Reductio Ad Absurdum | Definition & Examples
Reductio ad absurdum is the strategy of disproving a claim by demonstrating its logical contradictions. This involves assuming the claim is true to show that it leads to contradictions and cannot actually be true.
Reductio ad absurdum: “If the truth cannot be known, then it cannot be known whether the statement ‘the truth cannot be known’ is true.”
Reductio ad absurdum is used in philosophy, mathematics, law, and other disciplines where logical consistency is important.
What is reductio ad absurdum?
A reductio ad absurdum argument (Latin for “reduction to the absurd”) assumes that a position is true for the sake of argument, then disproves it by demonstrating that it leads to logical contradictions.
Reductio ad absurdum is also called “argumentum ad absurdum” (or, less commonly, “apagogical argument”).
Primarily used in deductive reasoning, reductio ad absurdum can also be used rhetorically in inductive reasoning.
Reductio ad absurdum and paradoxes can serve similar purposes in philosophy:
- Paradoxes aim to provoke further inquiry and reveal deeper truths; they sometimes disprove a claim.
- Reductio ad absurdum arguments aim to refute a claim; they sometimes provoke further inquiry.
Reductio ad absurdum arguments rely on the law of non-contradiction to demonstrate genuine logical impossibilities (not just subjective opinions).
- Law of non-contradiction: A proposition cannot be true and false in the same way at the same time (e.g., the statement “circles are round” cannot be both true and false).
Focusing on genuine logical contradictions (and avoiding distortions or ridicule) is crucial to avoiding logical fallacies.
Reductio ad absurdum examples
Examples of reductio ad absurdum are common in contexts that involve deductive reasoning such as philosophy, law, and mathematics.
In philosophy, reductio ad absurdum often reveals contradictions in theories by assuming a position is true and showing its absurdity.
This reductio ad absurdum argument is based on the Epicurean paradox, or “the problem of evil.” A branch of philosophy called theodicy is dedicated to exploring this problem.
In law, reductio ad absurdum highlights inconsistencies in legal principles that make them impractical or untenable.
In law, reductio ad absurdum can be used to demonstrate that a legal principle is impractical by showing that it results in logical contradictions or unreasonable requirements.
Mathematical proofs use reductio ad absurdum to show a claim is true by demonstrating the absurdity of its opposite.
Reductio ad absurdum can be used in mathematical proofs to demonstrate that one assumption (1 = 2) leads to a logical contradiction. This proves the truth of the opposite claim (1 ≠ 2).
Reductio ad absurdum and logical fallacies
Reductio ad absurdum is not a fallacy. The goal of reductio ad absurdum is to reveal genuine logical contradictions. However, misunderstanding of this strategy can lead to fallacies of distortion or ridicule.
Focus on accuracy, intellectual honesty, and sound reasoning to avoid these logical fallacies:
- Straw man fallacy: Misrepresenting an opponent’s argument to make it easier to attack
- Slippery slope fallacy: Arguing that a relatively small first step will inevitably lead to a chain of related (and usually negative) events or ideological shifts
- Appeal to ridicule: Mocking an argument to make it seem absurd rather than addressing legitimate flaws
- Argument from incredulity: Rejecting a claim because it seems unbelievable or difficult to understand
Frequently asked questions about reductio ad absurdum
- Who is the Greek philosopher known for reductio ad absurdum arguments?
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The Greek philosopher Zeno is renowned for his early examples of reductio ad absurdum, presented in the form of paradoxes. Zeno’s paradoxes challenged assumptions about time and space, laying the groundwork for later philosophers to formalize reductio ad absurdum.
- What’s an example of reductio ad absurdum in media?
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In media, reductio ad absurdum arguments can be used to demonstrate logical contradictions in policies or positions. For example, a news commentator might make the following argument against government surveillance:
“If total security requires total surveillance, then the government must monitor its own surveillance activities continuously to be consistent. This leads to the absurd conclusion that there must be an infinite number of layers of surveillance, each monitoring the previous layer.”
- How is reductio ad absurdum used in philosophy?
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Reductio ad absurdum is used in philosophy to uncover flaws and inconsistencies in various theories and beliefs.
For example, the following reductio ad absurdum argument is inspired by Emmanuel Kant:
“If moral relativism is true and all moral beliefs are equally valid, then the beliefs that ‘helping others is a moral duty’ and ‘helping others is never a moral duty’ must both be valid. This leads to a contradiction, as an action cannot be both a moral duty and not a moral duty simultaneously.”
This argument exposes how moral relativism defies the law of non-contradiction, encouraging further examination and refinement of moral theories.
