A survey of mathematical logic, part I: pre-1931

Abstract

… there would be no more need of dispute between two philosophers than between two accountants. It would suffice for them to take their pencils in their hands, sit down to their slates, and say to each other … :‘Let us calculate.’Gottfried Wilhelm LeibnizWir miissen wissen,Wir werden wissen.David Hilbert… I study Mathematics as a product of the human mind and not as absolute.Emil Leon PostIn the development of Mathematics in the past 2500 years we can discern two strands, namely, formal deduction or logic, associated initially with the Stoics and later with Aristotle and Euclid among others, and mathematical analysis, which we see emerging in the same era in the works, for example, of Archimedes and Eudoxus. These strands, for the most part, developed separately until the seventeenth century when Newton and Leibniz invented the calculus. Newton’s presentation, however, was controversial for his arguments deployed infinitesimals and fluxions which some, especially Bishop Berkeley, rightly considered contradictory.