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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. 183–198. 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.
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.
George Boole (1815–1864) introduced this principle into modern logic: Even though he changed from a monistic fixed-universe framework in his 1840s writings to a pluralistic multiple-universe framework in 1854, [1] he never wavered in his frank avowal of the principle of wholistic reference. Indeed, he took it as an essential accompaniment to ...
The philosopher and logician George Boolos discusses the power of the PM system in the preface to his Logic, logic & logic, stating that it is powerful enough to derive most classical mathematics, equating the power of PM to that of Z, a weaker form of set theory than ZFC (Zermelo-Fraenkel Set theory with Choice). In fact, ZFC actually does ...