{"product_id":"2940016305028","title":"The Logic of Algebra","description":"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.\u003cbr\u003eContents\u003cbr\u003e\u003cbr\u003ePreface\u003cbr\u003eBibliography\u003cbr\u003eIntroduction\u003cbr\u003eThe Two Interpretations of the Logical Calculus\u003cbr\u003eRelation of Inclusion\u003cbr\u003eDefinition of Equality\u003cbr\u003ePrinciple of Identity\u003cbr\u003ePrinciple of the Syllogism \u003cbr\u003eMultiplication and Addition\u003cbr\u003ePrinciples of Simplification and Composition\u003cbr\u003eThe Laws of Tautology and of Absorption\u003cbr\u003eTheorems on Multiplication and Addition\u003cbr\u003eThe First Formula for Transforming Inclusions into Equalities\u003cbr\u003eThe Distributive Law\u003cbr\u003eDefinition of 0 and 1\u003cbr\u003eThe Law of Duality \u003cbr\u003eDefinition of Negation\u003cbr\u003eThe Principles of Contradiction and of Excluded Middle\u003cbr\u003eLaw of Double Negation\u003cbr\u003eSecond Formulas for Transforming Inclusions into Equalities\u003cbr\u003eThe Law of Couturat  \u003cbr\u003ePostulate of Existence\u003cbr\u003eThe Development of 0 and of 1\u003cbr\u003eProperties of the Constituents\u003cbr\u003eLogical Functions\u003cbr\u003eThe Law of Development   \u003cbr\u003eThe Formulas of De Morgan\u003cbr\u003eDisjunctive Sums\u003cbr\u003eProperties of Developed Functions\u003cbr\u003eThe Limits of a Function\u003cbr\u003eFormula of Poretsky      \u003cbr\u003eSchroder's Theorem\u003cbr\u003eThe Resultant of Elimination  \u003cbr\u003eThe Case of Indetermination\u003cbr\u003eSums and Products of Functions","brand":"Louis Couturat","offers":[{"title":"Default Title","offer_id":47081300525296,"sku":"2940016305028","price":2.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/2940016305028_p0.jpg?v=1763632825","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/2940016305028","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}