Infinity in Theology and Metaphysics

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It would be profitless (even if it were possible) to catalog every nuance that the word infinity possesses in minor, as well as major, thinkers. Fortunately, the dominant strands are clear. Among these the theistic one is the most important both historically and in terms of contemporary debate.

Greek Philosophy


The first Western philosopher to speculate on infinity was the pre-Socratic Anaximander. By the infinite (to apeiron ) he meant a limitless substance from which the limited things that constitute the world have come. This substance is limitless in three respects: It is eternal, not having a beginning or an end; it is inexhaustible; and it lacks internal boundaries and distinctions. But it is not spatially unlimited, for Anaximander (almost certainly) conceived it as a sphere. Also, it is not qualitatively indeterminate, like Aristotle's unformed matter, for it contains nature's basic elements in a fused, nonseparated state.


The Pythagoreans adopted Anaximander's concept. Some of them identified it with air (which Anaximenes considered to be the basic constituent of the universe). But their main contribution was to posit a limit (peras ) as a principle that gives structure to the limitless or infinite. This limit was mathematical; the limitless once limited gives the point, twice limited the line, thrice limited the plane, and four times limited the solid. Later writers interpreted Pythagoras theologically. Thus in the Placita we are told that he believed in two principlesthe monad (God, the Good, the essential nature of the One, Nous alone and by itself) and the indefinite dyad (or evil, which is bound up with materiality and multitude).


Plato's speculations on infinity are contained in his Philebus. He gives a fourfold classification of "all that now exists in the universe." The whole world can be viewed in terms of the unlimited, limit, mixture, and the cause of the mixture. This theory is an application of the axiom that the nature (and therefore the good) of anything consists in an intelligible order or proportion. The cosmic cause mixes limit with the unlimited and so imposes structure on the world. In 15d17a Plato interprets the peras-apeiron contrast logically. The unlimited stands for particulars, and the limited for the species into which they can be put. But in 23c26d the contrast has an ontological significance of a Pythagorean kind. The limitless consists in a collection of opposites (for example, hot and cold, dry and moist). Limit consists in "all that puts an end to the conflict of opposites with one another, making them well proportioned and harmonious by the introduction of number" (25e). This principle of limitation is essential also in the moral realm. Plato affirms that human pleasures (which, in themselves, tend to unlimited excess) ought to be rationally controlled by a law and order that are marked by limit.

Thus, in classical Greek philosophy infinity represents a substratum that is formless, characterless, indeterminate. It is a pejorative word. An entity is good to the extent that it is limited by form. The Pythagoreans identified this form with numerical ratios. But, as the Philebus shows, it can be nonnumerical (such as a universal essence or the personal activity of reason).

An important fact emerges from this survey. Plato could not envisage God (or the divine) as infinite. If God is perfect, he must represent the principle of limit. The cause of cosmic mixture in the Philebus is equivalent to the Demiurge in the Timaeus. The latter's task is to impose intelligible form on preexistent matter and thereby make an ordered whole. Otherwise the world would be a vast apeiron a formless, unintelligible chaos. Hence, to say that he is apeiros, or that the Forms that he copies are apeira, would have seemed self-contradictory.


Plotinus occupies a place between Plato and Christian theologians who, if they are orthodox, regard infinity as the first among God's attributes. Plotinus applied the concept of the infinite, or unbounded (apeiron or aoriston ), to two categories of being. First, he applied it to matter, which is evil because it tends intrinsically to formlessness. In this he developed philosophical tradition. But second, he applied it to the divine hypostasis. Thus, he called Mind infinite because of its endless power, its complete unity, and its self-sufficiency. Yet while he says that the One is formless, he does not say that it is infinite. The history of apeiron prevented him from predicating it of the Absolute. He expressed the infinite nature of the One by denying that any positive idea abstracted from finite experience is applicable to it.

Medieval and Modern Philosophy and Theology

Throughout the postclassical period of Western thought it has been widely assumed that God, or the Absolute, is infinite, or limitless. The division lies between those philosophers (such as Giordano Bruno, Benedict de Spinoza, and G. W. F. Hegel) who interpret God pantheistically and those (especially Christian theists) who hold that he wholly transcends the world. According to the first group of thinkers, the world, being divine, is also infinite (even if particular things and persons reflect its infinity in limited degrees). According to the second group, the whole world is finite (as created), and only God (as the Creator) is infinite.


The clearest example of the pantheistic group is Spinoza. Having posited one substance (God or nature), he affirmed that it must be infinite both in its essence and in the number of its attributes. God must be infinite in his essence because if he were finite, we could suppose the existence of something else by which he is limited, so that he would not be the sole reality. His attributes must be infinite because if his essence is infinite, there must be an infinite number of ways in which it can be conceived.

Hegel's theory is more dynamic and complex. It was based on the conviction that finite and infinite are correlative terms within a single system of thought and reality. The Absolute Spirit (God) is infinite. But it does not exist outside the finite spirits through whom it manifests itself. Since the world is the manifestation of the Absolute, and since the Absolute requires the world for its development, we can predicate infinity either of the Absolute (considered as an identity-in-differences) or of the world (considered as a rational totality). Hegel considered Christianity to be the highest form of religion because it represents a perfect reconciliation between man and God, the finite and the infinite.

Any theory that views the finite as, in some sense, the self-expression of the infinite is exposed to two basic objections.

  1. The world (so the theist claims) is not limitless. It is limited in two main ways. First, it is morally imperfect. The premise of Immanuel Kant's moral argument for immortality is irrefutable. We cannot in this life bring our wills into complete accordance with the moral law, and even if we could do so, the spatiotemporal order could not fulfill our deepest longings (as A. E. Taylor argued in his Gifford Lectures). Second (and this is the core of theism), the world in all its aspects bears the marks of radical contingency, so that its existence cannot be explained unless we suppose it to be derived from a transcendent being who is infinite or absolute.
  2. In any case, the world is full of differences and discordances. How can these be reconciled within a unitary Absolute? How can a set of finite (that is, limited and mutually exclusive) entities constitute a nonlimited and all-inclusive whole? In particular, how can this whole, if it is complete and perfect (as it must be if it is infinite), contain within itself both good and evil? There is no satisfactory answer to these questions. Nicholas of Cusa, in his pantheistic moments, affirmed that in God there is a "synthesis of opposites" (coincidentia oppositorum ). Similarly, Friedrich von Schelling affirmed that the Absolute is a self-identity in which all differences vanish. But these affirmations are metaphysically vacuous, as Nicholas admitted when, using mystical terminology to conceal a contradiction, he called our knowledge of the all-inclusive Maximum a docta ignorantia.


Theists do not have to face the above problems. Certainly they hold that all perfections preexist in God eminently. But they also hold that the mode of this existence is determined by the infinity that God does not share with any creature. God's infinity means that he is "not-finite." He is free from the limitations that affect every other being. There are two fundamental limitations.

First, every other being is a mode of existence (or existing). A man exists in one way, a dog in another. But God is existence simpliciter. He does not suffer from the determinations that are reflected in genera and species. We can express this (with deliberate paradox) by saying that he is his own genus.

Second, if God is existence "in itself," he must be self-existent in the sense that he does not derive his being from any other source. Every other being is dependent or derived. It does not contain within itself the cause of its existence. It depends continuously on the creative act of God who alone exists a se (that is, by his own intrinsic power).

Both these aspects of God's infinity are affirmed by the Scholastic dictum that in him essence and existence are identical. The finitude of any being consists in the lack of this identity at both the points mentioned above. Its essence limits its existential act (or pattern of activity), and this limitation follows from its dependent character. It exists as "this" or "that" by its derivation from a being who is existence in a necessary and perfect form.

This view of God's infinity must be safeguarded by the following assertions.

  1. God's infinity is not to be interpreted as formlessness (as if it were equivalent to Plato's apeiron ). It is the nature of finite being (at any rate in the subangelic realm) to be a compositum of form and matter. The form limits matter. Without some degree of limitation there would be no difference (either generically or individually) between one finite being and another. But since God's essence and existence are identical, his form cannot be a principle of limitation. "Matter," Thomas Aquinas wrote, "is perfected and made definite by form. Infiniteness attributable to matter is imperfect and amorphous. On the other hand, form as such is not perfected by matter, but contracted rather; hence infiniteness attributable to form is perfection" (Summa Theologiae I, 7, 1).
  2. God's infinity is incomprehensible. We cannot imagine or conceive it. We can know that God is self-existent. But how he is self-existent is utterly unknowable by us in our present state. As soon as we try to represent his infinity through a univocal use of concepts, we commit three errors. We fall into anthropomorphism; we confuse infinity with formlessness; and, finally, we reach a self-contradiction, for the essence of a finite entity (however high it may be on the scale of being) is to possess a form that acts as a limit that excludes other forms.

However, the various attributes that constitute God's character are all deducible from his self-existence. He must be absolutely simple, for if in him essence and existence are identical, his qualities must be coinherent through the whole range of his activity. He must be spiritual and nontemporal, for corporeality entails spatial limitation and temporal successiveness implies divisibility. He must be omniscient and omnipotent, for there cannot be any externally imposed limit to his knowledge or his power. Finally, he must be absolutely good.

Two of these characteristics, spirituality and eternity, call for comment. Since God is nonspatial and nontemporal, the concept of his infinity is unaffected by the views we hold concerning space and time. Whether space and time are limited or unlimited makes no difference to the claims of the theist concerning God's infinity and his relation to the world. Thus, even if the world has existed for an endless length of time, it would still (according to the Cosmological Argument) be endlessly incomplete, so that we should still have grounds for positing a nontemporal act of divine creativity.

Yet the theistic view of God's infinity raises problems of its own. Four are especially urgent. First, if God is infinite and we are finite, how can we speak of him positively (as the biblical writers and doctrinal theologians do)? Second, Christians affirm that God is personal. But does not the idea of personality conflict with the idea of infinity? (This objection was first urged by Carneades and later elaborated by David Hume.) Third, is it not contradictory to say that all God's attributes (for example, justice and mercy) can coexist in a limitless degree? Are not even theists forced to posit a coincidentia oppositorum in the Godhead? Fourth, if God is infinite both in goodness and in power, how can we explain the presence of evil in the world?

The answers that theists normally give to these objections are as follows.

  1. While we cannot speak of God univocally, we can do so analogically. But in applying any analogue to God, we must distinguish between the manner of predication and the object signified. The only positive meaning that we can attach to a term we predicate of God is the one which it has when predicated of finite beings. Yet since God and the creature are ontologically related by an analogy of attribution, we can affirm that (although we cannot know how ) the divine analogate possesses the analogue, according to the analogy of proportionality, in a manner appropriate to his infinite existence.
  2. The basic answer to the second question is that we need not equate the essence, or norm, of personality with its human mode. On the contrary, the latter (according to the Bible) is a created image of an infinite archetype. The theist would claim that while we cannot see how God can be both infinite and personal, we can understand that an infinite existence, so far from being incompatible with personality, would represent it in its most perfect form. At any rate (so the theist would maintain), it is not contradictory to assert that individuality can exist without individuation and that God therefore can have a positive character without possessing characteristics of the kind that differentiate a member of one created genus from a member of another.
  3. If God's attributes were essentially incompatible, they could not be predicated of him infinitely and simultaneously without a logical contradiction that could be solved (as Nicholas and Schelling found) only by an asylum ignorantiae. But theists claim that any contradiction is only apparent. Everything depends on how we define our terms. Thus, if we take justice to mean retribution, it is bound to be incompatible with mercy, if both are infinitely conceived. But if we take it to mean the vindication of the moral order, mercy becomes (as St. Paul saw) the primary form of its expression.
  4. Most Christian theists would admit that the fact of evil seems to be incompatible with belief in a God who is infinite both in goodness and in power. But they would also claim that the apparent incompatibility disappears once we recognize first, that since God's power and goodness are inconceivable, his purposes are bound to be largely inscrutable and second, that in Christ he has shown that he not only can but also does bring the greatest good out of the greatest evil.

See also Absolute, The; Analogy in Theology; Anaximander; Bruno, Giordano; Carneades; Cosmological Argument for the Existence of God; Eternity; Hegel, Georg Wilhelm Friedrich; Hume, David; Nicholas of Cusa; Plato; Plotinus; Pythagoras and Pythagoreanism; Schelling, Friedrich Wilhelm Joseph von; Spinoza, Benedict (Baruch) de; Taylor, Alfred Edward; Theism.


For literature on Anaximander, see F. M. Cornford, "Anaximander's System," in Principium Sapientiae (Cambridge, U.K.: Cambridge University Press, 1952), pp. 159186. Plato's views in the Philebus are discussed by R. Hackforth in his commentary in Plato's Examination of Pleasure (Cambridge, U.K.: Cambridge University Press, 1945). A. H. Armstrong surveys Plotinus thoroughly in "Plotinus" Doctrine of the Infinite and Christian Thought," in Downside Review (Winter 19541955): 4758. The teaching of Thomas Aquinas on God's infinity (together with associated attributes) is collected by Thomas Gilby in his anthology Philosophical Texts (Oxford: Oxford University Press, 1956). Nicholas of Cusa, De Docta Ignorantia, is translated by G. Heron, with an introduction by D. J. B. Hawkins (New Haven, CT: Yale University Press, 1954). Bruno's theory of infinity can be found in On the Infinite Universe and Worlds, which has been translated by D. W. Singer in Giordano Bruno: His Life and Thought (New York: Schuman, 1950). A lucid summary of Hegel and Schelling (with ample references) is given by Frederick Copleston in A History of Philosophy, Vol. VII (London, 1963). For a discussion of infinity in traditional Christian theism (and the problems that it raises), see A. M. Farrer, Finite and Infinite (London: Dacre Press, 1943), and E. L. Mascall, Existence and Analogy (London: Longmans Green, 1949).

Adams, Robert. Finite and Infinite Goods: A Framework for Ethics. Oxford: Oxford University Press, 1999.

Benardete, José. Infinity: An Essay in Metaphysics. Oxford: Oxford University Press, 1964.

Bolzano, Bernard. Paradoxes of the Infinite. Translated by F. Prihonsky. London: Routledge and Kegan Paul, 1950.

Duhem, Pierre. Medieval Cosmology: Theories of Infinity, Place, Time, Void, and the Plurality of Worlds. Chicago: University of Chicago Press, 1985.

Ganssle, Gregory, and David Woodruff, eds. God and Time: Essays on the Divine Nature. Oxford: Oxford University Press, 2001.

Kretzmann, Norman, ed. Infinity and Continuity in Ancient and Medieval Thought. Ithaca, NY: Cornell University Press, 1982.

Le Poidevin, Robin, ed. Questions of Time and Tense. Oxford: Clarendon Press, 1998.

Moore, A.W. The Infinite. London: Routledge, 1990.

Moore, A.W., ed. Infinity. Aldershot, U.K.: Dartmouth, 1993.

Sweeney, Leo. Divine Infinity in Greek and Medieval Thought. New York: Peter Lang, 1992.

H. P. Owen (1967)

Bibliography updated by Christian B. Miller (2005)