AN EXAMINATION AND EVALUATION OF THE HISTORICAL IMPORTANCE OF THE PRINCIPAL INNOVATIVE CONTRIBUTIONS TO FORMAL LOGIC OF AUGUSTUS DE MORGAN.

摘要

This dissertation investigates, examines, compares, describes and evaluates the historical importance of the principal innovative contributions to formal logic of Augustus De Morgan. It treats his relationship to his precursors and to his contemporaries. Additionally, it studies in considerable detail, the development of De Morgan's logic of relations up to the present by detailing the contributions of his successors and considering the new problems generated in this important area of modern mathematics.;In Chapter II - Augustus De Morgan's Life and Relationship to His Contemporaries Concerning Logic - De Morgan's biography is sketched. His relationship with his Cambridge teachers Whewell and Peacock is described. His contact with George Boole is set forth. The controversy with Sir William Hamilton of Scotland over the quantification of the predicate is detailed. His postal twenty-five years correspondence friendship with Sir William Rowan Hamilton of Ireland is presented. Emerging from this chapter is the author's conclusion that De Morgan was an isolate in logic mainly because there was little or no interest in the subject both in England and on the continent.;Chapter III - Augustus De Morgan's Principal Innovative Contributions To Formal Logic - presents his contributions in an expository style. It is elicited that these contributions were: giving the method of Mathematical Induction its present name; the rediscovery of the laws of duality: (A(INTERSECT)B)' = A'(UNION) B', (A(UNION)B)' = A'(INTERSECT) B'; the idea of the universe of discourse - the universal set; the construction of an entirely new and comprehensive symbolic notation; the reclassification of all previous syllogisms and the original discovery of eight new syllogistic forms; the idea of conclusions from quantitatively defined propositions and the deduction of all Aristotellian forms in this manner; the placing of the quantification of the predicate on a sound mathematical basis by showing it was only a part of his work on the numerical syllogism; and, the founding of the logic of relations.;In Chapter IV - The Logic of Relations Subsequent To The Contribution of De Morgan - the outcome of De Morgan's most significant original contribution to formal logic is summarized. It gives the modifications and changes of De Morgan's work made by his successors. In indicates the kinds of new problems in the logic of relations that were generated by De Morgan's work. Presented are the contributions to the logic of relations of: C. S. Peirce, E. Schroder, G. Frege, G. Cantor, G. Peano, B. Russell, A. Tarski, J. C. C. McKinsey, C. J. Everett, A. B. Bednarek and S. M. Ulam.;Chapter I - Mathematical Logic Prior To The Work of Augustus De Morgan - An Overview - sets the stage for this 19th Century logician as well as his contemporaries. However, it is not a complete history of formal logic up to that time. It provides those facts of logic that have a direct bearing on De Morgan's work. To this end the work of Leibniz, The Bernoullis, Wolff, Ploucquet, von Segner, Lambert, Maimon, Castillion, Semmler, Gergonne, Twesten, Gauber, Bolzano, Bentham, Hamilton and Dobrish is summarized.;Chapter V is a presentation of the author's conclusions and suggestions for further research. The main conclusion that the author derives is that De Morgan's principal innovative contributions to formal logic are those of a transitional figure. His methods and symbolism are those of his predecessors. The substance of his contributions is modern in spirit and in current use. This is particularly apparent in view of his legacies of the laws of duality and the universe of discourse. His logic of relations is completely modern.