of a property F, exemplified by an entity, is the archetype of what it means to possess F tout court. Any other mode of givenness of this property is consequently a restriction of the archetype in question.

It follows that we obtain different questions concerning the syncategorematic infinity of the divine attributes depending on which interpretation of syncategorematic infinity we have in mind.

The question of whether God is infinite, according to the extensional quantitative approach that refers to discrete units (multitude), is this:

Q3: Does the deity mentioned in the Bible, specified by the minimal theological consensus, and rationally accessed as the ultimate source or goal of everything, exemplify a property the extension of which consists of infinitely many discrete units?

According to the extensional quantitative approach that deploys a continuous notion of extensional quantitative infinity, the question is as follows:

Q4: Does the deity mentioned in the Bible, specified by the minimal theological consensus, and rationally accessed as the ultimate source or goal of everything, exemplify a property the extension of which is an infinite continuum?

According to the intensional quantitative approach, the question of whether God is infinite can be stated as follows:

Q5: Does the deity mentioned in the Bible, specified by the minimal theological cons...

Table of contents

• Half Title
• Title Page
• Copyright
• Contents
• Preface
• CHAPTER 1 Introduction
• PART I Historical Approaches to the Infinity of God
• PART II Systematic Approaches to the Infinity of God
• Contributors List
• Index