An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities (Classic Reprint)

Politics & Social Sciences

George, Boole

Philosophy

Forgotten Books

An Investigation of the Laws of Thought: On Which Are Founded the Mathematical Theories of Logic and Probabilities

Franklin Classics Trade Press

A Treatise on Differential Equations

A Treatise On Differential Equations

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

History

Before 1854 when George Boole published The Laws of Thought, the subject of 'logic' in the western world was entirely restricted to the study of the Aristotelian syllogism, which was as old as 384-322 BC. In this work, Boole introduces a sort of algebra of propositions with probability. Boole's logic forms the basis for present day Boolean

An Investigation of the Laws of Thought

Barnes&Noble Publishing,Inc.

Calculus Of Finite Differences Fourth Edition

As outspoken in his day as Richard Dawkins or Christopher Hitchens are today, American freethinker and author ROBERT GREEN INGERSOLL (1833-1899) was a notorious radical whose uncompromising views on religion and slavery (they were bad, in his opinion), women's suffrage (a good idea, he believed), and other contentious matters of his era made him a wildly popular orator and critic of 19th-century American culture and public life. As a speaker dedicated to expanding intellectual horizons and celebrating the value of skepticism, Ingersoll spoke frequently on such topics as atheism, freedom from the pressures of conformity, and the lives of philosophers who espoused such concepts. This collection of his most famous speeches includes the lectures: [ "The Gods" (1872) [ "Humboldt" (1869) [ "Thomas Paine" (1870) [ "Individuality" (1873) [ "Heretics and Heresies" (1874)

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A Treatise on the Calculus of Finite Differences

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Science & Math

Mathematics

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1872 Excerpt: ...primitive of a singular integral of a differential equation of the second order will itself be a singular solution of that equation, but a singular solution of a singular integral will in general not be a solution at all of that equation. The proof of these propositions will afford an exercise for the student. See Lagrange's Lemons sur le Calcul des Fonctions, Legem 14me of the edition of 1806, or Legon 15me of the edition of 1808. A note by Poisson on page 239 of the edition of 1808 should be consulted; it relates to the second of the above two propositions. See also Lacroix, Traits du Calcul Bifferentiel..., Tome n. pp. 382 and 390. 10. We proceed to inquire how singular integrals may be determined from the differential equation. Expressing as before the first integral involving an arbitrary constant in the form y=f(x,y,y1...ylt,c) (47), we have as the derived equation (df(x, y, y,...#„_„ c) the brackets in the second member indicating that in effecting the differentiation y, y„_2, are to be regarded as functions of x. The differential equation of the nth order is found from (48) by substituting therein, after the differentiation, for c its value in terms of x, y, yx,...y_v given by (47). The result assumes the form yn = (x,y, y,...jO (49). Hence, we have or, representing fix, y, y1...y, c), by /, dyn-t dxdcj dc' Hence, A iog%-=i (50), dx b dc K' provided that the first member be obtained from the differential equation, and the second member from one of its first integrals involving c as arbitrary constant. It is to be borne in mind that in effecting the differentiation with respect to x in the second member, we must regard y, yl,---yn-i as functions of x. Now reasoning as in Chap. vin. since a singular solution makes = 0, it makes its l...

A treatise on differential equations

A Treatise on the Calculus of Finite Differences (Classic Reprint)

An Investigation of the Laws of ThoughtOn which are founded the mathematical theories of logic and probabilitiesBy George BooleThe Laws of Thought, more precisely, An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, was an influential 19th century book by George Boole, the second of his two monographs on algebraic logic. It was published in 1854. Boole was Professor of Mathematics of then Queen's College, Cork in Ireland.The following work is not a republication of a former treatise by the Author, entitled, “The Mathematical Analysis of Logic.” Its earlier portion is indeed devoted to the same object, and it begins by establishing the same system of fundamental laws, but its methods are more general, and its range of applications far wider. It exhibits the results, matured by some years of study and reflection, of a principle of investigation relating to the intellectual operations, the previous exposition of which was written within a few weeks after its idea had been conceived.That portion of this work which relates to Logic presupposes in its reader a knowledge of the most important terms of the science, as usually treated, and of its general object. On these points there is no better guide than Archbishop Whately’s “Elements of Logic,” or Mr. Thomson’s “Outlines of the Laws of Thought.” To the former of these treatises, the present revival of attention to this class of studies seems in a great measure due. Some acquaintance with the principles of Algebra is also requisite, but it is not necessary that this application should have been carried beyond the solution of simple equations. For the study of those chapters which relate to the theory of probabilities, a somewhat larger knowledge of Algebra is required, and especially of the doctrine of Elimination, and of the solution of Equations containing more than one unknown quantity.Preliminary information upon the subject-matter will be found in the special treatises on Probabilities in “Lardner’s Cabinet Cyclopaedia,” and the “Library of Useful Knowledge,” the former of these by Professor De Morgan, the latter by Sir John Lubbock; and in an interesting series of Letters translated from the French of M. Quetelet. Other references will be given in the work. On a first perusal the reader may omit at his discretion, Chapters x., xiv., and xix., together with any of the applications which he may deem uninviting or irrelevant.

Investigation of the Laws of Thought : On Which Are Founded the Mathematical Theories of Logic and Probabilities

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Books by George, Boole

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An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities (Classic Reprint)

An Investigation of the Laws of Thought: On Which Are Founded the Mathematical Theories of Logic and Probabilities

A Treatise on Differential Equations

An Investigation of the Laws of Thought

Calculus Of Finite Differences Fourth Edition

Calculus Of Finite Differences Fourth Edition

A Treatise on the Calculus of Finite Differences

A treatise on differential equations

A Treatise on the Calculus of Finite Differences (Classic Reprint)

Investigation of the Laws of Thought : On Which Are Founded the Mathematical Theories of Logic and Probabilities