If All Things are Possible with God, Could 2+2 = 5 Through God’s Will?
The answer is no, and the reason goes to the very nature of God Himself. The proposition "2+2=5" is not a mere mathematical error; it is a philosophical and theological challenge to the nature of truth, reason, and divine order. The claim that "all things are possible with God," and therefore that 2+2=5 could, in some sense, "be," is a dangerous extreme of a position known as voluntarism — the notion that the divine will (voluntas) is so absolute that it can override logic and reason itself. This essay argues, with St. Thomas Aquinas as its principal guide, that such a position fundamentally misunderstands the nature of God and of creation.
I. God's Nature: The Unity of Will and Intellect
At the heart of Catholic theology stands the doctrine that God's will and intellect are perfectly unified, each flowing from the other in the single, undivided act that is God Himself (Deus est actus purus).1 Aquinas explains that God's will does not act arbitrarily but always according to His own wisdom: Deus non vult aliquid nisi secundum rationem suae sapientiae ("God wills nothing except according to the order of His wisdom").2 Because God is absolutely simple — simplicitas Dei — there can be no fissure between what He wills and what He knows to be true.3 Will divorced from intellect is caprice; intellect divorced from will is inert. In God, voluntas and intellectus are unum et idem — one and the same — precisely because He is not composed of parts that could pull against one another.4 To suggest that God could will "2+2=5" is to posit an internal contradiction within the divine essence, a rupture Aquinas rejects outright, since a being of pure act (actus purus) admits no potency toward self-contradiction.5
II. Truth as Conformity to Reality
Truth, for Aquinas, is adaequatio intellectus et rei — the conformity of intellect to reality.6 Mathematical truths such as "2+2=4" are not human conventions but reflect the very structure of created being, which itself mirrors the eternal wisdom by which God conceived it (veritas rerum a Deo dependet sicut a causa).7 The scholastics went further still, holding that being and truth are convertible transcendentals — ens et verum convertuntur — such that whatever truly is is, by that very fact, intelligible and true.8 To sever "2+2=4" from reality is therefore not merely to err arithmetically but to attack the transcendental bond between being and truth itself.
Aristotle grounds this in the principle of non-contradiction: impossibile est idem simul esse et non esse ("it is impossible for the same thing to be and not to be at the same time").9 "2+2=5" violates this principium contradictionis, the first and most certain of all principles (principium firmissimum), upon which every other act of reasoning silently depends.10 Were this principle to fail even once, no proposition — theological, moral, or mathematical — could be known with certainty; reason itself would collapse into nihil.
Maimonides, whose Guide for the Perplexed deeply shaped the scholastics who followed him, including Aquinas, makes the identical point from within the Jewish philosophical tradition: "the power of God extends to everything possible, but the impossible remains impossible and cannot become possible."11 For Maimonides, God's potentia is perfect precisely because it need not extend to nonsense; omnipotence over the impossible is not a greater power but an incoherent one. Augustine anticipates the same insight when he insists that number itself participates in the eternal wisdom of God — numerus in mente Dei — and is therefore no more alterable than God's own wisdom.12
III. The Two Powers of God: Potentia Absoluta and Potentia Ordinata
The scholastic distinction between God's potentia absoluta (absolute power) and potentia ordinata (ordained power) sharpens this argument considerably.13Potentia ordinata names the power by which God acts in accordance with the order He has freely established for creation; potentia absoluta names, in the stricter Thomistic sense, God's capacity to do anything that does not involve contradictio in terminis — a contradiction in terms.14 Later voluntarist thinkers, particularly in the Ockhamist school, stretched potentia absoluta to suggest that God could, in principle, make false what is now true.15 Aquinas forecloses this move: even God's absolute power operates within the boundary of non-contradiction, for that boundary is not external to God but constitutive of what it means to be at all (ens qua ens).16 "2+2=5" is not a hard case at the edge of divine power; it is simpliciter impossibile — impossible without qualification — because it is not a "thing" (res) that omnipotence could, even hypothetically, will.
IV. The Immutability of Divine Order
Aquinas states this directly: Deus potest facere omnia quae sunt possibilia, sed non quae implicant contradictionem ("God can do all things that are possible, but not those that involve a contradiction").17 The laws of logic and mathematics are not arbitrary impositions but expressions of the lex aeterna, the eternal law by which God governs the universe: lex aeterna est ratio divina gubernans universum.18 To assert "2+2=5" is to introduce a contradiction into the created order itself (ordo creationis), which would not manifest divine power but would instead dissolve the coherence (coherentia) that divine wisdom has impressed upon being.
V. Voluntarism and the Arbitrary God
Voluntarism, pressed to its extreme, holds that the divine will is so absolute that it can alter the nature of truth itself, reducing God's freedom to sheer arbitrium — arbitrary caprice untethered from reason.19 This risks portraying God not as Veritas itself but as a tyrant whose word carries no guarantee of coherence. It is worth noting that even Bl. John Duns Scotus, often invoked as a forerunner of voluntarist thought for his emphasis on the primacy of will, did not go so far as to sever will from reason entirely; his voluntas ut ratio still situates the divine will within an intelligible order, even as he grants it greater priority than Aquinas does.20 The radical voluntarism later associated with nominalism is a further and more dangerous step, one the mainstream Catholic tradition has consistently declined to take.
Aquinas insists that God's will is always rational — voluntas Dei est rationabilis — such that divine freedom operates within the bounds of God's own nature, which is Truth itself (veritas).21 To claim that God could will "2+2=5" would render truth and reason mutable, in direct contradiction to the doctrine of divine immutability: Deus est immutabilis.22
VI. Moral and Philosophical Implications
The stakes are not merely speculative. If truth were subject to arbitrary divine fiat, natural law (lex naturalis) — itself grounded in the rational order of creation — would lose all stability, and with it, the possibility of moral knowledge.23 Aristotle's account of natural principles as self-evident and unchanging (per se nota) aligns with Aquinas's teaching that the created order is rationally discoverable precisely because it is rationally ordered.24 Were mathematical and logical truths revocable by divine decree, the entire fabric of creation (totum universum) would unravel, taking with it both human reason and the very possibility of faith in divine providence, since faith itself presupposes a Deus qui non mentitur — a God who does not lie, and therefore a God bound, by His own nature, to truth.25
VII. Impossibile Est
"2+2=5" is not a simple arithmetic error; it is a denial of the immutable nature of truth and of God's rational order. Aquinas, Aristotle, Maimonides, and Augustine converge on a single point: truth is not subject to arbitrary will but is grounded in reality and in divine wisdom. God's omnipotence is not diminished by His inability to will contradictions — it is affirmed by the perfect unity and coherence of His nature. Voluntarism in its extreme form reduces the divine will to caprice, severed from reason and truth. Catholic theology holds, against this, that God's will and intellect are one, so that truth, as a reflection of God's own nature, is eternal and unchanging (aeterna et immutabilis). "2+2" cannot equal "5" — not because God is limited, but quia Deus perfectus est: because God is perfect.
Endnotes
Thomas Aquinas, Summa Theologica I, q.3, art.1
Thomas Aquinas, Summa Theologica I, q.19, art.1–2
Thomas Aquinas, Summa Theologica I, q.3, art.7
Thomas Aquinas, Summa Theologica I, q.19, art.1, ad 1
Thomas Aquinas, Summa Contra Gentiles I, ch.16
Thomas Aquinas, Summa Theologica I, q.16, art.1 ; see also Thomas Aquinas, Quaestiones Disputatae de Veritate, q.1, art.1.
Thomas Aquinas, Summa Theologica I, q.16, art.1, ad 3.
Thomas Aquinas, Quaestiones Disputatae de Veritate, q.1, art.1 (on the convertibility of the transcendentals ens and verum).
Aristotle, Metaphysics bk. IV, ch.3, 1005b19–20.
Aristotle, Metaphysics bk. IV, ch.3, 1005b11–17 (describing the principle of non-contradiction as the firmest of all principles).
Moses Maimonides, The Guide for the Perplexed pt. III, ch.15
Augustine, De Libero Arbitrio bk. II, ch.8 (on number as residing eternally in the mind of God).
William J. Courtenay, Capacity and Volition: A History of the Distinction of Absolute and Ordained Power 15–20 .
Thomas Aquinas, Summa Theologica I, q.25, art.3.
Courtenay, supra note 13, at 92–98 (describing the Ockhamist expansion of potentia absoluta).
Thomas Aquinas, Summa Theologica I, q.25, art.3, ad 2.
Thomas Aquinas, Summa Theologica I, q.25, art.4.
Thomas Aquinas, Summa Theologica I-II, q.93, art.1.
Frederick Copleston, A History of Philosophy, vol. 2, pt. II, at 209–14 (Image Books 1962) (surveying voluntarist tendencies in medieval scholasticism).
John Duns Scotus, Ordinatio I, d.1, pars 2, q.2 (Allan B. Wolter trans., Franciscan Inst. Publ'ns 1986) (on the priority of will while remaining within an intelligible order).
Thomas Aquinas, Summa Theologica I, q.19, art.4.
Thomas Aquinas, Summa Theologica I, q.9, art.1.
Thomas Aquinas, Summa Theologica I-II, q.94, art.2 (Benziger Bros. ed. 1947).
Aristotle, Nicomachean Ethics bk. VI, ch.6, 1141a5–8 (W.D. Ross trans., Oxford Univ. Press 1925) (on first principles as self-evident).
Titus 1:2 (RSV-2CE, Ignatius Press 2006) ("in hope of eternal life, which God, who never lies, promised before the ages began").
