The Algebra of Logic

By Louis Couturat

Book Overview

The algebra of logic was founded by George Boole (1815-1864); it was developed and perfected by Ernst Schroder (1841-1902) The fundamental laws of this calculus were devised to express the principles of reasoning, the laws of thought But this calculus may be considered from the purely formal point of view, which is that of mathematics, as an algebra based upon certain principles arbitrarily laid down It belongs to the realm of philosophy to decide whether, and in what measure, this calculus corresponds to the actual operations of the mind, and is adapted to translate or even to replace argument; we cannot discuss this point here The formal value of this calculus and its interest for the mathematician are absolutely independent of the interpretation given it and of the application which can be made of it to logical problems In short, we shall discuss it not as logic but as algebra.ContentsPrefaceBibliographyIntroductionThe Two Interpretations of the Logical CalculusRelation of InclusionDefinition of EqualityPrinciple of IdentityPrinciple of the Syllogism Multiplication and AdditionPrinciples of Simplification and CompositionThe Laws of Tautology and of AbsorptionTheorems on Multiplication and AdditionThe First Formula for Transforming Inclusions into EqualitiesThe Distributive LawDefinition of 0 and 1The Law of Duality Definition of NegationThe Principles of Contradiction and of Excluded MiddleLaw of Double NegationSecond Formulas for Transforming Inclusions into EqualitiesThe Law of Couturat Postulate of ExistenceThe Development of 0 and of 1Properties of the ConstituentsLogical FunctionsThe Law of Development The Formulas of De MorganDisjunctive SumsProperties of Developed FunctionsThe Limits of a FunctionFormula of Poretsky Schroder's TheoremThe Resultant of Elimination The Case of IndeterminationSums and Products of Functions

• Format: Paperback
• Language: English
• ISBN: 148395739X
• ISBN13: 9781483957395
• Release Date: March 2013
• Publisher: CreateSpace Independent Publishing Platform
• Length: 92 Pages
• Weight: 0.42 lbs.
• Dimensions: 9.0" x 0.2" x 6.0"