Boolel's Logic Department of Philosophy George Boole undertook the algebraization of a modified syllogistic logic, extended to conditionals and probabilities. Boolean operators are known worldwide today because of the search engine pathways they make possible electronically. The electronic circuits by which search engine software transact the complex traffic of electronic signals across a circuit switching board are also generally described as Boolean. Boole’s logic is worth exploring both as a chapter in the history of nineteenth century logic, in the movement from Aristotelian term logic to a more flexible universal algebraic logic that was to find full fruition only later in the century and beginning of the twentieth century in Gottlob Frege’s Begriffsschrift and Grundgesetze der Arithmetik. Boole and Frege nevertheless have rather different visions both of logic as algebra, which is to say of how in general terms logic should be algebraized, and, more importantly, of the base logic to be cast as an algebraic formalism. Roughly, Boole takes a modified extended and amplified Aristotelian syllogistic term logic as given, and, himself a highly accomplished adept of mathematical algebra, makes use of all the substitution and simplification devices, often unspoken in his own complex derivations, in order to drive inferences of an algebraic logic of categoricals. Boole reinterprets syllogistic+plus in algebraic terms and adapts the tools of arithmetical algebra and trigonometry in his 1847 book, The Mathematical Analysis of Logic, and later in his much expanded 1854 treatise, An Investigation of the Laws of Thought on which are founded the mathematical theories of logic and probabilities, also known simply as the Laws of Thought. The purpose of this tutorial is to (1) introduce and explain Boole’s basic concepts and his model for the reconstruction of syllogistic as an algebra rather than logic of terms with selections from and commentary on Boole’s two main books of interest to logicians; (2) compare and contrast Boole’s logic with the more familiar functional calculus or predicate-quantificational logic as developed by Frege, by offering a close reading of Frege’s unpublished Nachlaß essays, translated as, ‘Boole’s Logical Calculus and the Concept-Script’ (written c. 1880-1881) and a revised version of the essay ‘Boole’s Logical Formula-Language and My Concept-Script’ (1882); (3) consider Boole’s philosophical interest and importance for contemporary logic, and in particular for such topics in philosophy of logic as the psychologism that seems to be implied by Boole’s reference to logic as laws of thought. Tutorial Sessions:
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Bibliography Boole, George. 1847. The Mathematical Analysis of Logic (Thoemmes reprint). Boole, George. 1854. The Laws of Thought (Dover). Dudman, V.H. 1976. ‘From Boole to Frege’, Studien zu Frege, 1, 109-138. Frege, Gottlob. 1979. ‘Boole’s Logical Calculus and the Concept-Script’ (1880-1881) AND ‘Boole’s Logical Formula-Language and My Concept-Script’ (1882), Posthumous Writings. Edited by Hermes, et al. (Blackwell). Hailperin, Theodore. 1981. ‘Boole’s Algebra Isn’t Boolean’, Mathematics Magazine, 54, 172-184. Hailperin, Theodore. 1984. ‘Boole’s Abandoned Propositional Logic’, History and Philosophy of Logic, 5, 39-48. Jacquette, Dale. 2002. On Boole (Wadsworth Philosophers). Jacquette, Dale. 2008. ‘Boole’s Logic’, Handbook of the History of Logic, Volume 4: British Logic in the Nineteenth Century, edited by Dov M. Gabbay and John Woods (Amsterdam: North-Holland (Elsevier Science)), 331-379. Musgrave, Alan. 1972. ‘George Boole and Psychologism’, Scientia, 107, 593-608. Prior, Arthur. 1948. ‘Categoricals and Hypotheticals in George Boole and his Successors’, Australasian Journal of Philosophy, 27, 171-196. Rudeanu, Sergiu. 1974. Boolean Functions and Equations (North-Holland). Whitesitt, John Eldon. 1961. Boolean Algebra and its Applications (Addison-Wesley).
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