Mathematical logic

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.

Quotes

 * Frege's development began with... "an epoch-making little book" called ', translated as Concept Script or Conceptual Notation... Just as Aristotle's ' is the foundation of traditional or syllogistic logic—the logic of the categorical three-term syllogism, Frege's Begriffsschrift is the keystone of modern or mathematical logic.
 * Michael Losonsky, Linguistic Turns in Modern Philosophy (2006) pp. 148-149.


 * In 1920 logic was mostly a philosopher's garden. There were also a few mathematicians there, cultivating the logical roots of the mathematical tree. Today, Recursion Theory, Set Theory, Model Theory and Proof Theory, logic's major subdisciplines, have become full-fledged branches of mathematics.