An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities

 
9780217682015: An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities

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. 1854 edition. Excerpt: ...and hence that " whatever exists necessarily is the one simple essence of the self-existent being." The conclusion is also made to flow from the following premises:--1. If there are two or more necessary and independent beings, either of them may be supposed to exist alone. 2. If either may be supposed to exist alone, it is not a contradiction to suppose the other not to exist. 3. If it is not a contradiction to suppose this, there are not two necessary and independent beings. Let us represent the elementary propositions as follows:--x = there exist two necessary independent beings. y = either may be supposed to exist alone. 2 = it is not a contradiction to suppose the other not to exist. We have then, on proceeding as before, st(l-y) = 0. (1) y(l-z)=0. (2) zx = 0. (3) Eliminating y and z, we have x = 0. "Whence, There do not exist two necessary and independent beings. 11. To the premises upon which the two previous propositions rest, it is well known that Bishop Butler, who at the time of the publication of the "Demonstration," was a student in a nonconformist academy, made objection in some celebrated letters, which, together with Dr. Clarke's replies to them, are usually appended to editions of the work. The real question at issue is the validity of the principle, that "whatsoever is absolutely necessary at all is absolutely necessary in every part of space, and in every point of duration,"--a principle assumed in Dr. Clarke's reasoning, and explicitly stated in his reply to Butler's first letter. In his second communication Butler says: "I do not conceive that the idea of ubiquity is contained in the idea of selfexistence, or directly follows from it, any otherwise than as whatever exists must exist somewhere." That is to say, necessary...

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Book Description:

George Boole, the father of Boolean algebra, published An Investigation of the Laws of Thought, a seminal work on algebraic logic, in 1854. In this investigation of the fundamental laws of human reasoning, Boole uses the symbolic language of mathematics to examine the nature of the human mind.

About the Author:

George Boole; 2 November 1815 – 8 December 1864) was an English mathematician, philosopher and logician. He worked in the fields of differential equations and algebraic logic, and is now best known as the author of The Laws of Thought. As the inventor of the prototype of what is now called Boolean logic, which became the basis of the modern digital computer, Boole is regarded in hindsight as a founder of the field of computer science. Boole said, ... no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognise ... those universal laws of thought which are the basis of all reasoning

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