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Begriffsschrift
''Begriffsschrift'' (German for, roughly, "concept-writing") is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book. ''Begriffsschrift'' is usually translated as ''concept writing'' or ''concept notation''; the full title of the book identifies it as "a formula language, modeled on that of arithmetic, for pure thought." Frege's motivation for developing his formal approach to logic resembled Gottfried Wilhelm Leibniz, Leibniz's motivation for his ''calculus ratiocinator'' (despite that, in the foreword Frege clearly denies that he achieved this aim, and also that his main aim would be constructing an ideal language like Leibniz's, which Frege declares to be a quite hard and idealistic—though not impossible—task). Frege went on to employ his logical calculus in his research on the foundations of mathematics, carried out over the next quarter-century. This is the first work in Analytical Philosophy, a field that later British and Anglo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gottlob Frege
Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, philosophy of logic, logic, and Philosophy of mathematics, mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever. His contributions include the History of logic#Rise of modern logic, development of modern logic in the ''Begriffsschrift'' and work in the foundations of mathematics. His book the ''Foundations of Arithmetic'' is the seminal text of the logicist project, and is ci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Characteristica Universalis
The Latin term ''characteristica universalis'', commonly interpreted as ''universal characteristic'', or ''universal character'' in English, is a universal and formal language imagined by Gottfried Leibniz able to express mathematical, scientific, and metaphysical concepts. Leibniz thus hoped to create a language usable within the framework of a universal logical calculation or '' calculus ratiocinator''. The ''characteristica universalis'' is a recurring concept in the writings of Leibniz. When writing in French, he sometimes employed the phrase ''spécieuse générale'' to the same effect. The concept is sometimes paired with his notion of a ''calculus ratiocinator'' and with his plans for an encyclopaedia as a compendium of all human knowledge. Uses International communication Many Leibniz scholars writing in English seem to agree that he intended his ''characteristica universalis'' or "universal character" to be a form of pasigraphy, or ideographic language. This was to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Connective
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective \lor can be used to join the two atomic formulas P and Q, rendering the complex formula P \lor Q . Common connectives include negation, disjunction, conjunction, implication, and equivalence. In standard systems of classical logic, these connectives are interpreted as truth functions, though they receive a variety of alternative interpretations in nonclassical logics. Their classical interpretations are similar to the meanings of natural language expressions such as English "not", "or", "and", and "if", but not identical. Discrepancies between natural language connectives and those of classical logic have motivated nonclassical approaches to natural language meaning as well as approaches which pair a classi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Ratiocinator
The ''calculus ratiocinator'' is a theoretical universal logical calculation framework, a concept described in the writings of Gottfried Leibniz, usually paired with his more frequently mentioned ''characteristica universalis'', a universal conceptual language. Two views There are two contrasting points of view on what Leibniz meant by ''calculus ratiocinator''. The first is associated with computer software, the second is associated with computer hardware. Analytic view The received point of view in analytic philosophy and formal logic, is that the ''calculus ratiocinator'' anticipates mathematical logic—an "algebra of logic". The analytic point of view understands that the ''calculus ratiocinator'' is a formal inference engine or computer program, which can be designed so as to grant primacy to calculations. That logic began with Frege's 1879 ''Begriffsschrift'' and C.S. Peirce's writings on logic in the 1880s. Frege intended his "concept script" to be a ''calcul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytical Philosophy
Analytic philosophy is a broad movement within Western philosophy, especially English-speaking world, anglophone philosophy, focused on analysis as a philosophical method; clarity of prose; rigor in arguments; and making use of formal logic, mathematics, and to a lesser degree the natural sciences.Mautner, Thomas (editor) (2005) ''The Penguin Dictionary of Philosophy'', entry for "Analytic philosophy", pp. 22–23 It is further characterized by an interest in language, semantics and Meaning (philosophy), meaning, known as the linguistic turn. It has developed several new branches of philosophy and logic, notably philosophy of language, philosophy of mathematics, philosophy of science, modern predicate logic and mathematical logic. The proliferation of analysis in philosophy began around the turn of the 20th century and has been dominant since the latter half of the 20th century. Central figures in its historical development are Gottlob Frege, Bertrand Russell, G. E. Moore, and L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic
Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers. Real number arithmetic is about calculations with real numbers, which include both rational and irrational numbers. Another distinction is based on the numeral system employed to perform calculations. Decimal arithmetic is the most common. It uses the basic numerals from 0 to 9 and their combinations to express numbers. Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of the basic numerals 0 and 1. Computer arithmetic deals with the specificities of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
