The Wax Nose of “Infinity”: A Critique of the Misuse of Divine Infinitude in Theology and Its Consequences for Atonement and Eschatology

By Rev. William M. Brennan, TH.D.

Introduction

Few theological terms have caused more confusion, equivocation, and inadvertent error than the word “infinite.” In philosophical theology, infinite has traditionally been applied to God’s being—a move that, if not understood carefully, can mislead both theologian and layperson alike. The term appears noble and venerable, but tradition has wrapped it in layers of conceptual ambiguity. Its modern mathematical meaning (“unending quantity”) competes with its classical metaphysical meaning (“unbounded, without defect”). The result is what Gordon H. Clark called a “nonsense term” when used incautiously, and what others have called a wax nose—a term flexible enough to be shaped into whatever argument one needs.

This essay seeks to accomplish four aims:

1. To clarify the original classical meaning of infinite as used by theologians.

2. To expose the modern quantitative meaning that often infiltrates doctrine unnoticed.

3. To show how the confusion between these two meanings undermines theological arguments, particularly the Anselmian claim that sin against an “infinitely majestic” God requires “infinite punishment.”

4. To argue that the term infinite should be either radically redefined or abandoned altogether, replaced with clearer concepts like “perfect,” “complete,” and “unchanging.”

The argument proceeds by showing that once infinite is properly understood in its classical sense, Anselm’s argument for eternal conscious torment collapses, because it depends on smuggling in the quantitative meaning of infinity. Theological language must therefore be purged of equivocation to maintain coherence and fidelity to Scripture.

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1. The Classical Meaning of “Infinite”: Not Quantity, but Perfection

The first and most important point is this: the classical theological tradition does not use the word “infinite” in the modern mathematical sense of unending quantity or endless process. Thomas Aquinas, Augustine, Boethius, and the Reformed scholastics all used the Latin infinitas to mean “not finite,” which in turn means:

• not limited

• not defective

• not composite

• not dependent

• not possessing unrealized potential

In classical metaphysics, infinite means fullness of actuality, not unbounded size or amount. It is a negative term (via negativa): God is “infinite” because He is not bounded by the limitations that characterize creatures.

Thus:

“Infinite” in classical theology = “perfect,” “complete,” “without defect or limitation.”

Yet in English, the plain meaning of infinite suggests:

• endless increase

• unending quantity

• unbounded expansion

• the mathematical infinite of the number line

This is why the term leads to confusion: it no longer means what classical theology intended. In the modern mind, infinite is nearly always taken quantitatively. The theologian’s meaning and the layman’s meaning have drifted so far apart that the word now functions ambiguously at best and deceptively at worst.

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2. The Modern Mathematical Meaning of “Infinity”: A Contradiction to Classical Theism

Modern mathematics defines “infinity” as potential infinity—a process without limit:

• counting forever

• adding moments endlessly

• extending time or number without completion

The key characteristic of mathematical infinity is that it is never complete. It is endless progression.

But classical theology defines God’s being precisely in terms of completeness, fullness, and the absence of potentiality. To say that God is “infinite” in the mathematical sense would contradict divine immutability, simplicity, and perfection. A God who grows, expands, or increases is not the God of Scripture or classical theism.

Thus:

The mathematical infinite is the opposite of the metaphysical infinite.

To call God “infinite” in the modern sense would make Him:

• mutable

• unactualized

• incomplete

• in process

• not simple

• not perfect

Therefore, theologians who use the word infinite but deny these implications are already using the term in a technical, non-mathematical sense—namely, as perfection.

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3. Gordon H. Clark’s Critique: Infinity as a “Nonsense Term” Misapplied to God

Gordon H. Clark offers three crucial criticisms of the term infinite as applied to God:

A. Biblical Objection

Clark showed that none of the biblical texts the Westminster Confession appeals to actually say God is “infinite.”
For example:

• Psalm 147:5: “His understanding is without number,” not “infinite.”

• Job 22:5: “Thine iniquities are infinite” clearly does not mean literally infinite.

• Nahum 3:9: “Infinite strength” in KJV is a bad translation.

Clark concludes that the Bible neither uses nor supports “divine infinity.”

B. Logical Objection

Clark argued that:

• Infinity is a mathematical concept.

• A truly infinite set can never be completed.

• But God’s knowledge must be complete.

• Therefore, God cannot have an infinite number of thoughts or propositions.

In his glossary:

“Infinite…a nonsense term. Nothing exists that is infinite.”
“If God were infinite, He could not know all things.”

In other words: infinity as quantity is incompatible with omniscience.

C. Methodological Objection

Clark accused some modern theologians of dishonesty: they affirm “God is infinite” but then redefine “infinite” to mean “perfect” or “complete,” which is not what the word means in normal English.

This is the “wax nose” problem: the term is so flexible that theologians can shape it however they want, often smuggling in illicit meanings.

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4. The Wax Nose of Infinity: How Theologians Accidentally Smuggle in Quantitative Meaning

Even theologians who think they are using the classical definition frequently slip into the modern one when building arguments.

Why? Because the word itself invites quantitative interpretation.

Examples:

• “God’s infinite love” becomes “love for every possible thing, even evil.”

• “God’s infinite justice” becomes “justice requiring infinite punishment.”

• “God’s infinite power” becomes “the power to do contradictions.”

• “God’s infinite wrath” becomes “endless retributive anger.”

Each of these is a quantitative misunderstanding, not a metaphysical one.

The moment one uses the word “infinite,” the modern mind automatically thinks of size, amount, or duration.

This is precisely how Anselm’s argument for eternal punishment sneaks in a quantitative notion of infinity, even though the classical definition does not support it.

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5. Anselm’s Argument and the Hidden Quantitative Infinity

Anselm’s classic reasoning in Cur Deus Homo is:

1. God is infinitely majestic.

2. Sin is therefore an offense of infinite magnitude.

3. A finite creature cannot make satisfaction for an infinite offense.

4. Therefore the punishment of the sinner is infinite (in duration).

5. Or only God can make satisfaction (which calls for the Incarnation and the God-man).

At first glance, this seems reasonable. But the logic only holds if “infinite” is used quantitatively at two crucial steps:

• Step 2: “Infinite magnitude”

• Step 4: “Infinite duration”

These are not metaphysical infinities; they are mathematical infinities.

Anselm begins with:

• qualitative infinity (God’s perfection)

but quietly converts it into:

• quantitative infinity (infinite offense)

and finally into:

• temporal infinity (eternal punishment)

This is a textbook equivocation fallacy.

Once we restore the classical meaning of “infinite” as “perfect,” the argument collapses:

• God is perfect in majesty.

• Sin is a maximal offense.

• Punishment must be fitting or perfect, not quantitatively infinite.

There is no logical pathway from perfection to infinite duration.

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6. Why “Infinite Punishment” Is Conceptually Absurd

Punishment cannot be “infinite” in any coherent sense.

A. Infinite Duration = Mathematical Infinity

“Infinite punishment” is usually taken to mean:

• unending temporal duration

• a series of moments without limit

• an unfinishable process

• a potential infinite

This is the infinity of numbers, not the infinity of metaphysics.

B. Perfect Punishment ≠ Infinite Punishment

A perfect punishment is:

• complete

• fitting

• just

• resolved

• finished

But “infinite duration” is never complete. It is always in progress.

Thus:

An endless punishment is, by definition, an imperfect punishment.

It never accomplishes its purpose.
It never resolves the offense.
It never reaches completion.

If divine perfection guides divine justice, punishment must be perfect, not endless.

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7. The Proper Conclusion: Perfect Majesty Requires Perfect Punishment

Your insight is the corrective:

If the offense is against a perfectly majestic Being,
the punishment must be perfect, not infinite.

A perfect punishment may be:

• proportional

• purifying

• restorative

• corrective

• temporary

• aimed at the healing of the offender

• fitting the moral order God wills to establish

But it need not, and indeed cannot, be infinite in the mathematical sense.

A perfect God administers perfect justice—not infinite suffering.

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8. Examples of Theological Missteps Due to Quantitative Infinity

A. Jonathan Edwards

Edwards argued that since God is infinite, sin incurs infinite guilt, requiring infinite punishment. This explicitly equates God’s metaphysical infinity with infinite magnitude.

B. Certain Reformed Scholastics

Some used “infinite justice” as a justification for eternal hell, inadvertently invoking a quantitative notion inconsistent with perfection.

C. Popular Evangelical Apologetics

The phrase “infinite offense against an infinite God deserves infinite punishment” has become a slogan detached from its metaphysical roots.

In all these cases, infinity becomes a wax nose—stretched far beyond its classical sense.

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9. The Way Forward: Abandoning or Radically Qualifying “Infinity”

Given all this, theologians should:

Option A: Abandon the term entirely

Instead of calling God “infinite,” describe Him as:

• perfect

• complete

• unchanging

• immutable

• simple

• fully actual

• lacking nothing

These terms are clearer, biblical, and immune to quantitative distortion.

Option B: Use “infinite” only with severe qualification

If the term must be used (e.g. for historical continuity), it should be defined explicitly as perfection, not quantity.

But the safer route is simply to drop the term.

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Conclusion

The term infinite, as traditionally applied to God, is conceptually unstable in modern contexts. Its classical meaning—“without defect or limitation”—has been eclipsed by its modern mathematical meaning—“unending quantity.” This shift has allowed theologians to smuggle quantitative concepts into doctrines where they do not belong, especially in the area of punishment, guilt, and atonement.

The most destructive example is Anselm’s argument for infinite punishment, which depends on equivocating between:

• metaphysical infinity (perfection)

• quantitative infinity (magnitude)

• temporal infinity (duration)

Once infinity is restored to its proper meaning—or abandoned altogether—Anselm’s deduction collapses. We are left not with eternal conscious torment, but with the demand for perfect, fitting, morally complete punishment, consistent with God’s goodness, wisdom, and ultimate purposes.

In this light, “infinite punishment” is not only unnecessary—it is logically impossible. What remains is the perfection of divine justice, which, rather than expressing itself through endless torment, fulfills its purposes in a manner consistent with the character of a perfect, complete, and unchanging God.