The Algebra of Logic - Couverture rigide

Couturat, Louis

Couverture rigide

ISBN 10 : 0486446387 ISBN 13 : 9780486446387

Editeur : Dover Publications Inc., 2006

Synopsis

Dans une forme admirablement succincte, ce volume offre une vue historique du développement du calcul de la logique, illustrant sa beauté, sa symétrie et sa simplicité d'un point de vue algébrique. Les sujets incluent les principes d'identité et de syllogisme, les principes de simplification et de composition, les lois de la tautologie et de l'absorption, la loi distributive et les lois de la dualité, la double négation et la contraposition, les formules de De Morgan et Poretsky, le théorème de Schr\u00f6der, les sommes et produits de fonctions, solution d'équité. impliquant un et plusieurs quantités inconnues ; le problème de Boole ; les diagrammes de Venn ; les tableaux des conséquences et des causes ; et les formules propres au calcul des propositions. Éd. 1914.

A propos du livre

Présentation de l'éditeur

Mathematical Logic is a necessary preliminary to logical Mathematics. Mathematical Logic is the name given by PEANO to what is also known (after VENN) asS ymbolic Logic ;~ andS ymbolic Logic is, in essentials, theL pgicpf A ristotle, given new life and power by being dressed up in the wonderful almost magical armour and accoutrements of A lgebra. In less than seventy years, logic, to use an expression of DE MORGAN S, has so thriven upon symbols and, in consequence, so grown and altered that the ancient logicians would not recognize it, and many old-fashioned logicians will not recognize it. The metaphor is not quite correct: Logic has neither grown nor altered, but we now see more of it and more into it. The primary significance of a symbolic calculus seems to lie in the economy of mental effort which it brings about, and to this is due the characteristic power and rapid development of mathematical knowledge. Attempts to treat the operations of formal logic in an analogous way had been made not in frequently by some of the more philosophical mathematicians, such as LEIBNIZ and LAMBERT; but their labors remained little known, and it was BOOLE and DE MORGAN, about the middle of the nineteenth century, to whom a mathematical though of course non-quantitative way of regarding logic was due. By this, not only was the traditional or Aristotelian doctrine of logic reformed and completed, but out of it has developed, in course of time, an instrument which deals in a sure manner with the task of investigating the fundamental concepts of mathematics a task which philosophers have repeatedly taken in hand, and in which they have as repeatedly failed.
(Typographical errors above are due to OCR software and don't occur in the book.)

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Détails de l'édition

• Éditeur: Dover Publications Inc.
• Date d'édition: 2006
• Langue: anglais
• ISBN 10: 0486446387
• ISBN 13: 9780486446387
• Reliure: Relié
• Nombre de pages: 98
• Coordonnées du fabricant: non disponible
• Personne responsable: Soc. Agr. La Raia Ss; http://www.la-raia.it; ; Strada Monterotondo, 79; Novi Ligure; 15067; Italie