Overview

The nineteenth century witnessed the formalization of traditional logic along symbolic lines, followed by an attempt to recast the foundations of mathematics in rigorous logical form. The extensive development of mathematical logic was motivated in part by the discoveries of new geometries and new number systems that caused many mathematicians to question the logical soundness of traditional mathematical ideas. The attempt to impose the strictest rigor on arithmetic, the most fundamental area of mathematics, would eventually lead to a number of surprising results, results that caused many philosophers and mathematicians to modify their views of the very nature of mathematics. The same developments would nonetheless provide techniques essential to the development of digital computers, artificial intelligence, and modern theories of language.

Background

Logic is the subject that deals with the drawing of correct conclusions from...