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Principle Of Identity
In logic, the law of identity states that each thing is identical with itself. It is the first of the historical 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 to occur 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion 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 analysis. In the early 20th century it was shaped by David Hilbert's program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in proving consistency. Work in set theory sho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gottfried Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history and philology. 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. In addition, he contributed to the field of library science: while serving as overseer of the Wolfenbüttel library in Germany, he devised a cataloging system that would have served as a guide for many of Europe's largest libraries. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Latin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meaning (philosophy Of Language)
In semantics, semiotics, philosophy of language, metaphysics, and metasemantics, meaning "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. Namely: *There are the things in the world, which might have meaning; *There are things in the world that are also signs of other things in the world, and so, are always meaningful (i.e., natural signs of the physical world and ideas within the mind); *There are 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 communicati ... [...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 referen ... [...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, logic, and 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 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 cited by Michael Dummett as where to pinpoint the linguistic turn. His philosop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foundations Of Arithmetic
''The Foundations of Arithmetic'' (german: Die Grundlagen der Arithmetik) is a book by Gottlob Frege, published in 1884, which investigates the philosophical foundations of arithmetic. Frege refutes other theories of number and develops his own theory of numbers. The ''Grundlagen'' also helped to motivate Frege's later works in logicism. 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. Criticisms of predecessors Psychologistic accounts of mathematics Frege objects to any account of mathematics based on psychologism, that is the view that math and numbers are relative to the subjective thoughts of the people who think of them. According to Frege, psychological accounts appeal to what is subjective, while mathematics i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ayn Rand
Alice O'Connor (born Alisa Zinovyevna Rosenbaum;, . Most sources transliterate her given name as either ''Alisa'' or ''Alissa''. , 1905 – March 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 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 plays, she achieved fame with her 1943 novel, '' The Fountainhead''. In 1957, Rand published her best-known work, the novel ''Atlas Shrugged''. Afterward, until her death in 1982, she turned to non-fiction to promote her philosophy, publishing her own periodicals and releasing several collections of essays. Rand advocated reason as the only means of acquiring knowledge; she rejected faith and religion. She supported rational and ethical egoism and rejected altruism. In politics, she condemned ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Objectivism
Objectivism is a philosophical system 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 with rea ... [...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 unde ... [...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 is credited with laying the foundations for the Information Age. Early life Boole was born in 1815 in Lincoln, Lincolnshire, England, the son of John Boole senior (1779–1848), a shoemaker and Mary Ann Joyce. He had a primary school education, and received lessons from his father, but due to a serious decline in business, he had little further formal and academic teaching. William Brooke, a bookseller in Lincoln, may have helped him with Latin, which he may also have learned at the school of Thomas Bainbridge. He was self-taught in modern langu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Afrikan Spir
Afrikan Aleksandrovich Spir (1837–1890) was a Russian neo-Kantian philosopher of German-Greek descent who wrote primarily in German. His book ''Denken und Wirklichkeit'' (''Thought and Reality'') exerted a "lasting impact" on the writings of Friedrich Nietzsche. Biography Spir was born on 15 November 1837 in his father's estates of Spirovska, near the city of Elisavetgrad (Elizabethgrad, Kherson Governorate, Russian Empire now Kropyvnytskyi, Ukraine). His father, Alexander Alexandrovich Spir, of German descent, was a Russian surgeon—Chief Physician of the military Hospital of Odessa specifically—and former professor of mathematics in Moscow. In 1812, he received the Order of St. Vladimir, was knighted, and became councillor and member of Kherson's Governorate hereditary nobility. His mother, Helena Constantinovna Spir, daughter of the major Poulevich, was on her mother's side the granddaughter of the Greek painter Logino, who arrived in Russia under the reign of Cather ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sir William Hamilton, 9th Baronet
Sir William Hamilton, 9th Baronet FRSE (8 March 1788 – 6 May 1856) was a Scottish metaphysician. He is often referred to as William Stirling Hamilton of Preston, in reference to his mother, Elizabeth Stirling. Early life He was born in rooms at the University of Glasgow, He was from an academic family: his father Professor William Hamilton, had in 1781, on the recommendation of William Hunter, been appointed to succeed his own father, Dr Thomas Hamilton, as Regius Professor of Anatomy, Glasgow; he died in 1790, aged 32. William Hamilton and his younger brother, Thomas Hamilton, were brought up by their mother. Hamilton received his early education at Glasgow Grammar School, except for two years which he spent in a private school at Chiswick in Kent, and in 1807 went as a Snell Exhibitioner, to Balliol College, Oxford. He obtained a first class in ''literis humanioribus'' and took his BA in 1811 (MA 1814). He had been intended for the medical profession, but soon aft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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