George Boole, John Venn and CS Peirce
Origins of Boolean Algebra in the Logic of Classes: George Boole, John Venn and C. S. Peirce Janet Heine Barnett∗ 9 March 2013 1 Introduction On virtually the same day in 1847, two major new works on logic were published by prominent British mathematicians. Augustus De Morgan (1806{1871) opened his Formal Logic with the following description of what is known today as `logical validity' [6, p. 1]: The first notion which a reader can form of Logic is by viewing it as the examination of that part of reasoning which depends upon the manner in which inferences are formed, and the investigation of general maxims and rules for constructing arguments, so that the conclusion may contain no inaccuracy which was not previously asserted in the premises. It has so far nothing to do with the truth of the facts, opinions, or presump- tions, from which an inference is derived; but simply takes care that the inference shall certainly be true, if the premises be true. Whether the premises be true or false, is not a question of logic, but of morals, philosophy, history, or any other knowledge to which their subject-matter belongs: the question of logic is, does the conclusion certainly follow if the premises be true? The second of these new nineteenth century works on logic was The Mathematical Analysis of Logic by George Boole (1815{1864). Like De Morgan, Boole sought to stretch the boundaries of traditional syllogistic1 logic by developing a general method for representing and manipulating all logically valid inferences or, as DeMorgan described it to Boole in a letter dated 28 November 1847, to develop `mechanical modes of making transitions, with a notation which represents our head work' [22, p.
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