linguistic:paraphrasing
Mathematical logic

In 1847, De Morgan published his laws and George Boole devised an algebra, now called Boolean algebra, that allows expressing Aristotle's logic in terms of formulas and algebraic operations. Boolean algebra is the starting point of mathematization logic and the basis of propositional calculus

Independently, in the 1870's, Charles Sanders Peirce and Gottlob Frege extended propositional calculus by introducing quantifiers, for building predicate logic.

Frege pointed out three desired properties of a logical theory: consistency (impossibility of proving contradictory statements), completeness (any statement is either provable or refutable; that is, its negation is provable), and decidability (there is a decision procedure to test every statement).

By near the turn of the century, Bertrand Russell popularized Frege's work and discovered Russel's paradox which implies that the phrase "the set of all sets" is self-contradictory. This paradox seemed to make the whole mathematics inconsistent and is one of the major causes of the foundational crisis of mathematics.