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The Laws of Thought

George Boole

Buy this book at Amazon.com or try Amazon.co.uk in England, Amazon.ca in Canada, Amazon.de in Germany, Amazon.fr in France, Amazon.it in Italy, Amazon.es in Spain. ASIN=0486600289, Category: Science, Language: E, cover: PB, pages: 424, year: 1958(1854).

This book is mentioned in Seeking Wisdom: From Darwin to Munger by Peter Bevelin.

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

Some quotes - selected and annotated by IBS:

Chap. IV, Division of Propositions:

after three short paragraphs Boole arrives at and he also explains why w = st(p+r) is wrong and then he elaborates this example further to explain the method of elimination, then reduction.

Then in chap. XIII on the analysis of Clarke's and Spinoza's theorems, it gets interesting, quote:

"Something has existed from eternity. The proof is a follows :- ..."

The proof takes "only" 40 pages.

And last but not least, in chap. XVII, "General Method of Probabilities" Boole explains Prof. Donkins principle with the following example:

Without looking up Boole's book, the first one who sends the correct solution to IBS will be credited in the hall of IBS-fame.

An example from chap VI, Method of Interpretation:

which after arriving at xw = v(1-z) and x(1-w) = vz leads to the conclusion that quote: Then he goes on to irrational persons where the solution is, quote:

Some quotes from chap. XXII, The Constitution of the Intellect:

"Although the perfect triangle, or square, or circle, exists not in nature, eludes all our powers of representative conception, and is presented to us in thought only, as the limit of an indefinite process of abstraction, yet, by a wonderful faculty of understanding, it may be made the subject of propositions which are absolutely true. The domain of reason is thus revealed to us as larger than that of imagination."
-- Quote from p405

"The truth that the ultimate laws of thought are mathematical in their form, viewed in connexion with the fact of the possibility of error, establishes a ground for some remarkable conclusions."
-- Quote from p407

"We can never be said to comprehend that which is represented to thought as a limit of an indefinite process of abstraction. A progression ad infinitum is impossible to finite powers. But though we cannot comprehend the infinite, there may be even scientific grounds for believing that human nature is constituted in some relation to the infinite."
-- Quote from p419

Although Boole's book is not about binary functions, it is worth noting, that Stuart Kauffman in "At Home in the Universe - The search for the laws of self-organization and complexity" pausibly shows that mathematics created life and Boole's binary functions laid the foundations for us to understand the logic behind this process.

Regarding to Boole's and Kauffman's book, borrowing CTM's words from the WESCO AGM, 2005 about his book, if you buy it and don't like it, you can always give it to a more intelligent friend.