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The Calculus of Logic by George Boole; a transcription of an article which originally appeared in Cambridge and Dublin Mathematical Journal, Vol. III (1848), pp. 183–98. George Boole's work as first Professor of Mathematics in University College, Cork, Ireland Archived 19 November 2017 at the Wayback Machine; George Boole website
An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities by George Boole, published in 1854, is the second of Boole's two monographs on algebraic logic. Boole was a professor of mathematics at what was then Queen's College, Cork, now University College Cork, in Ireland.
A timeline of mathematical logic ; see also history of logic. 19th century 1847 – George Boole proposes symbolic logic in The Mathematical Analysis of Logic, defining what is now called Boolean algebra. 1854 – George Boole perfects his ideas, with the publication of An Investigation of the Laws of Thought. 1874 – Georg Cantor proves that the set of all real numbers is uncountably ...
The title of George Boole's 1854 treatise on logic, An Investigation on the Laws of Thought, indicates an alternate path. The laws are now incorporated into an algebraic representation of his "laws of the mind", honed over the years into modern Boolean algebra .
The development of the modern "symbolic" or "mathematical" logic during this period by the likes of Boole, Frege, Russell, and Peano is the most significant in the two-thousand-year history of logic, and is arguably one of the most important and remarkable events in human intellectual history.
Square of opposition In the Venn diagrams black areas are empty and red areas are nonempty. The faded arrows and faded red areas apply in traditional logic. Boolean logic is a system of syllogistic logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the "empty set", that is, a class of non-existent entities, such as round squares, without resorting ...
George Boole's unwavering acceptance of Aristotle's logic is emphasized by the historian of logic John Corcoran in an accessible introduction to Laws of Thought. [10] [11] Corcoran also wrote a point-by-point comparison of Prior Analytics and Laws of Thought. [12] According to Corcoran, Boole fully accepted and endorsed Aristotle's logic.
Mathematical logic, also called 'logistic', 'symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the nineteenth century with the aid of an artificial notation and a rigorously deductive method. [5]