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64-596: The tetralemma is a figure that features prominently in the logic of India . It states that with reference to any a logical proposition (or axiom) X, there are four possibilities: The history of fourfold negation, the Catuskoti (Sanskrit), is evident in the logico-epistemological tradition of India, given the categorical nomenclature Indian logic in Western discourse. Subsumed within the auspice of Indian logic, ' Buddhist logic ' has been particularly focused in its employment of

128-444: A mediated reference theory . His paper " The Thought: A Logical Inquiry " (1918) reflects both his anti-idealism or anti-psychologism and his interest in language. In the paper, he argues for a Platonist account of propositions or thoughts. British philosophy in the 19th century had seen a revival of logic started by Richard Whately , in reaction to the anti-logical tradition of British empiricism . The major figure of this period

192-448: A criticism of Russell's theory of descriptions explained in the latter's famous "On Denoting" article. In his book Individuals (1959), Strawson examines our conceptions of basic particulars . Austin, in the posthumously published How to Do Things with Words (1962), emphasized the theory of speech acts and the ability of words to do things (e. g. "I promise") and not just say things. This influenced several fields to undertake what

256-511: A method Russell thought could expose the underlying structure of philosophical problems. Logical form would be made clear by syntax . For example, the English word "is" has three distinct meanings, which predicate logic can express as follows: From about 1910 to 1930, analytic philosophers like Frege, Russell, Moore, and Russell's student Ludwig Wittgenstein emphasized creating an ideal language for philosophical analysis, which would be free from

320-528: A result of his logicist project, Frege developed predicate logic in his book Begriffsschrift (English: Concept-script , 1879), which allowed for a much greater range of sentences to be parsed into logical form than was possible using the ancient Aristotelian logic . An example of this is the problem of multiple generality . Neo-Kantianism dominated the late 19th century in German philosophy. Edmund Husserl's 1891 book Philosophie der Arithmetik argued that

384-453: A result, Nyaya scholars again went to great pains to identify, in each case, what it took to make knowledge valid, in the process creating a number of explanatory schemes. In this sense, Nyaya is probably the closest Indian equivalent to contemporary analytic philosophy . Jainism made its own unique contribution to this mainstream development of logic by also occupying itself with the basic epistemological issues, namely, with those concerning

448-544: A set of thorough criticisms of Nyāya theories of thought and language. In his book, Gangeśa both addressed some of those criticisms and – more importantly – critically examined the Nyāya darśana himself. He held that, while Śrīharśa had failed successfully to challenge the Nyāya realist ontology, his and Gangeśa's own criticisms brought out a need to improve and refine the logical and linguistic tools of Nyāya thought, to make them more rigorous and precise. Tattvacintāmani dealt with all

512-441: A theory of meaning as use . It also contains the private language argument and the notion of family resemblance . The other trend was known as " Oxford philosophy", in contrast to earlier analytic Cambridge philosophers (including the early Wittgenstein) who thought philosophers should avoid the deceptive trappings of natural language by constructing ideal languages. Influenced by Moore's Common Sense and what they perceived as

576-540: Is English mathematician George Boole . Other figures include William Hamilton , Augustus de Morgan , William Stanley Jevons , Alice's Adventures in Wonderland author Lewis Carroll , Hugh MacColl , and American pragmatist Charles Sanders Peirce . British philosophy in the late 19th century was dominated by British idealism , a neo-Hegelian movement, as taught by philosophers such as F. H. Bradley (1846–1924) and T. H. Green (1836–1882). Analytic philosophy in

640-565: Is a member; for if we had any such universal, then, by hypothesis, we have got a given totality of all universals that exist and all of them belong to this big universal. But this universal is itself a universal and hence (since it cannot be a member of itself, because in Udayana's view no universal can be a member of itself) this universal too along with other universals must belong to a bigger universal and so on ad infinitum. What Udayana says here has interesting analogues in modern set theory in which it

704-451: Is an analysis focused , broad, contemporary movement or tradition within Western philosophy , especially anglophone philosophy. Analytic philosophy is characterized by a clarity of prose ; rigor in arguments; and making use of formal logic and mathematics, and, to a lesser degree, the natural sciences . It is further characterized by an interest in language and meaning known as

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768-641: Is called a performative turn . In Sense and Sensibilia (1962), Austin criticized sense-data theories. The school known as Australian realism began when John Anderson accepted the Challis Chair of Philosophy at the University of Sydney in 1927. His elder brother was William Anderson, Professor of Philosophy at Auckland University College from 1921 to his death in 1955, who was described as "the most dominant figure in New Zealand philosophy." J. N. Findlay

832-628: Is held that a set of all sets (i.e., a set to which every set belongs) does not exist. In the late 18th-century British scholars began to take an interest in Indian philosophy and discovered the sophistication of the Indian study of inference. This process culminated in Henry T. Colebrooke's The Philosophy of the Hindus: On the Nyaya and Vaisesika Systems in 1824, which provided an analysis of inference and comparison to

896-428: Is mere appearance; we reverted to the opposite extreme, and that everything is real that common sense, uninfluenced by philosophy of theology, supposes real. With a sense of escaping from prison, we allowed ourselves to think that grass is green, that the sun and stars would exist if no one was aware of them, and also that there is a pluralistic timeless world of Platonic ideas." Bertrand Russell, during his early career,

960-411: Is the name for a largely comparable, but not equatable, 'four corner argument' within the tradition of Classical logic . Nyāya ( ni-āyá , literally "recursion", used in the sense of " syllogism , inference") is the name given to one of the six orthodox or astika schools of Hindu philosophy — specifically the school of logic. The Nyaya school of philosophical speculation is based on texts known as

1024-404: Is to be the value of a variable ". He also dubbed the problem of nonexistence Plato's beard . Quine sought to naturalize philosophy and saw philosophy as continuous with science, but instead of logical positivism advocated a kind of semantic holism and ontological relativity , which explained that every term in any statement has its meaning contingent on a vast network of knowledge and belief,

1088-439: Is widespread influence and debate between the analytic and continental traditions; some philosophers see the differences between the two traditions as being based on institutions, relationships, and ideology, rather than anything of significant philosophical substance. The distinction has also been drawn between "analytic" being academic or technical philosophy and "continental" being literary philosophy. Analytic philosophy

1152-540: The Nyaya Sutras , which were written by Gotama in around the 2nd century CE. The most important contribution made by the Nyaya school to modern Hindu thought is its methodology. This methodology is based on a system of logic that has subsequently been adopted by most of the other Indian schools (orthodox or not), much in the same way that Western philosophy can be said to be largely based on Aristotelian logic . Followers of Nyaya believed that obtaining valid knowledge

1216-452: The Rigveda ( RV 10 .129) contains ontological speculation in terms of various logical divisions that were later recast formally as the four circles of catuskoti : "A", "not A", "A and 'not A'", and "not A and not not A". Medhatithi Gautama (c. 6th century BCE) founded the anviksiki school of logic. The Mahabharata (12.173.45), around the 4th century BCE to 4th century CE, refers to

1280-596: The School of Brentano and its members, such as Edmund Husserl and Alexius Meinong —gave to analytic philosophy the problem of intentionality or of aboutness. For Brentano, all mental events have a real, non-mental intentional object, which the thinking is directed at or "about". Meinong is known for his unique ontology of real nonexistent objects as a solution to the problem of empty names . The Graz School followed Meinong. The Polish Lwów–Warsaw school , founded by Kazimierz Twardowski in 1895, grew as an offshoot of

1344-482: The Tractatus . The criticisms of Frank P. Ramsey on color and logical form in the Tractatus led to some of Wittgenstein's first doubts with regard to his early philosophy. Philosophers refer to them like two different philosophers: "early Wittgenstein" and "later Wittgenstein". In his later philosophy, Wittgenstein develops the concept of a " language-game " and, rather than his prior picture theory of meaning, advocates

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1408-468: The anviksiki and tarka schools of logic. Pāṇini (c. 5th century BCE) developed a form of logic (to which Boolean logic has some similarities) for his formulation of Sanskrit grammar . Logic is described by Chanakya (c. 350-283 BCE) in his Arthashastra as an independent field of inquiry anviksiki . Vaisheshika, also Vaisesika, (Sanskrit: वैशेषिक) is one of the six Hindu schools of Indian philosophy . It came to be closely associated with

1472-581: 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 Ludwig Wittgenstein . Other important figures in its history include Franz Brentano ,

1536-497: The logical positivists (particularly Rudolf Carnap ), the ordinary language philosophers , W. V. O. Quine , and Karl Popper . After the decline of logical positivism, Saul Kripke , David Lewis , and others led a revival in metaphysics . Analytic philosophy is often contrasted with continental philosophy , which was coined as a catch-all term for other methods that were prominent in continental Europe , most notably existentialism , phenomenology , and Hegelianism . There

1600-460: The verification principle , according to which every meaningful statement is either analytic or synthetic. The truths of logic and mathematics were tautologies , and those of science were verifiable empirical claims. These two constituted the entire universe of meaningful judgments; anything else was nonsense. This led the logical positivists to reject many traditional problems of philosophy, especially those of metaphysics , as meaningless. It had

1664-467: The "manifest image" and the "scientific image" of the world. Sellars's goal of a synoptic philosophy that unites the everyday and scientific views of reality is the foundation and archetype of what is sometimes called the Pittsburgh School, whose members include Robert Brandom , John McDowell , and John Haugeland . Also among the developments that resulted in the decline of logical positivism and

1728-450: The English speaking world to logical positivism. The logical positivists saw their rejection of metaphysics in some ways as a recapitulation of a quote by David Hume : If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to

1792-580: The Graz School. It was closely associated with the Warsaw School of Mathematics . Gottlob Frege (1848–1925) was a German geometry professor at the University of Jena who is understood as the father of analytic philosophy. Frege proved influential as a philosopher of mathematics in Germany at the beginning of the 20th century. He advocated logicism , the project of reducing arithmetic to pure logic. As

1856-641: The Greek view and followed a course which seems to have originated in India and which has been transmitted, with additions, to us by the Arabs; in it the concept of number appears as logically prior to the concepts of geometry. [...] But the present trend in mathematics is clearly in the direction of a return to the Greek standpoint; we now look upon each branch of mathematics as determining its own characteristic domain of quantities." Analytic philosophy Analytic philosophy

1920-539: The Hindu school of logic, Nyaya. Vaisheshika espouses a form of atomism and postulates that all objects in the physical universe are reducible to a finite number of atoms. Originally proposed by Kanāda (or Kana-bhuk, literally, atom-eater) from around the 2nd century BCE. In the 2nd century, the Buddhist philosopher Nagarjuna refined the Catuskoti form of logic. The Catuskoti is also often glossed Tetralemma (Greek) which

1984-523: The Navya-Nyaya theory of "restrictive conditions for universals" anticipating some of the developments in modern set theory . Udayana in particular developed theories on "restrictive conditions for universals" and " infinite regress" that anticipated aspects of modern set theory. According to Kisor Kumar Chakrabarti: In the third part we have shown how the study of the so-called 'restrictive conditions for universals' in Navya-Nyaya logic anticipated some of

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2048-626: The Nineteenth Century" written in 1901. De Morgan himself wrote in 1860 of the significance of Indian logic: "The two races which have founded the mathematics, those of the Sanskrit and Greek languages, have been the two which have independently formed systems of logic." Mathematicians became aware of the influence of Indian mathematics on the European. For example, Hermann Weyl wrote: "Occidental mathematics has in past centuries broken away from

2112-413: The Nyāya concepts into four main categories: sense or perception (pratyakşa), inference (anumāna), comparison or similarity ( upamāna ), and testimony (sound or word; śabda). This later school began around eastern India and Bengal , and developed theories resembling modern logic, such as Gottlob Frege 's "distinction between sense and reference of proper names" and his "definition of number," as well as

2176-544: The additional effect of making (ethical and aesthetic) value judgments (as well as religious statements and beliefs) meaningless. Logical positivists therefore typically considered philosophy as having a minimal function . For them, philosophy concerned the clarification of thoughts, rather than having a distinct subject matter of its own. Several logical positivists were Jewish, such as Neurath, Hans Hahn , Philipp Frank , Friedrich Waissmann , and Reichenbach. Others, like Carnap, were gentiles but socialists or pacifists. With

2240-412: The ambiguities of ordinary language that, in their opinion, often made philosophy invalid. During this phase, they sought to understand language (and hence philosophical problems) by using logic to formalize how philosophical statements are made. An important aspect of Hegelianism and British idealism was logical holism —the opinion that there are aspects of the world that can be known only by knowing

2304-492: The ancient Indian philosophy , especially in the areas of skepticism and relativity. Following is the list of Jain philosophers who contributed to Jain Logic: Indian Buddhist logic (called Pramana ) flourished from about 500 CE up to 1300 CE. The three main authors of Buddhist logic are Vasubandhu (400–800 CE), Dignāga (480–540 CE), and Dharmakīrti (600–660 CE). The most important theoretical achievements are

2368-565: The coming to power of Adolf Hitler and Nazism in 1933, many members of the Vienna and Berlin Circles fled to Britain and the United States, which helped to reinforce the dominance of logical positivism and analytic philosophy in anglophone countries. In 1936, Schlick was murdered in Vienna by his former student Hans Nelböck . The same year, A. J. Ayer 's work Language Truth and Logic introduced

2432-553: The concept of the cardinal number derived from psychical acts of grouping objects and counting them. In contrast to this " psychologism ", Frege in The Foundations of Arithmetic (1884) and The Basic Laws of Arithmetic (German: Grundgesetze der Arithmetik , 1893–1903), argued similarly to Plato or Bolzano that mathematics and logic have their own public objects, independent of the private judgments or mental states of individual mathematicians and logicians. Following Frege,

2496-625: The debates remains active. The rise of metaphysics mirrored the decline of logical positivism, first challenged by the later Wittgenstein. Wilfred Sellars 's criticism of the "Myth of the Given", in Empiricism and the Philosophy of Mind (1956), challenged logical positivism by arguing against sense-data theories. In his "Philosophy and the Scientific Image of Man" (1962), Sellars distinguishes between

2560-501: The developments of modern set theory. [...] In this section the discussion will center around some of the 'restrictive conditions for universals ( jatibadhaka ) proposed by Udayana. [...] Another restrictive condition is anavastha or vicious infinite regress. According to this restrictive condition, no universal ( jati ) can be admitted to exist, the admission of which would lead to a vicious infinite regress. As an example Udayana says that there can be no universal of which every universal

2624-526: The doctrine of Trairūpya (Skrt. त्रैरूप्य) and the highly formal scheme of the Hetucakra (Skrt. हेतुचक्र) ("Wheel of Reasons") given by Dignāga . There is still a vibrant living tradition of Buddhist logic in the Tibetan Buddhist traditions, where logic is an important part of the education of monks. The Navya-Nyāya or Neo-Logical darśana (school) of Indian philosophy was founded in the 13th century CE by

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2688-504: The early Russell claimed that the problems of philosophy can be solved by showing the simple constituents of complex notions. Wittgenstein developed a comprehensive system of logical atomism with a picture theory of meaning in his Tractatus Logico-Philosophicus ( German : Logisch-Philosophische Abhandlung , 1921) sometimes known as simply the Tractatus . He claimed the universe is the totality of actual states of affairs and that these states of affairs can be expressed and mirrored by

2752-474: The flames: for it can contain nothing but sophistry and illusion. After World War II , from the late 1940s to the 1950s, analytic philosophy became involved with ordinary-language analysis. This resulted in two main trends. One strain of language analysis continued Wittgenstein's later philosophy, from the Philosophical Investigations (1953), which differed dramatically from his early work of

2816-671: The formulation of logic (such as algebraic logic and Boolean logic ), and has suggested that these figures were likely to be aware of these studies in xeno-logic, and further that their acquired awareness of the shortcomings of propositional logic are likely to have stimulated their willingness to look outside the system. Indian logic attracted the attention of many Western scholars, and had an influence on pioneering 19th-century logicians such as Charles Babbage (1791-1871), Augustus De Morgan , and particularly George Boole , as confirmed by Boole's wife Mary Everest Boole in an "open letter to Dr Bose" titled "Indian Thought and Western Science in

2880-587: The fourfold negation, as evidenced by the traditions of Nagarjuna and the Madhyamaka , particularly the school of Madhyamaka given the retroactive nomenclature of Prasangika by the Tibetan Buddhist logico-epistemological tradition. Though tetralemma was also used as a form inquiry rather than logic in the Nasadiya Sukta of Rigveda (creation hymn) though seems to be rarely used as a tool of logic before Buddhism. Indian logic Indian logic stands as one of

2944-461: The important aspects of Indian philosophy, logic, set theory , and especially epistemology , which Gangeśa examined rigorously, developing and improving the Nyāya scheme, and offering examples. The results, especially his analysis of cognition, were taken up and used by other darśanas. Navya-Nyāya developed a sophisticated language and conceptual scheme that allowed it to raise, analyse, and solve problems in logic and epistemology. It systematised all

3008-447: The language of first-order predicate logic. Thus a picture of the universe can be constructed by expressing facts in the form of atomic propositions and linking them using logical operators . Wittgenstein thought he had solved all the problems of philosophy with the Tractatus . The work further ultimately concludes that all of its propositions are meaningless, illustrated with a ladder one must toss away after climbing up it. During

3072-722: The late 1920s to 1940s, a group of philosophers known as the Vienna Circle , and another one known as the Berlin Circle , developed Russell and Wittgenstein's philosophy into a doctrine known as " logical positivism " (or logical empiricism). The Vienna Circle was led by Moritz Schlick and included Rudolf Carnap and Otto Neurath . The Berlin Circle was led by Hans Reichenbach and included Carl Hempel and mathematician David Hilbert . Logical positivists used formal logical methods to develop an empiricist account of knowledge. They adopted

3136-501: The later Wittgenstein's quietism , the Oxford philosophers claimed that ordinary language already represents many subtle distinctions not recognized in the formulation of traditional philosophical theories or problems. While schools such as logical positivism emphasize logical terms, which are supposed to be universal and separate from contingent factors (such as culture, language, historical conditions), ordinary-language philosophy emphasizes

3200-403: The logicists tended to advocate a kind of mathematical Platonism . Frege also proved influential in the philosophy of language and analytic philosophy's interest in meaning . Michael Dummett traces the linguistic turn to Frege's Foundations of Arithmetic and his context principle . Frege's paper " On Sense and Reference " (1892) is seminal, containing Frege's puzzles and providing

3264-483: The narrower sense of 20th and 21st century anglophone philosophy is usually thought to begin with Cambridge philosophers Bertrand Russell and G. E. Moore's rejection of Hegelianism for being obscure; or the "revolt against idealism"—see for example Moore's " A Defence of Common Sense ". Russell summed up Moore's influence: "G. E. Moore...took the lead in rebellion, and I followed, with a sense of emancipation. Bradley had argued that everything common sense believes in

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3328-687: The nature of knowledge, how knowledge is derived, and in what way knowledge can be said to be reliable. Jain logic developed and flourished from 6th century BCE to 17th century CE. According to Jains, the ultimate principle should always be logical and no principle can be devoid of logic or reason. Thus one finds in the Jain texts , deliberative exhortations on any subject in all its facts, may they be constructive or obstructive, inferential or analytical, enlightening or destructive. The Jains have doctrines of relativity used for logic and reasoning: These Jain philosophical concepts made most important contributions to

3392-418: The philosopher Gangesha Upadhyaya of Mithila . It was a development of the classical Nyāya darśana. Other influences on Navya-Nyāya were the work of earlier philosophers Vācaspati Miśra (900–980 CE) and Udayana (late 10th century). Gangeśa's book Tattvacintāmaṇi ("Thought-Jewel of Reality") was written partly in response to Śrīharśa's Khandanakhandakhādya, a defence of Advaita Vedānta, which had offered

3456-742: The received Aristotelian logic , resulting in the observation that the Aristotelian syllogism could not account for the Indian syllogism. Max Mueller contributed an appendix to the 1853 edition of Thomson 's Outline of the Laws of Thought , in which he placed Greek and Indian logic on the same plane: "The sciences of Logic and Grammar were, as far as history allows us to judge, invented or originally conceived by two nations only, by Hindus and Greeks." Jonardon Ganeri has observed that this period saw George Boole (1815-1864) and Augustus De Morgan (1806-1871) make their pioneering applications of algebraic ideas to

3520-704: The revival of metaphysical theorizing was Harvard philosopher W. V. O. Quine 's attack on the analytic–synthetic distinction in " Two Dogmas of Empiricism ", published in 1951 in The Philosophical Review and republished in Quine's book From A Logical Point of View (1953), a paper "sometimes regarded as the most important in all of twentieth-century philosophy ". From a Logical Point of View also contains Quine's essay " On What There Is " (1948), which elucidates Russell's theory of descriptions and contains Quine's famous dictum of ontological commitment , "To be

3584-508: The seminal text of classical logic and of the logicist project, encouraged many philosophers to renew their interest in the development of symbolic logic . It used a notation from Italian logician Giuseppe Peano , and it uses a theory of types to avoid the pitfalls of Russell's paradox. Whitehead developed process metaphysics in Process and Reality . Additionally, Russell adopted Frege's predicate logic as his primary philosophical method,

3648-425: The speaker's conception of the entire world. In his magnum opus Word and Object (1960), Quine introduces the idea of radical translation , an introduction to his theory of the indeterminacy of translation , and specifically to prove the inscrutability of reference . Important also for the revival of metaphysics was the further development of modal logic , first introduced by pragmatist C. I. Lewis , especially

3712-592: The three original traditions of logic , alongside the Greek and the Chinese logic . The Indian tradition continued to develop through early to modern times, in the form of the Navya-Nyāya school of logic. Who really knows? Who will here proclaim it? Whence was it produced? Whence is this creation? The gods came afterwards, with the creation of this universe. Who then knows whence it has arisen? The Nasadiya Sukta of

3776-608: The use of language by ordinary people. The most prominent ordinary-language philosophers during the 1950s were P. F. Strawson , J. L. Austin , and Gilbert Ryle . Ordinary-language philosophers often sought to resolve philosophical problems by showing them to be the result of misunderstanding ordinary language. Ryle, in The Concept of Mind (1949), criticized Cartesian dualism , arguing in favor of disposing of " Descartes' myth " via recognizing " category errors ". Strawson first became well known with his article "On Referring" (1950),

3840-427: The whole world. This is closely related to the doctrine of internal relations , the opinion that relations between items are internal relations , that is, essential properties of the nature of those items. Russell and Moore in response promulgated logical atomism and the doctrine of external relations —the belief that the world consists of independent facts. Inspired by developments in modern formal logic ,

3904-534: Was a student of Ernst Mally of the Austrian realists and taught at the University of Otago . The Finnish Georg Henrik von Wright succeeded Wittgenstein at Cambridge in 1948. One striking difference with respect to early analytic philosophy was the revival of metaphysical theorizing during the second half of the 20th century, and metaphysics remains a fertile topic of research. Although many discussions are continuations of old ones from previous decades and centuries,

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3968-467: Was deeply influenced by what is called Austrian realism in the former state of Austria-Hungary , so much so that Michael Dummett has remarked that analytic philosophy is better characterized as Anglo-Austrian rather than the usual Anglo-American. University of Vienna philosopher and psychologist Franz Brentano —in Psychology from an Empirical Standpoint (1874) and through the subsequent influence of

4032-1012: Was much influenced by Frege. Russell famously discovered the paradox in Basic Law V which undermined Frege's logicist project. However, like Frege, Russell argued that mathematics is reducible to logical fundamentals, in The Principles of Mathematics (1903). He also argued for Meinongianism . Russell sought to resolve various philosophical problems by applying Frege's new logical apparatus, most famously in his theory of definite descriptions in " On Denoting ", published in Mind in 1905. Russell here argues against Meinongianism. He argues all names (aside from demonstratives like "this" or "that") are disguised definite descriptions, using this to solve ascriptions of nonexistence. This position came to be called descriptivism . Later, his book written with Alfred North Whitehead , Principia Mathematica (1910–1913),

4096-402: Was the only way to obtain release from suffering. They therefore took great pains to identify valid sources of knowledge and to distinguish these from mere false opinions. According to the Nyaya school, there are exactly four sources of knowledge (pramanas): perception, inference, comparison and testimony. Knowledge obtained through each of these can, of course, still be either valid or invalid. As

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