Peirce: Basing the Algebra of Logic on Subsumption. Jevons: An Algebra of Logic Based on Total Operations. 1854-Boole's Final Presentation of his Algebra of Logic. 1847-The Beginnings of the Modern Versions of the Algebra of Logic. This entry is divided into 10 sections: 0. The tradition of the algebra of logic played a key role in the notion of Logic as Calculus as opposed to the notion of Logic as Universal Language. Furthermore, this tradition motivated the investigations of Leopold Löwenheim (1878-1957) that eventually gave rise to model theory. The methodology initiated by Boole was successfully continued in the 19th century in the work of William Stanley Jevons (1835-1882), Charles Sanders Peirce (1839-1914), Ernst Schröder (1841-1902), among many others, thereby establishing a tradition in (mathematical) logic. The algebra of logic, as an explicit algebraic system showing the underlying mathematical structure of logic, was introduced by George Boole (1815-1864) in his book The Mathematical Analysis of Logic (1847). By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’-tautologies and laws such as excluded middle and non-contradiction- Boole became the founder of logic as formal ontology. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. One of themain conclusions is that Boole’s contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. his confused attempt to apply differential calculus to logic, his misguided effort tomake his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. Accordingly, this article does not discuss many other historically and philosophically important aspects of Boole’s book, e.g. This comparison merits an article itself. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. Prior Analytics by theGreek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematicianGeorge Boole (1815 – 1864) are the twomost important surviving original logical works frombefore the advent of modern logic.
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