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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] |
Logicism
In the philosophy of mathematics, logicism is a programme comprising one or more of the theses that — for some coherent meaning of 'logic' — mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and Alfred North Whitehead championed this programme, initiated by Gottlob Frege and subsequently developed by Richard Dedekind and Giuseppe Peano. Overview Dedekind's path to logicism had a turning point when he was able to construct a model satisfying the axioms characterizing the real numbers using certain sets of rational numbers. This and related ideas convinced him that arithmetic, algebra and analysis were reducible to the natural numbers plus a "logic" of classes. Furthermore by 1872 he had concluded that the naturals themselves were reducible to sets and mappings. It is likely that other logicists, most importantly Frege, were also guided by the new theories of the r ... [...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] |
Hans Sluga
Hans D. Sluga (; born April 24, 1937) is a German philosopher who spent most of his career as professor of philosophy at the University of California, Berkeley. Sluga teaches and writes on topics in the history of analytic philosophy, the history of continental philosophy, as well as on political theory, and ancient philosophy in Greece and China. He has been particularly influenced by the thought of Gottlob Frege, Ludwig Wittgenstein, Martin Heidegger, Friedrich Nietzsche, and Michel Foucault. Education and career Hans Sluga studied at the University of Bonn and the University of Munich. He subsequently obtained a BPhil at Oxford, where he studied under R. M. Hare, Isaiah Berlin, Gilbert Ryle and Michael Dummett. Since 1970, Sluga has been a professor of philosophy at the University of California, Berkeley, serving from 2009 as the William and Trudy Ausfahl Professor of Philosophy until his retirement in 2020. He previously served as a lecturer in philosophy at University Coll ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Mathematics
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts. The philosophy of mathematics has two major themes: mathematical realism and mathematical anti-realism. History The origin of mathematics is subject to arguments and disagreements. Whether the birth of mathematics was a random happening or induced by necessity during the development of other subjects, like physics, is still a matter of prolific debates. Many thinkers have contributed their ideas concerning the nature of mathematics. Today, some philosophers of mathematics aim to give accounts of this form of inquiry and its products as they stand, while others emphasize a role for themselves t ... [...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] |
Philosophy Of Language
In analytic philosophy, philosophy of language investigates the nature of language and the relations between language, language users, and the world. Investigations may include inquiry into the nature of meaning, intentionality, reference, the constitution of sentences, concepts, learning, and thought. Gottlob Frege and Bertrand Russell were pivotal figures in analytic philosophy's "linguistic turn". These writers were followed by Ludwig Wittgenstein ('' Tractatus Logico-Philosophicus''), the Vienna Circle, logical positivists, and Willard Van Orman Quine. In continental philosophy, language is not studied as a separate discipline. Rather, it is an inextricable part of many other areas of thought, such as phenomenology, structural semiotics, language of mathematics, hermeneutics, existentialism, deconstruction and critical theory. History Ancient philosophy In the West, inquiry into language stretches back to the 5th century BC with Socrates, Plato, Aristotl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Philosophy
Analytic philosophy is a branch and tradition of philosophy using analysis, popular in the Western world and particularly the Anglosphere, which began around the turn of the 20th century in the contemporary era in the United Kingdom, United States, Canada, Australia, New Zealand, and Scandinavia, and continues today. Analytic philosophy is often contrasted with continental philosophy, coined as a catch-all term for other methods prominent in Europe. Central figures in this historical development of analytic philosophy are Gottlob Frege, Bertrand Russell, G. E. Moore, and Ludwig Wittgenstein. Other important figures in its history include the logical positivists (particularly Rudolf Carnap), W. V. O. Quine, and Karl Popper. After the decline of logical positivism, Saul Kripke, David Lewis, and others led a revival in metaphysics. Elizabeth Anscombe, Peter Geach, Anthony Kenny and others brought analytic approach to Thomism. Analytic philosophy is characterized by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Western Philosophy
Western philosophy encompasses the philosophical thought and work of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the pre-Socratics. The word ''philosophy'' itself originated from the Ancient Greek (φιλοσοφία), literally, "the love of wisdom" grc, φιλεῖν , "to love" and σοφία '' sophía'', "wisdom"). History Ancient The scope of ancient Western philosophy included the problems of philosophy as they are understood today; but it also included many other disciplines, such as pure mathematics and natural sciences such as physics, astronomy, and biology (Aristotle, for example, wrote on all of these topics). Pre-Socratics The pre-Socratic philosophers were interested in cosmology; the nature and origin of the universe, while rejecting mythical answers to such questions. They were specifically interested in the (the cause or first principle) of the w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Resnik
Michael David Resnik (; born March 20, 1938) is a leading contemporary American philosopher of mathematics. Biography Resnik obtained his B.A. in mathematics and philosophy at Yale University in 1960, and his PhD in Philosophy at Harvard University in 1964. He wrote his thesis on Frege. He was appointed Associate Professor at the University of North Carolina at Chapel Hill in 1967, Professor in 1975, and University Distinguished Professor in 1988. He is Professor Emeritus of University of North Carolina at Chapel Hill and currently resides in rural Chatham County, North Carolina Chatham County ( ) , from the North Carolina Collection's website at the |
Linguistic Turn
The linguistic turn was a major development in Western philosophy during the early 20th century, the most important characteristic of which is the focusing of philosophy and the other humanities primarily on the relations between language, language users, and the world. Very different intellectual movements were associated with the "linguistic turn", although the term itself is commonly thought to have been popularised by Richard Rorty's 1967 anthology ''The Linguistic Turn'', in which he discusses the turn towards linguistic philosophy. According to Rorty, who later dissociated himself from linguistic philosophy and analytic philosophy generally, the phrase "the linguistic turn" originated with philosopher Gustav Bergmann. Analytic philosophy Traditionally, the linguistic turn is taken to also mean the birth of analytic philosophy. One of the results of the linguistic turn was an increasing focus on logic and philosophy of language, and the cleavage between ideal language phi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bruno Bauch
Bruno Bauch (; 19 January 1877 – 27 February 1942) was a German neo-Kantian philosopher. Life and career Bauch was born in Groß-Nossen, Münsterberg District, Silesia, Prussia (now in Poland) and studied philosophy at Freiburg, Strasbourg, and Heidelberg. In 1901, he received his doctorate under Heinrich Rickert at Freiburg, which entitled him to teach some courses (one of his doctoral students was Rudolf Carnap, who later became a central figure of the Vienna Circle). Bauch completed his habilitation, entitling him to a professorship, at the University of Halle in 1903. He taught as a "titular professor" at Halle from 1903 to 1910, and from 1911 onward as an "ordinary professor" at the University of Jena. At Jena, he befriended Gottlob Frege and collaborated with the neo-Kantian philosopher of language Richard Hönigswald. Bauch was an influential figure in the Kant-Gesellschaft (Kant Society) and helped publish the Prussian Academy's edition of Kant's collected works. U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Immanuel Kant
Immanuel Kant (, , ; 22 April 1724 – 12 February 1804) was a German philosopher and one of the central Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works in epistemology, metaphysics, ethics, and aesthetics have made him one of the most influential figures in modern Western philosophy. In his doctrine of transcendental idealism, Kant argued that space and time are mere "forms of intuition" which structure all experience, and therefore that, while " things-in-themselves" exist and contribute to experience, they are nonetheless distinct from the objects of experience. From this it follows that the objects of experience are mere "appearances", and that the nature of things as they are in themselves is unknowable to us. In an attempt to counter the skepticism he found in the writings of philosopher David Hume, he wrote the '' Critique of Pure Reason'' (1781/1787), one of his most well-known works. In it, he developed his theory of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
