Predicates and quantifiers

Try writing “every prime greater than 2 is odd” in propositional logic. You cannot: there are infinitely many primes and a proposition has no way to range over them. Aristotle's syllogisms handled a few fixed patterns of “all” and “some”, and for two thousand years that was the state of the art.

In 1879 the German mathematician Gottlob Frege published a short book, the Begriffsschrift (“concept script”), that introduced variables bound by quantifiers. It is the logic mathematicians, database engines and program verifiers still use.