Originally published in 1962. A clear and simple account of the growth and structure of Mathematical Logic, no earlier knowledge of logic being required. After outlining the four lines of thought that have been its roots - the logic of Aristotle, the idea of all the parts of mathematics as systems to be designed on the same sort of plan as that used by Euclid and his Elements, and the discoveries in algebra and geometry in 1800-1860 - the book goes on to give some of the main ideas and theories of the chief writers on Mathematical Logic: De Morgan, Boole, Jevons, Pierce, Frege, Peano, Whitehead, Russell, Post, Hilbert and Goebel. Written to assist readers who require a general picture of current logic, it will also be a guide for those who will later be going more deeply into the expert details of this field.
1. Purpose and Language of the Book 2. Aristotle’s Syllogistic 3. The Idea of a Complete, Automatic Language for Reasoning 4. Changes in Algebra and Geometry, 1825-1900 5. Consistency and Metamathematics 6. Boole’s Algebra of Logic 7. The Algebra of Logic after Boole: Jevons, Peirce and Schroeder 8. Frege’s Logic 9. Cantor’s Arithmetic of Classes 10. Peano’s Logic 11. Whitehead and Russell’s ‘Principia Mathematica’ 12. Mathematical Logic after ‘Principia Mathematica’: Hilbert’s Metamathematics
Reissuing works originally published between 1931 and 1990, this set of twenty-four books covers the full range of the philosophy of logic, from introductions to logic, to calculus and mathematical logic, to logic in language and linguistics and logical reasoning in law and ethics. An international array of authors are represented in this comprehensive collection.