Mathematical Logic

Abstract

The study of logic was initiated by Aristotle, who sought a systematic way to expose the false reasoning of sophists. The latter were highly educated orators with great eloquence. Their goal was to convince the audience through their speeches, whether these were true or not. Thus, the role of philosophers was the search for truth, while that of the sophists was the pursuit of persuasion. Logic is seen as the analysis of reasoning methods where we focus on the form (syntax) rather than the content (semantics) of the argument. Mathematical logic thus originated from an attempt to codify and formalize the language of mathematics, its basic assumptions, and the permissible rules of proof. Although logic is the foundation of all other studies, its fundamental character (perhaps due to its focus on form rather than content) and apparently self-evident nature discouraged any indepth logical research until the end of the 19th century. Then, driven by the discovery of nonEuclidean geometry and the desire to provide a rigorous foundation for calculus and higher analysis, interest in logic revived. This new interest, however, was still quite lukewarm until, at the turn of the century, the mathematical world was shocked by the discovery of paradoxes.