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Proof

Below is the Lewis argument, a formal proof of the principle of explosion using symbolic logic.

This proof was published by C. I. Lewis and is named after him, though versions of it were known to medieval logicians.

This is just the symbolic version of the informal argument given in the introduction, with P {\displaystyle P} standing for "all lemons are yellow" and Q {\displaystyle Q} standing for "Unicorns exist". We start out by assuming that (1) all lemons are yellow and that (2) not all lemons are yellow. From the proposition that all lemons are yellow, we infer that (3) either all lemons are yellow or unicorns exist. But then from this and the fact that not all lemons are yellow, we infer that (4) unicorns exist by disjunctive syllogism.