Definition
Plain language
The standard rules of reasoning where every statement is either true or false — and where a claim starting from something false counts as technically correct no matter what it concludes.
As stated in the literature
Two-valued logic with the law of excluded middle; a conditional with a false antecedent is vacuously true, so falsifying a hypothesis makes any conclusion derivable.
Why it matters: This quirk means an argument can be perfectly valid and still tell you nothing, which is exactly what happens when someone sneaks a false assumption into the setup of a proof.
For example, the sentence "if the moon is made of cheese, then I am the king of France" counts as true in classical logic, simply because the moon is not made of cheese.
Heard on the show
“In classical logic, a false premise lets you prove any conclusion.”Episode 260 — One Line of Lean Faked 34 Proofs, and 99 Agents Copied It