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How does reductio ad absurdum attempt to refute a claim?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — Applied logic Aristotle, marble portrait bust, Roman copy (2nd century bce) of a Greek original (c. 325 bce); in the Museo Nazionale Romano, Rome.

In the context of applied logic, reductio ad absurdum (Latin for "reduction to absurdity") attempts to refute a claim by demonstrating that it leads to contradictory or absurd consequences as a matter of logical necessity.1

Rather than attacking a premise directly, this method assumes the claim is true and follows its implications to their logical conclusion. If that process results in a contradiction—or an outcome that is clearly false or impossible—the original claim is proven to be invalid.21

A specific application of this technique is known as indirect proof, or reductio ad impossibile. In this form, a proposition is proven by showing that its denial, when combined with other accepted or previously proved propositions, inevitably leads to a contradiction. By showing that the negation of a statement is untenable, the argument establishes the truth of the original proposition.1