history of logic

This logos holds always but humans always prove unable to understand it, both before hearing it and when they have first heard it. History of logic by Dumitriu, Anton. Using it, Frege provided a definition of the ancestral relation, of the many-to-one relation, and of mathematical induction. Traditional logic generally means the textbook tradition that begins with Antoine Arnauld's and Pierre Nicole's Logic, or the Art of Thinking, better known as the Port-Royal Logic. It was also subjected to an extended and destructive critique by Edmund Husserl in the first volume of his Logical Investigations (1900), an assault which has been described as "overwhelming". {\displaystyle D} [24] It is believed that Thales learned that an angle inscribed in a semicircle is a right angle during his travels to Babylon. i [141] The priority method, discovered independently by Albert Muchnik and Richard Friedberg in the 1950s, led to major advances in the understanding of the degrees of unsolvability and related structures. Thales was said to have had a sacrifice in celebration of discovering Thales' theorem just as Pythagoras had the Pythagorean theorem. [65] Al-Razi's work was seen by later Islamic scholars as marking a new direction for Islamic logic, towards a Post-Avicennian logic. On Interpretation contains a comprehensive treatment of the notions of opposition and conversion; chapter 7 is at the origin of the square of opposition (or logical square); chapter 9 contains the beginning of modal logic. The fact that Zeno’s arguments were all of this form suggests that he recognized and reflected on the general pattern. [18] In the case of the classical Greek city-states, interest in argumentation was also stimulated by the activities of the Rhetoricians or Orators and the Sophists, who used arguments to defend or attack a thesis, both in legal and political contexts. [5] Medhatithi Gautama (c. 6th century BC) founded the anviksiki school of logic. [118] Boole's early work also lacks the idea of the logical sum which originates in Peirce (1867), Schröder (1877) and Jevons (1890),[119] and the concept of inclusion, first suggested by Gergonne (1816) and clearly articulated by Peirce (1870). In China, a contemporary of Confucius, Mozi, "Master Mo", is credited with founding the Mohist school, whose canons dealt with issues relating to valid inference and the conditions of correct conclusions. {\displaystyle j} 261–288. M from propositions having only two terms to those having arbitrarily many. In proof theory, Gerhard Gentzen developed natural deduction and the sequent calculus. A The Rise of Contemporary Logic Left to right: Pioneers of Boolean algebra George Boole, John Venn, and Charles Sanders Peirce (Source: MacTutor History of Mathematics Archive) On virtually the same day in 1847, two major new works on logic were published by prominent British mathematicians: Formal Logic [ 3 ] by Augustus De Morgan (1806–1871) and The Mathematical Analysis of Logic [ 1 ] by George Boole (1815–1864). [84] The Port-Royal introduces the concepts of extension and intension. {\displaystyle D} [127] Frege argued that the quantifier expression "all men" does not have the same logical or semantic form as "all men", and that the universal proposition "every A is B" is a complex proposition involving two functions, namely ' – is A' and ' – is B' such that whatever satisfies the first, also satisfies the second. The Entscheidungsproblem asked for a procedure that, given any formal mathematical statement, would algorithmically determine whether the statement is true. Despite the title, Hegel's Logic is not really a contribution to the science of valid inference. He remarked that a complete statement (logos) cannot consist of either a name or a verb alone but requires at least one of each. [107] Bolzano anticipated a fundamental idea of modern proof theory when he defined logical consequence or "deducibility" in terms of variables:[108]. History of logic, the history of the discipline from its origins among the ancient Greeks to the present time. Boole's goals were "to go under, over, and beyond" Aristotle's logic by 1) providing it with mathematical foundations involving equations, 2) extending the class of problems it could treat — from assessing validity to solving equations — and 3) expanding the range of applications it could handle — e.g. Premium Membership is now 50% off! {\displaystyle O} a \w It originally referred to the trivium, three tal fundamen curriculae: grammar, rhetorics, and logic. Zeno famously used this method to develop his paradoxes in his arguments against motion. {\displaystyle B} , The last great works in this tradition are the Logic of John Poinsot (1589–1644, known as John of St Thomas), the Metaphysical Disputations of Francisco Suarez (1548–1617), and the Logica Demonstrativa of Giovanni Girolamo Saccheri (1667–1733). [143] Deontic logics are closely related to modal logics: they attempt to capture the logical features of obligation, permission and related concepts. j [66], "Medieval logic" (also known as "Scholastic logic") generally means the form of Aristotelian logic developed in medieval Europe throughout roughly the period 1200–1600. The second is that if such a system is also capable of proving certain basic facts about the natural numbers, then the system cannot prove the consistency of the system itself. D Second, in the realm of logic's problems, Boole's addition of equation solving to logic — another revolutionary idea — involved Boole's doctrine that Aristotle's rules of inference (the "perfect syllogisms") must be supplemented by rules for equation solving. [60] Avicenna wrote on the hypothetical syllogism[61] and on the propositional calculus, which were both part of the Stoic logical tradition. As a result, some commentators see the traditional Indian syllogism as a rhetorical form that is entirely natural in many cultures of the world, and yet not as a logical form—not in the sense that all logically unnecessary elements have been omitted for the sake of analysis. [14] The proofs of Euclid of Alexandria are a paradigm of Greek geometry.

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