ABSTRACT
This chapter is divided into four sections. The first, ‘The Close of the Nineteenth Century’, summarizes the logical work of Boole, Frege and others prior to 1900. The second, ‘From Russell to Godel’, discusses advances made in formal logic from 1901, the year in which Russell discovered his famous paradox, to 1931, the year in which Godel's seminal incompleteness results appeared. The third section, ‘From Godel to Friedman’, discusses developments in formal logic made during the fifty years following Godel's remarkable achievement. Finally, the fourth section, ‘The Expansion of Logic’, discusses logic in the broader sense as it has flourished throughout the latter half of the twentieth century. Boole had been prompted to write The Mathematical Analysis of Logic by a public dispute between DeMorgan and the philosopher William Hamilton over the quantification of the predicate.
