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Law Of Identity
In logic, the law of identity states that each thing is identical with itself. It is the first of the traditional three laws of thought, along with the law of noncontradiction, and the law of excluded middle. However, few systems of logic are built on just these laws. History Ancient philosophy The earliest recorded use of the law appears in Plato's dialogue '' Theaetetus'' (185a), wherein Socrates attempts to establish that what we call "sounds" and "colours" are two different classes of thing: It is used explicitly only once in Aristotle, in a proof in the '' Prior Analytics'': Medieval philosophy Aristotle believed the law of non-contradiction to be the most fundamental law. Both Thomas Aquinas (''Met.'' IV, lect. 6) and Duns Scotus (''Quaest. sup. Met.'' IV, Q. 3) follow Aristotle in this respect. Antonius Andreas, the Spanish disciple of Scotus (d. 1320), argues that the first place should belong to the law "Every Being is a Being" (''Omne Ens est Ens'', Qq. in Met ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gottfried Leibniz
Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Isaac Newton, Sir Isaac Newton, with the creation of calculus in addition to many other branches of mathematics, such as binary arithmetic and statistics. Leibniz has been called the "last universal genius" due to his vast expertise across fields, which became a rarity after his lifetime with the coming of the Industrial Revolution and the spread of specialized labor. He is a prominent figure in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history, philology, games, music, and other studies. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science. Leibniz contributed to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, and public intellectual. He had influence on mathematics, logic, set theory, and various areas of analytic philosophy.Stanford Encyclopedia of Philosophy"Bertrand Russell", 1 May 2003. He was one of the early 20th century's prominent logicians and a founder of analytic philosophy, along with his predecessor Gottlob Frege, his friend and colleague G. E. Moore, and his student and protégé Ludwig Wittgenstein. Russell with Moore led the British "revolt against British idealism, idealism". Together with his former teacher Alfred North Whitehead, A. N. Whitehead, Russell wrote ''Principia Mathematica'', a milestone in the development of classical logic and a major attempt to reduce the whole of mathematics to logic (see logicism). Russell's article "On Denoting" has been considered a "paradigm of philosophy". Russell was a Pacifism, pacifist who ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meaning (philosophy Of Language)
In philosophymore specifically, in its sub-fields semantics, semiotics, philosophy of language, metaphysics, and metasemanticsmeaning "is a relationship between two sorts of things: signs and the kinds of things they intend, express, or signify". The types of meanings vary according to the types of the thing that is being represented. There are: *the things, which might have meaning; *things that are also signs of other things, and therefore are always meaningful (i.e., natural signs of the physical world and ideas within the mind); *things that are necessarily meaningful, such as words and nonverbal symbols. The major contemporary positions of meaning come under the following partial definitions of meaning: *psychological theories, involving notions of thought, intention, or understanding; *logical theories, involving notions such as intension, cognitive content, or sense, along with extension, reference, or denotation; *message, content, information, or communication; * trut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
On Sense And Reference
In the philosophy of language, the distinction between sense and reference was an idea of the German philosopher and mathematician Gottlob Frege in 1892 (in his paper "On Sense and Reference"; German: "Über Sinn und Bedeutung"), reflecting the two ways he believed a singular term may have meaning. The reference (or "referent"; ''Bedeutung'') of a ''proper name'' is the object it means or indicates (''bedeuten''), whereas its sense (''Sinn'') is what the name expresses. The reference of a ''sentence'' is its truth value, whereas its sense is the thought that it expresses."On Sense and Reference" Über Sinn und Bedeutung" '' Zeitschrift für Philosophie und philosophische Kritik'', vol. 100 (1892), pp. 25–50, esp. p. 31. Frege justified the distinction in a number of ways. #Sense is something possessed by a name, whether or not it has a reference. For example, the name "Odysseus" is intelligible, and therefore has a sense, even though there is no individual object (its refer ... [...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] |
Foundations Of Arithmetic
''The Foundations of Arithmetic'' () is a book by Gottlob Frege, published in 1884, which investigates the philosophical foundations of arithmetic. Frege refutes other idealist and materialist theories of number and develops his own platonist theory of numbers. The ''Grundlagen'' also helped to motivate Frege's later works in logicism. The book was also seminal in the philosophy of language. Michael Dummett traces the linguistic turn to Frege's ''Grundlagen'' and his context principle. The book was not well received and was not read widely when it was published. It did, however, draw the attentions of Bertrand Russell and Ludwig Wittgenstein, who were both heavily influenced by Frege's philosophy. An English translation was published (Oxford, 1950) by J. L. Austin, with a second edition in 1960. Linguistic turn ;Gottlob Frege, Introduction to ''The Foundations of Arithmetic'' (1884/1980) : In the enquiry that follows, I have kept to three fundamental principles: :: always to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ayn Rand
Alice O'Connor (born Alisa Zinovyevna Rosenbaum; , 1905March 6, 1982), better known by her pen name Ayn Rand (), was a Russian-born American writer and philosopher. She is known for her fiction and for developing a philosophical system which she named ''Objectivism''. Born and educated in Russia, she moved to the United States in 1926. After two early novels that were initially unsuccessful and two Broadway theatre, Broadway plays, Rand achieved fame with her 1943 novel ''The Fountainhead''. In 1957, she published her best-selling work, the novel ''Atlas Shrugged''. Afterward, until her death in 1982, she turned to non-fiction to promote her philosophy, publishing her own Objectivist periodicals, periodicals and releasing several collections of essays. Rand advocated reason and rejected faith and religion. She supported Rational egoism, rational and ethical egoism as opposed to Altruism (ethics), altruism and hedonism. In politics, she condemned the initiation of force as immor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Objectivism
Objectivism is a philosophical system named and developed by Russian-American writer and philosopher Ayn Rand. She described it as "the concept of man as a heroic being, with his own happiness as the moral purpose of his life, with productive achievement as his noblest activity, and reason as his only absolute"."About the Author" in Rand first expressed Objectivism in her fiction, most notably ''The Fountainhead'' (1943) and ''Atlas Shrugged'' (1957), and later in non-fiction essays and books. Leonard Peikoff, a professional philosopher and Rand's designated intellectual heir, later gave it a more formal structure. Peikoff characterizes Objectivism as a "closed system" insofar as its "fundamental principles" were set out by Rand and are not subject to change. However, he stated that "new implications, applications and integrations can always be discovered". Objectivism's main tenets are that reality exists independently of consciousness, that human beings have direct contact ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Laws Of Thought
''An Investigation of the Laws of Thought: on Which are Founded the Mathematical Theories of Logic and Probabilities'' by George Boole, published in 1854, is the second of Boole's two monographs on algebraic logic. Boole was a professor of mathematics at what was then Queen's College, Cork, now University College Cork, in Ireland. Review of the contents The historian of logic John Corcoran wrote an accessible introduction to ''Laws of Thought''George Boole. 1854/2003. ''The Laws of Thought'', facsimile of 1854 edition, with an introduction by J. Corcoran. Buffalo: Prometheus Books (2003). Reviewed by James van Evra in Philosophy in Review.24 (2004) 167–169. and a point by point comparison of '' Prior Analytics'' and ''Laws of Thought''.John Corcoran, Aristotle's Prior Analytics and Boole's Laws of Thought, ''History and Philosophy of Logic'', 24 (2003), pp. 261–288. According to Corcoran, Boole fully accepted and endorsed Aristotle's logic. Boole's goals were “to go und ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Boole
George Boole ( ; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland. He worked in the fields of differential equations and algebraic logic, and is best known as the author of ''The Laws of Thought'' (1854), which contains Boolean algebra. Boolean logic, essential to computer programming, is credited with helping to lay the foundations for the Information Age. Boole was the son of a shoemaker. He received a primary school education and learned Latin and modern languages through various means. At 16, he began teaching to support his family. He established his own school at 19 and later ran a boarding school in Lincoln. Boole was an active member of local societies and collaborated with fellow mathematicians. In 1849, he was appointed the first professor of mathematics at Queen's College, Cork (now University C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Afrikan Spir
Afrikan Alexandrovich Spir, also spelled African Spir (1837–1890), was a Russian philosopher of German- Greek descent who wrote primarily in German, but also French.Afrikan Spir Dictionnaire historique de la Suisse. His book ''Denken und Wirklichkeit'' (''Thought and Reality'', 1873) had a significant influence on several eminent philosophers, scholars and writers such as Hans Vaihinger, , |
