The Laws of Thought
This groundbreaking work on logic by the brilliant 19th-century English mathematician George Boole remains influential to this day. Boole's major contribution was to demonstrate conclusively that the symbolic expressions of algebra could be adapted to convey the fundamental principles and operations of logic, which hitherto had been expressed only in words. Boole was thus the founder of today's science of symbolic logic. Summing up his innovative approach, Boole stated, "We ought no longer to associate Logic and Metaphysics, but Logic and Mathematics." As the great English logician Augustus De Morgan later put it, in praise of Boole, his genius consisted in showing that "the symbolic processes of algebra, invented as tools of numerical calculation, should be competent to express every act of thought, and to furnish the grammar and dictionary of an all-containing system of logic." The Laws of Thought lays out this new system in detail and also explores a "calculus of probability."
The story of Boole's life is as impressive as his work. Besides rudimentary lessons from his father and a few years at local schools, Boole was largely self-taught. Revealing his aptitude for many subjects at an early age, he began his career already at age 16 as a teacher at a village school. In his leisure time he tackled the daunting works of Newton, Laplace, and Lagrange on physics and mathematics. By the age of twenty-four he was submitting original papers to the Cambridge Mathematical Journal and at age twenty-nine he won a medal from the Royal Society for his contributions to mathematical analysis. He continued to so impress his contemporaries that five years later he was appointed professor of mathematics at Queens College, Cork in Ireland, even though he had no university degree. At his untimely death of forty-nine, Boole could never have guessed that his new symbolic logic would become essential in the next century for telephone switching and the design of computers. For this practical reason, as well as the sheer intellectual importance of his accomplishment, The Laws of Thought merits our attention today. |
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a₁ Algebra application Aristotle Aristotle's assume babilities Boole Boole's c₁ C₂ cause chapter coefficients conception conclusion condition connexion constituents deduce definition deliberative assembly denoted determine discourse disjunctive proposition elements elimination equa equal events whose probabilities evils exist expression factor function George Boole given Hence hypothesis implied indefinite independent inference interpretation involved laws of thought logical equation m₁ mathematical Mathematical Analysis mathematical logic method minor limit nature necessary occur p₁ P₂ particular phænomenon premises present primary propositions principle Prob problem processes productive of pleasure Prop question reasoning reduced relation represent respect result second member secondary propositions simple events sition solution supposed syllogism system of equations t₁ t₂ theory of probabilities things tion treatise true truth universe universe of discourse V₁ whence καὶ