reductio ad absurdum

Reductio ad absurdum (Latin for "reduction to absurdity") or proof by contradiction is the form of argument that attempts to establish a claim by showing that following the logic of a contrary proposition or argument would lead to absurdity or contradiction.

Aristotle's law of noncontradiction states that

"It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect."

The principle may be expressed as the propositional formula $\mathrm{\neg }(\mathrm{\neg }P)\Rightarrow P$, or even more formally, $(\mathrm{\neg }P\Rightarrow \mathrm{\perp })\Rightarrow P$, which reads, "If assuming $P$ to be false implies falsehood, then $P$ is true."