The Laws of Thought by George Boole

The Laws of Thought

George Boole

Find this book at buch7.de | eurobuch.com | buchhandel.de | books.google.com 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:

"Wealth w consists of things transferable t, limited in supply s, and either productive of pleasure p or preventive of pain r." after three short paragraphs Boole arrives at

w = st{p(1-r)+r(1-p)} 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:

"Suppose that in the drawing of balls from an urn attention had only been paid to those cases in which the balls drawn were either of a particular colour, "white", or of a particular composition, "marble," or were marked by both these characters, no record having been kept of those cases in which a ball that was neither white nor marble had been drawn. Let it then have been found, that whenever the supposed condition was satisfied, there was a probability p that a white ball would be drawn, and a probabilbity q that a marble ball would have been drawn: and from these data alone let it be required to find the probability that in the next drawing, without reference at all to the condition above metioned, a white ball will be drawn; also the probability that a marble ball will be drawn. Here if x represents the drawing of a white ball, y that of a marble ball." 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:

Responsible beings x are all rational beings y who are either free to act z, or have voluntarily sacrified their freedom w." 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:

"Irrational persons consist of all irresponsible beings who are either free to act, or have voluntarily sacrified their liberty, and are not free to act; together with an indefinite remainder of irresponsible beings who have not sacrified their liberty, and are not free to act.

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.