Theopedia

Law of noncontradiction

Definition

The law of noncontradiction is the principle that the same attribute cannot both belong and not belong to the same subject, at the same time and in the same respect. First given precise statement by Aristotle, it functions as one of the most basic laws of thought: not itself provable by some more fundamental argument, since every argument already depends on it, but self-evident to any mind capable of reasoning at all. A claim that violates it is incoherent: it cannot be affirmed or denied at all.

Confessional Witness

The 1689 Second London Baptist Confession has no chapter addressing logic or the laws of thought as such; the law of noncontradiction was not a live confessional dispute the way, say, the extent of the atonement was. The confession’s own epistemology depends on it nonetheless. Its opening chapter holds that sound doctrine may be reached not only where Scripture states it in so many words but also wherever it “by good and necessary consequence may be deduced from Scripture.”1 Valid deduction is only as reliable as the laws of logic governing it, so a confession willing to found doctrine on necessary inference is committed, without naming it, to the law of noncontradiction holding good of the God who inspired Scripture and the world Scripture describes.

Biblical Basis

Scripture nowhere states the law of noncontradiction as a formal principle the way Aristotle later would, but it assumes and applies it throughout. Jesus reasons directly from it: “every kingdom divided against itself is laid waste, and no city or house divided against itself will stand” (Matt. 12:25). The same impossibility, that a single thing be simultaneously for and against itself, is his argument that his own exorcisms cannot serve Satan’s kingdom while opposing it. Paul’s defense of his own reliability leans on the same principle, grounding it in God’s: his plans were not made “according to the flesh, ready to say Yes and No at once,” because “the Son of God… was not Yes and No, but in him it is always Yes” (2 Cor. 1:17-19). That God’s own character admits no contradiction is stated repeatedly in its own right: he “is not man, that he should lie” (Num. 23:19); he “never lies” (Titus 1:2); he “cannot deny himself” (2 Tim. 2:13); and he is “not a God of confusion” (1 Cor. 14:33). None of these texts argue for the law of noncontradiction as a philosophical claim; they simply take it as true of God himself. Paul treats human reliability as an image of that same divine consistency.

Historical Development

Aristotle’s formulation

Aristotle gave the law its classical statement in the Metaphysics: “the same attribute cannot at the same time belong and not belong to the same subject and in the same respect.”2 He treated it as the starting point for rational argument rather than a conclusion reached by one. Denying it, he argued, costs the denier the ability to say anything intelligible at all: a denial only means something if it excludes its opposite, which is already an instance of the very law being denied.3 On Aristotle’s own account, the law cannot be demonstrated from something more basic, because nothing more basic is available to demonstrate it from.

Aquinas’s use of the law

Thomas Aquinas relied on the same principle in the first of his Five Ways. The argument holds that whatever is moved must be moved by another, and that the resulting chain cannot regress infinitely, because it is impossible, in the same respect and the same way, for a thing to be both mover and moved.4 Without the law of noncontradiction ruling out a thing setting itself in motion in the very respect in which it is moved, the argument has no way to reach a first, unmoved mover.

Reformed orthodoxy

Reformed scholastic theology treated the law as binding on theology itself, not only on philosophy. Francis Turretin held:

“Basic rational principles like the law of noncontradiction apply in both the sphere of nature and the sphere of grace. As grace perfects nature, so faith perfects and utilizes reason in the formulation of doctrine.”5

On this view, grace renews reason rather than abolishing it. Turretin calls reason theology’s “handmaiden,” used to draw valid conclusions from what Scripture teaches; revelation does not suspend the law of noncontradiction for theological subject matter, it presupposes that the law holds of God as much as of anything else.

Doctrinal Significance

The law of noncontradiction is commonly classed among the self-evident “laws of thought”: principles the mind presupposes in order to reason at all, rather than principles reasoned to. Herman Bavinck groups it with the “seeds of the sciences” implanted in every person, holding that “the laws of thought are the same for all.”6 On this account the law is not itself an item of special revelation; it belongs to the natural knowledge every person already possesses as a creature made in God’s image, prior to and apart from any particular argument for God’s existence.

That the law actually holds of reality, rather than being a mere convention of human language, is itself grounded in who God is. John Oswalt locates “a basis for the law of noncontradiction in the recognition that God is not the world and the world is not God.”7 Because one transcendent Creator, not a plurality of competing, capricious deities, stands behind the created order, that order is coherent and stable enough for the law to describe it reliably, not merely a human habit of speech imposed on chaos.

Opposing Views

Evidentialist and presuppositional apologetics

Christian apologists disagree over whether the laws of logic can be treated as neutral common ground with an unbeliever. Harold Netland has argued that the law of noncontradiction functions “neutrally” as a worldview-independent criterion of truth, not itself dependent on the Christian worldview being true.8 Michael Kruger answers that this concedes too much: an atheistic, materialistic universe governed by chance gives no reason to expect immaterial, transcendent, universal laws of thought to exist at all, and treating the laws of logic as more basic than God reverses the biblical order, in which right thinking depends on God rather than the reverse (Prov. 1:7; Matt. 22:37; 1 Cor. 1:20; 2 Cor. 10:5; Col. 2:3).8 On Kruger’s account the law of noncontradiction is not neutral ground shared equally by every worldview; it is itself evidence for the God who grounds it.

Ancient Near Eastern mythopoeic thought

Ancient Near Eastern religious literature did not treat consistency as a governing constraint on its own accounts of the gods and the world: two mutually exclusive versions of the same event or deity could stand side by side without being felt as a problem needing resolution. Oswalt reads this as evidence of a genuinely different worldview, not a stylistic quirk, one tied to a realm of many competing, finite deities rather than one transcendent Creator.7

Objections and Responses

Doesn’t the Trinity, three persons in one being, violate the law of noncontradiction? The objection assumes the doctrine affirms and denies the same thing of the same subject in the same respect, which is exactly what the law forbids. But the doctrine does not say God is one and three in the same respect: he is one in respect of being, and three in respect of person.9 Craig Carter calls the doctrine “a paradox, not a contradiction, because there is a difference” between being and person, even though theologians cannot fully articulate the exact nature of that difference.9 John Gill made substantially the same move nearly three centuries earlier against the charge that a Trinity of persons in one God, and the Son’s eternal generation from the Father, are contradictions in terms: no more so, he answered, than any other case of one thing being truly described under two really distinct aspects.10 The same answer extends to the hypostatic union: Christ is one in respect of person and two in respect of nature, not one and two in the same respect.

If the law of noncontradiction is self-evident and cannot itself be demonstrated, how can anyone be sure it is true rather than merely assumed? Aristotle’s own answer is that denying the law is self-defeating rather than merely unproven: a denial only counts as a denial if it means one thing and not its opposite, which is already an application of the very law supposedly being denied.3 The law cannot be proved from something more basic because nothing more basic is available for an argument to stand on; its truth shows itself in the impossibility of coherently denying it, not in a prior proof of it.

Related Doctrines

References

  1. The Second London Baptist Confession of Faith (1689), chap. 1, “Of the Holy Scriptures,” para. 6. ↩

  2. Louis Markos, From Aristotle to Christ: How Aristotelian Thought Clarified the Christian Faith (Downers Grove, IL: IVP Academic, 2024), “The Law of Noncontradiction,” quoting Aristotle, Metaphysics IV.3. ↩

  3. Markos, “The Law of Noncontradiction”: “Aristotle states, boldly and unapologetically, that anyone who thinks that the self-evident law of noncontradiction needs to be demonstrated lacks true philosophical training.” ↩ ↩2

  4. Markos, From Aristotle to Christ, “How to Read the Heavens and the Earth.” ↩

  5. Steven J. Duby, God in Himself: Scripture, Metaphysics, and the Task of Christian Theology, Studies in Christian Doctrine and Scripture (Downers Grove, IL: IVP Academic, 2019), chap. 2, “Preparation for the School of Grace,” discussing Francis Turretin. ↩

  6. Herman Bavinck, Reformed Dogmatics: Abridged in One Volume, ed. John Bolt (Grand Rapids: Baker Academic, 2011), chap. 7, “Knowing God.” ↩

  7. John N. Oswalt, The Bible among the Myths: Unique Revelation or Just Ancient Literature?, Ancient Context, Ancient Faith (Grand Rapids: Zondervan, 2009), chap. 2, “The Bible and Myth: A Problem of Definition.” ↩ ↩2

  8. Michael J. Kruger, Canon Revisited: Establishing the Origins and Authority of the New Testament Books (Wheaton, IL: Crossway, 2012), chap. 2, “Tracing the Origins,” n. 49, discussing Harold A. Netland, “Apologetics, Worldviews, and the Problem of Neutral Criteria,” in The Gospel and Contemporary Perspectives, ed. Douglas Moo (Grand Rapids: Kregel, 1997), 147-48. ↩ ↩2

  9. Craig A. Carter, “What Is Trinitarian Classical Theism?,” in Contemplating God with the Great Tradition: Recovering Trinitarian Classical Theism (Grand Rapids: Baker Academic, 2021), chap. 2. ↩ ↩2

  10. John Gill, A Body of Doctrinal Divinity; or, A System of Evangelical Truths, Deduced from the Sacred Scriptures, 2 vols. (London: Printed for the Author, and Sold by George Keith, 1769), book I, chap. 28. ↩