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calculus


Subject Philosophy

DOI: 10.1111/b.9781405106795.2004.x


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L ogic [from Latin for pebbles (plural: calculi)] A rule-governed formal symbolic system that can be mechanistically applied for calculation and reasoning in mathematics and logic. The word was adopted because in ancient times calculation was done with pebbles. All axiomatic systems, together with other systems of calculation, measurement, or comparison, are calculi. As a branch of mathematical analysis, calculus was principally developed by Leibniz , Newton , Lagrange, Cauchy, Cantor , and Peano. Leibniz also developed calculus as a formal system of reasoning, that is, to reduce valid argument forms or structures to a calculus by whose rules we can construct and criticize arguments. This is what he called calculus ratiocinatur (a calculus of reasoning), or what we generally mean by a logical calculus.Based on the work of Frege , modern logical calculus is generally divided into propositional calculus, which deals with the truth functions of propositions, and predicate calculus, which is concerned with items such as the quantifiers, variables, and predicates of first-order languages. “A calculus is, in fact, any system wherein we may calculate.” Langer, An Introduction to Symbolic Logic ... log in or subscribe to read full text

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