Divine Infinity

When Calvin wrote his doctrine of God section of the Institutes he limited himself to only two divine attributes: the infinity and spirituality of God. Naturally this has inspired many an anti-intellectualist in the Reformed tradition to conclude that we shouldn’t be talking about too many of the attributes of God. And there are even statements by Calvin that seem to suggest this very thing.

The Scriptural teaching concerning God’s infinite and spiritual essence ought to be enough … But even if God to keep us sober speaks sparingly of his essence, yet by those two titles that I have used [immeasurable and spiritual], he banishes stupid imaginings and restrains the boldness of the human mind. Surely, his infinity ought to make us afraid to try to measure him by our own senses. Indeed, his spiritual nature forbids our imagining anything earthly or carnal of him [1].

So, it is concluded, Calvin was meeting head on the Scholastic theology proper that treated all of the attributes by logical analysis. But I would like to suggest a different thesis. As Richard Muller has conclusively demonstrated, there was no radical break between Calvin and the early Reformers and the later Reformed Scholastics. Rather the first generation was doing what a first generation always must do: reform, polemics, and demonstrating from the main sourcebook, namely the Scriptures. Dogmatic theology takes stages of building. Arguably Calvin’s doctrine of God, in the Institutes, is not even a “theology proper section” so much as a polemic against Roman idolatry. So why divine infinity and spirituality? The answer is quite simply that these are the two divine attributes most directly lied about in the fashioning of an idol. 

Defining Infinity 

The concept of infinity we have in mind, when spoken of God, is that of limitless or boundless essence. Berkhof offers this as a concise definition: “The infinity of God is that perfection of God by which He is free from all limitations” [2]. Bavinck says, “When applied to time, God’s infinity is called eternity; when applied to space, it is called omnipresence … Infinity is not a negative but a positive concept: it means, not that God has no distinct being of his own, but that he is not limited by anything finite and creaturely” [3]. So in other words, infinity is fundamentally not of number, but of essence. Hodge is in agreement that the very aspect of limitlessness of being makes infinity “a positive idea” [4] and not merely a negation. The negation comes in its application to time, space, knowledge, power, and so forth. 

We must distinguish between absolute infinite and relative infinity. There are relative senses of infinity, such as when the species of a thing are said to be innumerable (e. g. the stars in the universe, or the sands on the shore or in the sea), but absolute infinity belongs to God alone.

Absolute infinity is that limitless sense about necessary being; relative infinity is relativized, first, by its being theoretical of collections and not traversable as an actual infinite, as has already been proven in the kalam cosmological argument. Thus it follows that only a single and simple Being can be absolutely infinite. There can be no more than One, possessing absolute infinity in Himself. Likewise as divine infinity is not the superlative of discrete mathematical entities, neither is He the superlative of continuous geometric entities. As Berkhof says, we must conceive of this infinity as “intensive rather than extensive” [5], since even boundless extension can be subdivided, and thus imply parts. 

Searching Out Infinity 

We can show divine infinity from Scripture in the following passages: “Great is the Lord, and greatly to be praised, and his greatness is unsearchable (Ps. 145:3);

Can you find out the deep things of God? Can you find out the limit of the Almighty? It is higher than heaven—what can you do? Deeper than Sheol—what can you know? Its measure is longer than the earth and broader than the sea (Job 11:7-9).

Who has measured the Spirit of the Lord? … To whom then will you liken God, or what likeness compare with him? (Isa. 40:13, 18) 

Turretin affirmed infinity “against Socinus and Vorstius” [6]. The Westminster Shorter Catechism answers the question What is God? By answering, “God is a spirit, infinite, eternal, and unchangeable, in his being” [7], and so forth with more communicable attributes. Note the influence of Calvin on that answer, but note also its consistency with the Thomist order. Then there are the opening words of Chapter 2 of the Confession: “There is but one only living and true God, who is infinite in being and perfection, a most pure spirit, invisible, without body, parts, or passions.” The Belgic Confession also lists “spiritual Being” and “infinite” within its definition of God [8].

It has already been said that the Reformation principle finitum non capax infinitum is often misunderstood. This is only to set the boundary where Scripture itself does in places like Deuteronomy 29:29. There is that which is hidden and that which is revealed. The essence of this line, however, is not merely God’s freedom to reveal what he pleases—though that is certainly important—but rather that, by definition, the divine essence cannot be grasped. God dwells in “unapproachable light” (1 Tim. 6:16). Hence the incomprehensibility of God is an entailment of his infinity. Not that we cannot know him truly, as he has revealed himself to us, but only that we cannot know him in the depths of this essence. To put it in colloquial terms, we can only “scratch the surface.” That will be true in the eternal state, as God will never cease to be infinite, and we will never make headway against that in our finitude.

Objections to the Infinite God

The objections that Thomas fields to God’s infinity instantly reveal category mistakes that have already been overthrown. Infinity is conceived, by the objections, to be the superlative of either (i) parts or (ii) substance. In other words, since God is not the maximum amount of whatever he is, or since he is not absolutely everything (in other words, he is A and not ~A), then clearly he is defined. And since to be defined is to be finite — limited to be oneself and not another — then it follows that the notion of divine infinity is incoherent. Thomas responds in general by saying that “We must consider … that a thing is infinite because it is not finite” [9]. In other words, the basic meaning of the word infinite is apophatic in nature: that is, understood by what it is not. 

But can’t other things be infinite? Or why must there be only one? Thomas replies that “The infinite cannot have a beginning … But everything outside God is from God as from its first principle. Therefore besides God nothing can be infinite.” The notions that God, being infinite in power, thus has the ability to make another infinite being, or that the capacities of created intellect are infinite, are both category mistakes. So Thomas adds that, “Things other than God can be relatively infinite, but not absolutely infinite” [10]. As already introduced, this is no convenient word play. This is a real distinction between that which is fundamentally cumulative and sequential, on the one hand, as opposed to that which is singular and indivisible, on the other. The two concepts are very different: rooted in the metaphysical difference between magnitude (or multitude) and essence (Articles 3 and 4).

The misunderstanding that “the infinite” must mean “the sum of all things,” has been famously made by the Puritan theologian, John Howe, the early fideist, Jacob Böhme, and perhaps most notoriously, by Spinoza, who more explicitly worked this out in his rationalist pantheism. But note again the error in reasoning: If a thing is infinite, it is every-thing. Surely this is a category mistake.

Hodge counters with what should be obvious: “A thing may be infinite in its own nature without precluding the possibility of the existence of things of a different nature” [11]. Notice that the argument predicates infinity to being, so that the conclusion “All is infinite” is really to beg the whole question. Whether a [some] thing is infinite implies that all things are infinite, let alone that this “one thing” really is “all things,” is to commit the fallacy of composition in a most egregious manner. 

Implications of Infinity

We may derive God’s infinity as a logical consequence of God’s perfection and power. In almost Anselmian language, Turretin says, “it is evident that nothing can be or be conceived better and more perfect. Thus he must necessarily be infinite because an infinite good is better than a finite … he embraces every degree of perfection without any limitation” [12]. For example, God’s love is infinite: “For as high as the heavens are above the earth, so great is his love for those who fear him” (Ps.103:11).

Turretin also shows how the infinity of God may be derived from simplicity and, from there, safeguards all other divine attributes from any attempt to limit God: “The infinity of God follows from his simplicity and is equally diffused through the other attributes of God, and by it the divine nature is conceived as free from all limit in imperfection” [13].

That God is infinite per se implies the immensity of God, with respect to space, and eternity of God, with respect to time, and the incomprehensibility of God, with respect to essence. It implies these, but, as suggested already, it is not defined or exhausted by any of these.

Divine infinity has implications for theological method. Bavinck says, “God, therefore, is not really named after things present in creatures, but creatures are named after that which exists in an absolute sense in God” [14]. With divine infinity we see the clearest necessity for the via negativa, or apophatic theology. Applied to the other attributes it causes us to say in reply to this or that notion about God, “No, not that … or that either.” This is bound to frustrate the modern mind already so intoxicated on its own perceived limitless capacities. Moreover there is a modern sensibility to be for things and never against things. In this way divine infinity is at once the ultimate rebuke to our intellectual pretensions and the surest way to expand the mind.

Charles Spurgeon once said,

There is something exceedingly improving to the mind in a contemplation of the Divinity. It is a subject so vast, that all our thoughts are lost in its immensity; so deep, that our pride is drown in its infinity. Other subjects we can compass and grapple with; in them we feel a kind of self-content, and go our way with the thought, “Behold I am wise.” But when we come to this master science, finding that our plumbline cannot sound its depths, and that our eagle eye cannot see its height, we turn away with the thought that vain man would be wise, but he is like a wild ass’s colt; and with solemn exclamation, “I am but of yesterday, and know nothing.” No subject of contemplation will tend more to humble the mind, than thoughts of God [15].

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1. Calvin, Institutes, I.13.1.

2. Berkhof, Systematic Theology, 59.

3. Bavinck, Reformed Dogmatics, II.159, 160.

4. Hodge, Systematic Theology, II.5.5.

5. Berkhof, Systematic Theology, 59.

6. Turretin, Institutes, I.3.8

7. Westminster Shorter Catechism, Q.4

8. Belgic Confession, Article 1.

9. Aquinas, Summa Theologica, I. Q.7, Art. 1

10. Aquinas, Summa Theologica, I. Q.7, Art. 2

11. Hodge, Systematic Theology, II.5.5.

12. Turretin, Institutes, I.3.8.6

13. Turretin, Institutes, I.3.8.1

14. Bavinck, Reformed Dogmatics, II.130.

15. Charles Spurgeon, quoted in J. I. Packer, Knowing God (Downers Grove, IL: InterVarsity Press, 1973), 17-18.