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Saturday, August 25, 2018

George Boole and the logical mind


Photo source: Wikimedia Commons, Haks


George Boole (1815-1864) was an English mathematician best known for the development of Boolean algebra. Astrophysicist Mario Livio said,


"Boole literally transformed logic into a type of algebra (which came to be known as Boolean algebra) and extended the analysis of logic even to probabilistic reasoning... Boole managed to mathematically tame the logical connectives 'and', 'or', 'if... then', and 'not', which are currently at the very core of computer operations and various switching circuits." (Is God a Mathematician? 2009)


The rest of this post is some quotes from Boole.


Logic and the mind


"There is not only a close analogy between the operations of the mind in general reasoning and its operation int he particular science of algebra, but there is to a considerable extent an exact agreement in the laws by which the two classes of operations are conducted." (An Investigation into the Laws of Thought, 1854)


"The design of the following treatise is to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in symbolical language of a calculus, and upon this foundation to establish the science of logic and construct its method..." (An Investigation into the Laws of Thought, 1854)


"A successful attempt to express logical propositions by symbols, the laws of whose combinations should be found upon the laws of the mental processes which they represent, would, so far, be a step towards a philosophical language." (The Mathematical Analysis of Logic, 1847)


History of mathematics


"I presume that few who have paid any attention to the history of the mathematical analysis, will doubt that it has been developed in a certain order... by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived." (A Treatise on Differential Equations, 1859)