Abstract

Charles S. Peirce, 1839-1914, was a mathematical logician, a research scientist, and a philosopher; he made major contributions to each of these fields. ;Peirce discovered many of the important ideas used in today's mathematical logic. Building on earlier work by Boole and De Morgan, he invented an algebra of binary relations in a paper of 1870. Using abstract algebraic ideas, especially the semigroup algebra, he discovered the quantifiers and developed first- and second-order quantificational logic, which he presented in his important paper of 1885. A two stage method is used to investigate the importance and influence of these ideas of Peirce's: State One is a reconstruction of the mathematical content using present-day concepts, especially set-theoretic semantics; Stage Two involves an analysis of the differences between Peirce's notation and techniques and present-day ones. ;Peirce espoused a mathematical realism in regard to the foundations of mathematics and to philosophy in general--especially in his philosophy of pragmatism. He strove to establish such a viewpoint with respect to an organization of the sciences which regarded mathematics as the most abstract science and the most successful in its method, that is, in its logic. ;Peirce has not been sufficiently recognized for his pioneering work in mathematical logic because the model-theoretic line of development which includes Boole, De Morgan, Peirce, Schroder, Lowenheim, and Skolem has not been generally understood or promoted as much as the deduction-theoretic line which includes Frege, Peano, Russell, and Whitehead. Peirce's relational algebra is the basis of present-day relational data bases; his approach to quantificational logic is the basis of present-day expert systems, and especially of the Prolog language