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in Indian philosophy, the concept of adventitious limiting conditions. In logic, upadhi operates as follows: a syllogism requires a ground (hetu) to prove the proposition—e.g., that there is fire on the mountain is proved by the presence of smoke. But this ground needs a qualification: there can be fire...Indian philosophy (in Indian philosophy: Common concerns) ...that includes mathematical knowledge or historical knowledge. Possibly connected with their indifference toward mathematics is the significant fact that Indian philosophers have not developed formal logic. The theory of the syllogism (a valid deductive argument having two premises and a conclusion) is, however, developed, and much sophistication has been achieved in logical theory. Indian logic...Islamic philosophy ...Alexandrian philosophical schools, al-Farabi broadened the range of philosophical inquiry and fixed its form. He paid special attention to the study of language and its relation to logic. In his numerous commentaries on Aristotle's logical works, he expounded for the first time in Arabic the entire range of the scientific and nonscientific forms of argument and established the...contribution by: Ajdukiewicz Polish logician and semanticist who was the chief contributor to the Warsaw school of philosophy and logic, which analyzed the relationship of language and knowledge. He is credited with developing in 1920 the first deductive theory for the study of logic based on syntax.Aristotle ...began and elaborated his theoretical and formal analysis of the arguments used in various Socratic discussions—an enterprise that, when completed, resulted in the corpus of his works on logic. Aristotle rightly claimed to have invented this discipline; indeed, until rather recent times it was said that he completed it in such a way that hardly anything could be added.Boole English mathematician who helped establish modern symbolic logic and whose algebra of logic, now called Boolean algebra, is basic to the design of digital computer circuits.Carnap For several years afterward Carnap was engaged in private research in logic and the foundations of physics and wrote a number of essays on problems of space, time, and causality, as well as a textbook in symbolic, or mathematical, logic (Abriss der Logistik, 1929; a considerably different later German version appeared in English translation: Introduction to Symbolic Logic and Its...Chrysippus ...by Cleanthes (c. 331–c. 232 BC), the second head of the school, and by Chrysippus (c. 280–c. 206 BC), its third head. Chrysippus elaborated a new kind of logic, which did not receive much attention outside the Stoic school until recent times; this “propositional logic” has been hailed by some logicians as superior to the “conceptual...De Morgan Asserting that logic as it had come down from Aristotle was unnecessarily restricted in scope, De Morgan made his greatest contributions as a reformer of logic. The renaissance of logic studies, which began in the first half of the 19th century, came about almost entirely because of the writings of De Morgan and another British mathematician, George Boole. Alternate forms and generalizations of...Frege German mathematician and logician, who founded modern mathematical logic. Working on the borderline between philosophy and mathematics—viz., in the philosophy of mathematics and mathematical logic (in which no intellectual precedents existed)—Frege discovered, on his own, the fundamental ideas that have made possible the whole modern development of logic and thereby invented an...Hamilton Scottish metaphysical philosopher and influential educator, also remembered for his contributions in the field of logic.Lesniewski Polish logician and mathematician who was a co-founder and leading representative of the Warsaw school of logic.Lewis In logic, Lewis criticized contemporary formal systems using material implication and proposed an alternative system of logic based upon strict implication. That is, he rejected systems that do not limit themselves strictly to what is implicit in experience. Because concepts arise from experience, in his system no concept is fixed or indispensable, and the abstract categories of traditional...Mill During these years Mill also wrote his great systematic works on logic and on political economy. His reawakened enthusiasm for humanity had taken shape as an aspiration to supply an unimpeachable method of proof for conclusions in moral and social science; the French positivist philosopher Auguste Comte had some influence here, but the main inspiration undoubtedly came from the English...Peirce Though Peirce's career was in physical science, his ambitions were in logic. By the age of 31, he had published a number of technical papers in that field, besides papers and reviews in chemistry, philology, the philosophy of history and of religion, and the history of philosophy. He had also given two series of Harvard University lectures and one of Lowell Institute lectures, all in logic....Plato ...the Sophist and the Statesman are closely connected, both being ostensibly concerned with a problem of definition. The real purpose of the Sophist, however, is logical or metaphysical; it aims at explaining the true nature of negative predication, or denials that something is so. The object of the Statesman, on the other hand, is to consider...Quine American logician and philosopher, widely considered one of the dominant figures in Anglo-American philosophy in the last half of the 20th century.Ramus Educated at Cuts and later at the Collège de Navarre, in Paris, Ramus became master of arts in 1536. He taught a reformed version of Aristotelian logic at the Collège du Mans, in Paris, and at the Collège de l'Ave Maria, where he worked with Audomarus Talaeus (Omer Talon). Talaeus, under Ramus' influence, reformed Ciceronian rhetoric upon the principles applied by Ramus to...Russell ...philosopher, logician, and social reformer, founding figure in the analytic movement in Anglo-American philosophy, and recipient of the Nobel Prize for Literature in 1950. Russell's contributions to logic, epistemology, and the philosophy of mathematics established him as one of the foremost philosophers of the 20th century. To the general public, however, he was best known as a campaigner for...Stoics ...he had studied at Plato's Academy both with Xenocrates of Chalcedon and with Polemon of Athens, successive heads of the Academy. Zeno was responsible for the division of philosophy into three parts: logic, physics, and ethics. He also established the central Stoic doctrines in each part, so that later Stoics were to expand rather than to change radically the views of the founder. With some...William of Ockham ...composed by St. Francis of Assisi concerning the strictness of the poverty that should be practiced within the order. Ockham's early schooling in a Franciscan convent concentrated on the study of logic; throughout his career, his interest in logic never waned, because he regarded the science of terms as fundamental and indispensable for practicing all the sciences of things, including God,...
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