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The Great Formal Machinery WorksTheories of Deduction and Computation at the Origins of the Digital Age$
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Jan von Plato

Print publication date: 2017

Print ISBN-13: 9780691174174

Published to Princeton Scholarship Online: May 2018

DOI: 10.23943/princeton/9780691174174.001.0001

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The Algebraic Tradition of Logic

The Algebraic Tradition of Logic

(p.81) 3 The Algebraic Tradition of Logic
The Great Formal Machinery Works

Jan von Plato

Princeton University Press

This chapter explores how algebraic logic began in 1847 when George Boole presented his “calculus of deductive reasoning” in a short book titled The Mathematical Analysis of Logic. His calculus reduced known ways of logical reasoning into the solution of algebraic equations. The known ways of logical reasoning were not just accounted for but were extended to full classical propositional logic. Boole reduced Aristotelian syllogistic reasoning to calculation, which was a wonderful achievement. Encouraged by the success, he wrote a book with the bold title An Investigation of the Laws of Thought (1854). However, his logic was not able to treat relations but just one-place predicates.

Keywords:   algebraic logic, George Boole, calculus, deductive reasoning, algebraic equations, one-place predicates

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