# Law of Non-Contradiction ## Intro A statement cannot be both true and false in the same sense at the same time. That is the Law of Non-Contradiction, or LNC. It sounds obvious. It is also the most powerful tool in clear thinking. Aristotle called it the most certain of all principles. He noticed that any attempt to deny it has to use it. Try saying *"LNC is false."* That sentence is either true or it isn't. If it is true, then LNC holds (because the sentence is asserting something definite, not also not-asserting it). If it is false, then LNC holds (because the denial of LNC is not the same as the assertion of LNC). Either way, you cannot escape it. That is why philosophers call LNC a *first principle*: it is presupposed in the very act of denying it. LNC is the engine that drives the most powerful argument form in philosophy: *reductio ad absurdum*. If a claim leads to a contradiction, the claim must be false. Want to show subjectivism about truth is false? Just point out that the claim *"all truth is subjective"* is, if true, itself only subjectively true, which means it might be objectively false. Contradiction inside the claim. Reject the claim. For Christian theology, LNC matters because it grounds rational thought about God. Without LNC, "God exists" and "God does not exist" would be equally acceptable; theology would be impossible. It also undercuts certain modern moves that try to escape critique by accepting both sides of a contradiction (sometimes called dialetheism). If your worldview requires throwing out LNC, it does not "transcend logic." It just collapses into incoherence. The deeper Christian point is that LNC is not just a feature of human thought. It reflects the nature of a God who is rational, consistent, and not a deceiver. Logic is not arbitrary. It runs through reality because reality runs through Christ, *"in whom all things hold together"* ([Col 1:17](/codex/colossians-1-17/)). ## In full The Law of Non-Contradiction (LNC) holds that a proposition cannot be both true and false in the same sense and at the same time, formally, ¬(P ∧ ¬P). With Identity and Excluded Middle it forms one of the three classical laws of logic, and it is the most-cited law across ris3n's Philosophy and Logic notes. LNC is treated both as a foundational axiom (denying it is unintelligible) and, in the theological tradition, as a property grounded in the divine nature. ## Status - **[Aristotle](/codex/aristotle/)** identifies LNC as the most certain of all principles in *Metaphysics* IV, so basic that no demonstration of it is possible (any demonstration would presuppose it). - LNC underwrites *reductio ad absurdum*: showing that an assumption entails a contradiction is sufficient to reject the assumption. - Denying LNC is self-defeating: the denial itself either is or is not its own negation. ## Theological framing ris3n's notes anchor LNC in God's character. **[2 Timothy 2:13](/codex/2-timothy-2-13/)** ("he cannot deny himself") is read as scriptural witness that non-contradiction is a feature of the divine being: God's word and nature are non-contradictory because God himself is. On the presuppositional reading, LNC's universality and invariance require a transcendent rational mind as their ground, see the [Transcendental Argument for God](/codex/transcendental-argument-for-god/). ## See also - Aristotle, the originator of the formal account of LNC. - [Reductio ad Absurdum](/codex/reductio-ad-absurdum/), the inference rule that depends on LNC. - [Transcendental Argument for God](/codex/transcendental-argument-for-god/), argues LNC's universality requires God. - [Self-refutation](/codex/self-refutation/), denying LNC is the paradigm self-refuting move. - [Laws of Logic](/codex/laws-of-logic/), the broader cluster (Identity, LNC, Excluded Middle).
## Common questions this page answers **Q: What is the Law of Non-Contradiction?** The Law of Non-Contradiction (LNC) holds that a proposition cannot be both true and false in the same sense and at the same time. Formally, ¬(P ∧ ¬P). [Aristotle](/codex/aristotle/) called it the most certain of all principles. With Identity and Excluded Middle, it is one of the three classical [Laws of Logic](/codex/laws-of-logic/). **Q: Can the Law of Non-Contradiction be proven?** Not directly, because any proof would have to assume it. But [Aristotle](/codex/aristotle/) showed it cannot be coherently denied: any attempt to deny LNC has to use it. "LNC is false" is itself either true or not, which presupposes LNC. The denier of LNC has to assert something definite (not also not-asserting it) to make the denial, so the denial uses what it denies. This makes LNC a *first principle*, presupposed in the very act of denial. See [Self-refutation](/codex/self-refutation/). **Q: Why does LNC matter for theology?** It grounds rational thought about God. Without LNC, "God exists" and "God does not exist" would be equally acceptable, and theology would be impossible. The deeper Christian point is that LNC is not arbitrary; it reflects the nature of a God who is rational, consistent, and not a deceiver. Logic runs through reality because reality runs through Christ, "in whom all things hold together" ([Colossians 1:17](/codex/colossians-1-17/)). **Q: What is reductio ad absurdum?** A deductive refutation built on LNC: if a claim leads (by valid steps) to a contradiction, the claim must be false. To show subjectivism about truth is false, point out that "all truth is subjective" is, if true, itself only subjectively true, which means it might be objectively false. Contradiction inside the claim. Reject the claim. See [Reductio ad Absurdum](/codex/reductio-ad-absurdum/). **Q: Are there philosophers who deny LNC?** Yes; the position is called *dialetheism* (Graham Priest, *In Contradiction*, 1987). Dialetheists allow that some contradictions are true. But the position is widely rejected because: (i) it makes the standard rules of inference collapse (from a contradiction, anything follows by *ex falso quodlibet*); (ii) every attempt to motivate dialetheism uses LNC against rival positions; (iii) Aristotle's anti-denial argument still applies. See [Transcendental Argument for God](/codex/transcendental-argument-for-god/) for the argument that LNC's universality is most naturally grounded in God.