1.
Ludwig Wittgenstein
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Ludwig Josef Johann Wittgenstein was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. From 1929 to 1947, Wittgenstein taught at the University of Cambridge, during his lifetime he published just one slim book, the 75-page Tractatus Logico-Philosophicus, one article, one book review and a childrens dictionary. His voluminous manuscripts were edited and published posthumously, Philosophical Investigations appeared as a book in 1953, and has since come to be recognised as one of the most important works of philosophy in the twentieth century. His teacher Bertrand Russell described Wittgenstein as the most perfect example I have ever known of genius as traditionally conceived, passionate, profound, intense, born in Vienna into one of Europes richest families, he inherited a large fortune from his father in 1913. Three of his brothers committed suicide, with Wittgenstein contemplating it too and he described philosophy as the only work that gives me real satisfaction. His philosophy is divided into an early period, exemplified by the Tractatus. The later Wittgenstein rejected many of the assumptions of the Tractatus, ludwigs grandmother Fanny was a first cousin of the famous violinist Joseph Joachim. They had 11 children—among them Wittgensteins father, Karl Otto Clemens Wittgenstein became an industrial tycoon, and by the late 1880s was one of the richest men in Europe, with an effective monopoly on Austrias steel cartel. Thanks to Karl, the Wittgensteins became the second wealthiest family in Austria-Hungary, however, their wealth diminished due to post-1918 hyperinflation and subsequently during the Great Depression, although even as late as 1938 they owned 13 mansions in Vienna alone. Wittgensteins mother was Leopoldine Maria Josefa Kalmus, known among friends as Poldi and her father was a Bohemian Jew and her mother was Austrian-Slovene Catholic—she was Wittgensteins only non-Jewish grandparent. She was an aunt of the Nobel Prize laureate Friedrich Hayek on her maternal side, Wittgenstein was born at 8,30 pm on 26 April 1889 in the so-called Wittgenstein Palace at Alleegasse 16, now the Argentinierstrasse, near the Karlskirche. Karl and Poldi had nine children in all, the children were baptized as Catholics, received formal Catholic instruction, and raised in an exceptionally intense environment. The family was at the center of Viennas cultural life, Bruno Walter described the life at the Wittgensteins palace as an atmosphere of humanity. Karl was a patron of the arts, commissioning works by Auguste Rodin and financing the citys exhibition hall and art gallery. Gustav Klimt painted Wittgensteins sister for her portrait, and Johannes Brahms. For Wittgenstein, who highly valued precision and discipline, contemporary music was never considered acceptable at all, music, he said to his friend Drury in 1930, came to a full stop with Brahms, and even in Brahms I can begin to hear the noise of machinery. He also learnt to play the clarinet in his thirties, a fragment of music, composed by Wittgenstein, was discovered in one of his 1931 notebooks, by Michael Nedo, Director of the Wittgenstein Institute in Cambridge. Three of the five brothers would commit suicide
2.
Frank P. Ramsey
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Frank Plumpton Ramsey was a British philosopher, mathematician and economist who died at the age of 26. Like Wittgenstein, he was a member of the Cambridge Apostles, Ramsey was born on 22 February 1903 in Cambridge where his father Arthur Stanley Ramsey, also a mathematician, was President of Magdalene College. His mother was Mary Agnes Stanley and he was the eldest of two brothers and two sisters, and his brother Michael Ramsey, the only one of the four siblings who was to remain Christian, later became Archbishop of Canterbury. He entered Winchester College in 1915 and later returned to Cambridge to study mathematics at Trinity College, while studying mathematics at Trinity College, Ramsey became a student to John Maynard Keynes, and an active member in the Apostles, a Cambridge discussion group. In 1923, he received his bachelors degree in mathematics, passing his examinations with the result of first class with distinction, easy-going, simple and modest, Ramsey had many interests besides his scientific work. After about an hour I said ‘Margaret will you fuck with me and he, like many of his contemporaries, including his Viennese flatmate and fellow Apostle Lionel Penrose, was intellectually interested in psychoanalysis. Ramseys analyst was Theodor Reik, a disciple of Freud, as one of the justifications for undertaking the therapy, he asserted in a letter to his mother that unconscious impulses might even affect the work of a mathematician. While in Vienna, he visited Wittgenstein in Puchberg, was befriended by the Wittgenstein family, neills experimental school four hours from Vienna at Sonntagsberg. In the summer of 1924, he continued his analysis by joining Reik at Dobbiaco, Ramsey returned to England in October 1924, with John Maynard Keyness support he became a fellow of Kings College, Cambridge. Ramsey married Lettice Baker in September 1925, the taking place in a Register Office since Ramsey was, as his wife described him. Despite his atheism, Ramsey was quite tolerant towards his brother when the decided to become a priest in the Church of England. In 1926 he became a university lecturer in mathematics and later a Director of Studies in Mathematics at Kings College, the Vienna Circle manifesto lists three of his publications in a bibliography of closely related authors. When I. A. Richards and C. K. Ogden, according to Richards, he mastered the language in almost hardly over a week, although other sources show he took before that one year of German in school. Ramsey was then able, at the age of 19, to make the first draft of the translation of the German text of Wittgensteins Tractatus Logico Philosophicus, for two weeks Ramsey discussed the difficulties he was facing in understanding the Tractatus. Wittgenstein made some corrections to the English translation in Ramseys copy and some annotations, Ramsey and John Maynard Keynes cooperated to try to bring Ludwig Wittgenstein back to Cambridge. Once Wittgenstein had returned to Cambridge, Ramsey became his nominal supervisor, Wittgenstein submitted the Tractatus Logico-Philosophicus as his doctoral thesis. G. E. Moore and Bertrand Russell acted as examiners, later, the three of them arranged financial aid for Wittgenstein to help him continue his research work. The contributions of Ramsey to these conversations were acknowledged by both Sraffa and Wittgenstein in their later work, suffering from chronic liver problems, Ramsey developed jaundice after an abdominal operation and died on 19 January 1930 at Guys Hospital in London at the age of 26
3.
Charles Kay Ogden
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Charles Kay Ogden was an English linguist, philosopher, and writer. He is typically defined as a linguistic psychologist, and is now remembered as the inventor and propagator of Basic English. Charles Kay Ogden was born at Rossall School in Fleetwood, Lancashire on 1 June 1889 to Charles Burdett Ogden and Fanny Hart, Charles Burdett Ogden was employed at the Rossall School during the years 1873-1909. His son Charles Kay Ogden was educated at Buxton and Rossall, winning a scholarship to Magdalene College, Cambridge and he visited continental Europe to investigate methods of language teaching in 1912 and 1913. Ogden obtained an M. A. in 1915 and he founded the weekly Cambridge Magazine in 1912 while still an undergraduate, editing it until it ceased publication in 1922. Ogden was studying for Part II of the Classical Tripos when offered the chance to start the magazine by Charles Granville, thinking that the editorship would mean giving up first class honours, Ogden consulted Henry Jackson, who advised him not to miss the opportunity. Shortly after, Stephen Swift & Co. went bankrupt, Ogden continued to edit the magazine during World War I, when its nature changed, because rheumatic fever as a teenager had left him unfit for military service. Ogden often used the pseudonym Adelyne More in his journalism, the magazine included literary contributions by Siegfried Sassoon, John Masefield, Thomas Hardy, George Bernard Shaw, and Arnold Bennett. In 1919 Claude McKay was in London, and Ogden published his poetry in the Magazine, Buxton was in fact then leading a large team translating and collating articles from up to 100 foreign newspapers, for instance Italian articles were supplied in translation in numbers by Dent. This digest of European press coverage was exclusive to the Magazine, for example, Robert Reid, 1st Earl Loreburn used the Notes from the foreign press to advocate to the Marquess of Lansdowne in 1916 against bellicose claims and attitudes on the British side. Dorothy Buxtons husband Charles Roden Buxton was closely associated with the Union of Democratic Control, gilbert Murray, a supporter of Fight for Right but also a defender of many conscientious objectors and the freedom of the press, intervened to protest, gaining support from Bennett and Hardy. John George Butcher, Conservative Member of Parliament for the City of York, asked a question in Parliament about government advertising in the Magazine, during November 1917. The parliamentary exchange had two Liberal Party politicians, William Pringle and Josiah Wedgwood, pointing out that the Magazine was the way they could read German press comments. The Cambridge Magazine continued in the years, but wound down to quarterly publication before closing down in 1922. The Heretics began as a group of 12 undergraduates interested in Chawners agnostic approach, the talk of the following day was from J. M. E. McTaggart, and was also published, as Dare to Be Wise. Another early member with anthropological interests was John Layard, Herbert Felix Jolowicz, Frank Plumpton Ramsey, alix Sargant Florence, sister of Philip, was active both as a Heretic and on the editorial board of the Cambridge Magazine. Ogden was President of the Heretics from 1911, for more than a decade, he invited a variety of prominent speakers and linked the Society to his role as editor. In November 1911 G. K. Chesterton used a talk to the Heretics to reply to George Bernard Shaw who had recently talked on The Future of Religion
4.
Logic
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Logic, originally meaning the word or what is spoken, is generally held to consist of the systematic study of the form of arguments. A valid argument is one where there is a relation of logical support between the assumptions of the argument and its conclusion. Historically, logic has been studied in philosophy and mathematics, and recently logic has been studied in science, linguistics, psychology. The concept of form is central to logic. The validity of an argument is determined by its logical form, traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic. Informal logic is the study of natural language arguments, the study of fallacies is an important branch of informal logic. Since much informal argument is not strictly speaking deductive, on some conceptions of logic, formal logic is the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as an application of a wholly abstract rule, that is. The works of Aristotle contain the earliest known study of logic. Modern formal logic follows and expands on Aristotle, in many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language, Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference. Symbolic logic is divided into two main branches, propositional logic and predicate logic. Mathematical logic is an extension of logic into other areas, in particular to the study of model theory, proof theory, set theory. Logic is generally considered formal when it analyzes and represents the form of any valid argument type, the form of an argument is displayed by representing its sentences in the formal grammar and symbolism of a logical language to make its content usable in formal inference. Simply put, formalising simply means translating English sentences into the language of logic and this is called showing the logical form of the argument. It is necessary because indicative sentences of ordinary language show a variety of form. Second, certain parts of the sentence must be replaced with schematic letters, thus, for example, the expression all Ps are Qs shows the logical form common to the sentences all men are mortals, all cats are carnivores, all Greeks are philosophers, and so on. The schema can further be condensed into the formula A, where the letter A indicates the judgement all - are -, the importance of form was recognised from ancient times
5.
Latin
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Latin is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets, Latin was originally spoken in Latium, in the Italian Peninsula. Through the power of the Roman Republic, it became the dominant language, Vulgar Latin developed into the Romance languages, such as Italian, Portuguese, Spanish, French, and Romanian. Latin, Italian and French have contributed many words to the English language, Latin and Ancient Greek roots are used in theology, biology, and medicine. By the late Roman Republic, Old Latin had been standardised into Classical Latin, Vulgar Latin was the colloquial form spoken during the same time and attested in inscriptions and the works of comic playwrights like Plautus and Terence. Late Latin is the language from the 3rd century. Later, Early Modern Latin and Modern Latin evolved, Latin was used as the language of international communication, scholarship, and science until well into the 18th century, when it began to be supplanted by vernaculars. Ecclesiastical Latin remains the language of the Holy See and the Roman Rite of the Catholic Church. Today, many students, scholars and members of the Catholic clergy speak Latin fluently and it is taught in primary, secondary and postsecondary educational institutions around the world. The language has been passed down through various forms, some inscriptions have been published in an internationally agreed, monumental, multivolume series, the Corpus Inscriptionum Latinarum. Authors and publishers vary, but the format is about the same, volumes detailing inscriptions with a critical apparatus stating the provenance, the reading and interpretation of these inscriptions is the subject matter of the field of epigraphy. The works of several hundred ancient authors who wrote in Latin have survived in whole or in part and they are in part the subject matter of the field of classics. The Cat in the Hat, and a book of fairy tales, additional resources include phrasebooks and resources for rendering everyday phrases and concepts into Latin, such as Meissners Latin Phrasebook. The Latin influence in English has been significant at all stages of its insular development. From the 16th to the 18th centuries, English writers cobbled together huge numbers of new words from Latin and Greek words, dubbed inkhorn terms, as if they had spilled from a pot of ink. Many of these words were used once by the author and then forgotten, many of the most common polysyllabic English words are of Latin origin through the medium of Old French. Romance words make respectively 59%, 20% and 14% of English, German and those figures can rise dramatically when only non-compound and non-derived words are included. Accordingly, Romance words make roughly 35% of the vocabulary of Dutch, Roman engineering had the same effect on scientific terminology as a whole
6.
Philosopher
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A philosopher is someone who practices philosophy, which involves rational inquiry into areas that are outside of either theology or science. The term philosopher comes from the Ancient Greek φιλόσοφος meaning lover of wisdom, the coining of the term has been attributed to the Greek thinker Pythagoras. Typically, these brands of philosophy are Hellenistic ones and those who most arduously commit themselves to this lifestyle may be considered philosophers. The separation of philosophy and science from theology began in Greece during the 6th century BC, thales, an astronomer and mathematician, was considered by Aristotle to be the first philosopher of the Greek tradition. While Pythagoras coined the word, the first known elaboration on the topic was conducted by Plato, in his Symposium, he concludes that Love is that which lacks the object it seeks. Therefore, the philosopher is one who seeks wisdom, if he attains wisdom, therefore, the philosopher in antiquity was one who lives in the constant pursuit of wisdom, and living in accordance to that wisdom. Disagreements arose as to what living philosophically entailed and these disagreements gave rise to different Hellenistic schools of philosophy. In consequence, the ancient philosopher thought in a tradition, as the ancient world became schism by philosophical debate, the competition lay in living in manner that would transform his whole way of living in the world. Philosophy is a discipline which can easily carry away the individual in analyzing the universe. The second is the change through the Medieval era. With the rise of Christianity, the way of life was adopted by its theology. Thus, philosophy was divided between a way of life and the conceptual, logical, physical and metaphysical materials to justify that way of life, philosophy was then the servant to theology. The third is the sociological need with the development of the university, the modern university requires professionals to teach. Maintaining itself requires teaching future professionals to replace the current faculty, therefore, the discipline degrades into a technical language reserved for specialists, completely eschewing its original conception as a way of life. In the fourth century, the word began to designate a man or woman who led a monastic life. Gregory of Nyssa, for example, describes how his sister Macrina persuaded their mother to forsake the distractions of life for a life of philosophy. Later during the Middle Ages, persons who engaged with alchemy was called a philosopher - thus, many philosophers still emerged from the Classical tradition, as saw their philosophy as a way of life. Among the most notable are René Descartes, Baruch Spinoza, Nicolas Malebranche, with the rise of the university, the modern conception of philosophy became more prominent
7.
G. E. Moore
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George Edward G. E. Moore OM FBA was an English philosopher. He was, with Bertrand Russell, Ludwig Wittgenstein, and Gottlob Frege and he was Professor of Philosophy at the University of Cambridge, highly influential among the Bloomsbury Group, and the editor of the influential journal Mind. He was elected a fellow of the British Academy in 1918 and he was a member of the Cambridge Apostles, the intellectual secret society, from 1894 to 1901, and the Cambridge University Moral Sciences Club. Moore was born in Upper Norwood, Croydon, Greater London, on 4 November 1873 and his grandfather was the author Dr George Moore. His eldest brother was Thomas Sturge Moore, a poet, writer and engraver and he was educated at Dulwich College and in 1892 went up to Trinity College Cambridge to study classics for moral sciences. He became a Fellow of Trinity in 1898, and went on to hold the University of Cambridge chair of Mental Philosophy and Logic, from 1925 to 1939. Moore is best known today for his defence of ethical non-naturalism, his emphasis on common sense in philosophical method, and he was admired by and influential among other philosophers, and also by the Bloomsbury Group, but is mostly unknown today outside of academic philosophy. Moores essays are known for their clear, circumspect writing style and he was critical of modern philosophy for its lack of progress, which he believed was in stark contrast to the dramatic advances in the natural sciences since the Renaissance. Among Moores most famous works are his book Principia Ethica, and his essays, The Refutation of Idealism, A Defence of Common Sense and he was president of the Aristotelian Society from 1918-19. Paul Levy wrote in Moore, G. E. Moore, together they had two sons, the poet Nicholas Moore and the composer Timothy Moore. His influential work Principia Ethica is one of the inspirations of the movement against ethical naturalism and is partly responsible for the twentieth-century concern with meta-ethics. Moore asserted that philosophical arguments can suffer from a confusion between the use of a term in an argument and the definition of that term. He named this confusion the naturalistic fallacy, for example, an ethical argument may claim that if a thing has certain properties, then that thing is good. A hedonist may argue that pleasant things are good things, other theorists may argue that complex things are good things. Moore contends that if such arguments are correct, they do not provide definitions for the term good. The property of goodness cannot be defined and it can only be shown and grasped. Any attempt to define it will shift the problem. Moores argument for the indefinability of good is called the open-question argument
8.
Tractatus Theologico-Politicus
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Written by the Dutch philosopher Baruch Spinoza, the Tractatus Theologico-Politicus or Theologico-Political Treatise was one of the most controversial texts of the early modern period. It was a defense of Spinozas later work, Ethics, published posthumously in 1677. The treatise was published anonymously in 1670 by Jan Rieuwertsz in Amsterdam, in order to protect the author and publisher from political retribution, the title page identified the city of publication as Hamburg and the publisher as Henricus Kunraht. It was written in New Latin rather than the vernacular Dutch in an attempt to censorship by the secular Dutch authorities. In the treatise, Spinoza put forth his most systematic critique of Judaism, Spinoza argued that theology and philosophy must be kept separate, particularly in the reading of scripture. Whereas the goal of theology is obedience, philosophy aims at understanding rational truth, scripture does not teach philosophy and thus cannot be made to conform with it, otherwise the meaning of scripture will be distorted. Conversely, if reason is made subservient to scripture, then, Spinoza argues, will gain a hold on his understanding and darken it. He reinterpreted the belief there were such things as prophecy, miracles. He argued that God acts solely by the laws of his own nature. He rejected the view that God had an end game or purpose to advance in the course of events, to Spinoza. Spinoza was not only the father of modern metaphysics and moral and political philosophy. He was particularly attuned to the idea of interpretation, he felt that all organized religion was simply the defense of particular interpretations. He rejected in its entirety the view that Moses composed the first five books of the Bible, to achieve his object, Spinoza had to show what is meant by a proper understanding of the Bible. And this gave him occasion to apply criticism to the Bible, to appreciate his services in this connection it must be remembered that his age was remarkably lacking in historical sense, especially in matters relating to religion. Nevertheless, many have adopted his views, agreeing with him that the real word of God, or true religion, is not something written in books but inscribed on the heart. The treatise also rejected the Jewish notion of chosenness, to Spinoza, all peoples are on par with each other, Spinoza also offered a sociological explanation as to how the Jewish people had managed to survive for so long, despite facing relentless persecution. In his view, the Jews had been preserved due to a combination of Gentile hatred and he also gave one final, crucial reason for the continued Jewish presence, which in his view, was by itself sufficient to maintain the survival of the nation forever, circumcision. It was the ultimate expression of bodily marking, a tangible symbol of separateness which was the ultimate identifier
9.
Baruch Spinoza
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Baruch Spinoza was a Dutch philosopher of Sephardi/Portuguese origin. Spinozas magnum opus, Ethics, was published posthumously in 1677, the work opposed René Descartes philosophy on mind–body dualism, and earned Spinoza recognition as one of Western philosophys most important thinkers. In the Ethics, Spinoza wrote the last indisputable Latin masterpiece, hegel said, You are either a Spinozist or not a philosopher at all. His philosophical accomplishments and moral character prompted 20th-century philosopher Gilles Deleuze to name him the prince of philosophers, Spinozas given name, which means Blessed, varies among different languages. In Hebrew, it is written ברוך שפינוזה, in Portuguese, hes called Benedito Bento de Espinosa and in Latin, Benedictus de Spinoza. Spinoza was raised in a Portuguese Jewish community in Amsterdam and he developed highly controversial ideas regarding the authenticity of the Hebrew Bible and the nature of the Divine. Jewish religious authorities issued a herem against him, causing him to be shunned by Jewish society at age 23. His books were later put on the Catholic Churchs Index of Forbidden Books. Spinoza lived a simple life as a lens grinder, turning down rewards and honours throughout his life. He died at the age of 44 allegedly of a lung illness and he is buried in the churchyard of the Christian Nieuwe Kerk in The Hague. The Spinoza family probably had its origins in Espinosa de los Monteros, near Burgos, or in Espinosa de Cerrato, near Palencia, the family was expelled from Spain in 1492 and fled to Portugal. Portugal compelled them to convert to Catholicism in 1498, attracted by the Decree of Toleration issued in 1579 by the Union of Utrecht, Portuguese conversos first sailed to Amsterdam in 1593 and promptly reconverted to Judaism. In 1598 permission was granted to build a synagogue, and in 1615 an ordinance for the admission, as a community of exiles, the Portuguese Jews of Amsterdam were highly proud of their identity. Spinozas father was born roughly a century after this conversion in the small Portuguese city of Vidigueira. When Spinozas father was still a child, Spinozas grandfather, Isaac de Spinoza and they were expelled in 1615 and moved to Rotterdam, where Isaac died in 1627. Spinozas father, Miguel, and his uncle, Manuel, then moved to Amsterdam where they resumed the practice of Judaism, Miguel was a successful merchant and became a warden of the synagogue and of the Amsterdam Jewish school. He buried three wives and three of his six children died before reaching adulthood, Amsterdam and Rotterdam operated as important cosmopolitan centres where merchant ships from many parts of the world brought people of various customs and beliefs. This flourishing commercial activity encouraged a relatively tolerant of the play of new ideas
10.
World War I
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World War I, also known as the First World War, the Great War, or the War to End All Wars, was a global war originating in Europe that lasted from 28 July 1914 to 11 November 1918. More than 70 million military personnel, including 60 million Europeans, were mobilised in one of the largest wars in history and it was one of the deadliest conflicts in history, and paved the way for major political changes, including revolutions in many of the nations involved. The war drew in all the worlds great powers, assembled in two opposing alliances, the Allies versus the Central Powers of Germany and Austria-Hungary. These alliances were reorganised and expanded as more nations entered the war, Italy, Japan, the trigger for the war was the assassination of Archduke Franz Ferdinand of Austria, heir to the throne of Austria-Hungary, by Yugoslav nationalist Gavrilo Princip in Sarajevo on 28 June 1914. This set off a crisis when Austria-Hungary delivered an ultimatum to the Kingdom of Serbia. Within weeks, the powers were at war and the conflict soon spread around the world. On 25 July Russia began mobilisation and on 28 July, the Austro-Hungarians declared war on Serbia, Germany presented an ultimatum to Russia to demobilise, and when this was refused, declared war on Russia on 1 August. Germany then invaded neutral Belgium and Luxembourg before moving towards France, after the German march on Paris was halted, what became known as the Western Front settled into a battle of attrition, with a trench line that changed little until 1917. On the Eastern Front, the Russian army was successful against the Austro-Hungarians, in November 1914, the Ottoman Empire joined the Central Powers, opening fronts in the Caucasus, Mesopotamia and the Sinai. In 1915, Italy joined the Allies and Bulgaria joined the Central Powers, Romania joined the Allies in 1916, after a stunning German offensive along the Western Front in the spring of 1918, the Allies rallied and drove back the Germans in a series of successful offensives. By the end of the war or soon after, the German Empire, Russian Empire, Austro-Hungarian Empire, national borders were redrawn, with several independent nations restored or created, and Germanys colonies were parceled out among the victors. During the Paris Peace Conference of 1919, the Big Four imposed their terms in a series of treaties, the League of Nations was formed with the aim of preventing any repetition of such a conflict. This effort failed, and economic depression, renewed nationalism, weakened successor states, and feelings of humiliation eventually contributed to World War II. From the time of its start until the approach of World War II, at the time, it was also sometimes called the war to end war or the war to end all wars due to its then-unparalleled scale and devastation. In Canada, Macleans magazine in October 1914 wrote, Some wars name themselves, during the interwar period, the war was most often called the World War and the Great War in English-speaking countries. Will become the first world war in the sense of the word. These began in 1815, with the Holy Alliance between Prussia, Russia, and Austria, when Germany was united in 1871, Prussia became part of the new German nation. Soon after, in October 1873, German Chancellor Otto von Bismarck negotiated the League of the Three Emperors between the monarchs of Austria-Hungary, Russia and Germany
11.
Vienna Circle
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In 2015, as part of its 650th anniversary, the University of Vienna organized an exhibition on the Vienna Circle. Ludwig Wittgenstein and Karl Popper were in contact to the Vienna Circle. The philosophical position of the Vienna Circle was called Logical Empiricism and it was influenced by Ernst Mach, David Hilbert, French Conventionalism, Gottlob Frege, Bertrand Russell, Ludwig Wittgenstein and Albert Einstein. The Vienna Circle was pluralistic and committed to the ideals of Enlightenment and it was unified by the aim of making philosophy scientific with the help of modern logic. Its public profile was provided by the Ernst Mach Society through which members of the Vienna Circle sought to popularize their ideas in the context of programmes for education in Vienna. During the era of Austrofascism and after the annexation of Austria by Nazi Germany most members of the Vienna Circle were forced to emigrate, the murder of Schlick in 1936 by a former student put an end to the Vienna Circle in Austria. The Vienna Circles influence on 20th-century philosophy, especially philosophy of science, Hans Hahn, the oldest of the three, was a mathematician. He received his degree in mathematics in 1902, afterwards he studied under the direction of Ludwig Boltzmann in Vienna and David Hilbert, Felix Klein and Hermann Minkowski in Göttingen. In 1905 he received the Habilitation in mathematics and he taught at Innsbruck and Vienna. Otto Neurath studied mathematics, political economy, and history in Vienna, from 1907 to 1914 he taught in Vienna at the Neue Wiener Handelsakademie. Neurath married Olga, Hahns sister, in 1911, Philipp Frank, the youngest of the group, studied physics at Göttingen and Vienna with Ludwig Boltzmann, David Hilbert and Felix Klein. From 1912, he held the chair of physics in the German University in Prague. Their meetings were held in Viennese coffeehouses from 1907 onward, Frank remembered, A number of further authors were discussed in the meetings such as Brentano, Meinong, Helmholtz, Hertz, Husserl, Freud, Russell, Whitehead, Lenin and Frege. Presumably the meetings stopped in 1912, when Frank went to Prague, Hahn left Vienna during World War I and returned in 1921. The formation of the Vienna Circle began with Hahn returning to Vienna in 1921, together with the mathematician Kurt Reidemeister he organized seminars on Ludwig Wittgenstein’s Tractatus logico-philosophicus and on Whitehead and Russell’s Principia Mathematica. Schlick had already published two important works Raum und Zeit in die gegenwärtigen Physik in 1917 and Allgemeine Erkenntnislehre in 1918, immediately after Schlick’s arrival in Vienna, he organized discussions with the mathematicians around Hahn. In 1924 Schlick’s students Friedrich Waismann and Herbert Feigl suggested to their teacher a sort of regular “evening circle”, from winter term 1924 on regular meetings were held at the Institute of Mathematics in Vienna’s Boltzmanngasse 5 on personal invitation by Schlick. These discussions can be seen as the beginning of the Vienna Circle, in addition, the group invited foreign visitors
12.
Rudolf Carnap
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Rudolf Carnap was a German-born philosopher who was active in Europe before 1935 and in the United States thereafter. He was a member of the Vienna Circle and an advocate of logical positivism. He is considered one of the giants among twentieth-century philosophers, Carnaps father had risen from the status of a poor ribbon-weaver to become the owner of a ribbon-making factory. His mother came from stock, her father was an educational reformer and her oldest brother was the archaeologist Wilhelm Dörpfeld. As a ten-year-old, Carnap accompanied his uncle on an expedition to Greece, Carnap was raised in a religious family, but later became an atheist. He began his education at the Barmen Gymnasium. From 1910 to 1914, he attended the University of Jena, but he also studied carefully Kants Critique of Pure Reason during a course taught by Bruno Bauch, and was one of very few students to attend Gottlob Freges courses in mathematical logic. While Carnap held moral and political opposition to World War I, after three years of service, he was given permission to study physics at the University of Berlin, 1917–18, where Albert Einstein was a newly appointed professor. Carnap then attended the University of Jena, where he wrote a thesis defining a theory of space. The physics department said it was too philosophical, and Bruno Bauch of the department said it was pure physics. Carnap then wrote another thesis in 1921, with Bauchs supervision, on the theory of space in a more orthodox Kantian style, in it he makes the clear distinction between formal, physical and perceptual spaces. Freges course exposed him to Bertrand Russells work on logic and philosophy and he accepted the effort to surpass traditional philosophy with logical innovations that inform the sciences. In 1924 and 1925, he attended seminars led by Edmund Husserl, the founder of phenomenology, Carnap discovered a kindred spirit when he met Hans Reichenbach at a 1923 conference. Reichenbach introduced Carnap to Moritz Schlick, a professor at the University of Vienna who offered Carnap a position in his department, when Wittgenstein visited Vienna, Carnap would meet with him. He wrote the 1929 manifesto of the Circle, and initiated the philosophy journal Erkenntnis, the formal system of the Aufbau was grounded in a single primitive dyadic predicate, which is satisfied if two individuals resemble each other. The Aufbau was greatly influenced by Principia Mathematica, and warrants comparison with the mereotopological metaphysics A. N. Whitehead developed over 1916–29 and it appears, however, that Carnap soon became somewhat disenchanted with this book. In particular, he did not authorize an English translation until 1967, pseudoproblems in Philosophy asserted that many philosophical questions were meaningless, i. e. the way they were posed amounted to an abuse of language. An operational implication of this opinion was taken to be the elimination of metaphysics from responsible human discourse and this is the statement for which Carnap was best known for many years
13.
Bertrand Russell
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Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, writer, social critic, political activist and Nobel laureate. At various points in his life he considered himself a liberal, a socialist, and a pacifist and he was born in Monmouthshire into one of the most prominent aristocratic families in the United Kingdom. In the early 20th century, Russell led the British revolt against idealism and he is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege, colleague G. E. Moore, and protégé Ludwig Wittgenstein. He is widely held to be one of the 20th centurys premier logicians, with A. N. Whitehead he wrote Principia Mathematica, an attempt to create a logical basis for mathematics. His philosophical essay On Denoting has been considered a paradigm of philosophy, Russell mostly was a prominent anti-war activist, he championed anti-imperialism. Occasionally, he advocated preventive nuclear war, before the opportunity provided by the monopoly is gone. He went to prison for his pacifism during World War I, in 1950 Russell was awarded the Nobel Prize in Literature in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought. Bertrand Russell was born on 18 May 1872 at Ravenscroft, Trellech, Monmouthshire and his parents, Viscount and Viscountess Amberley, were radical for their times. Lord Amberley consented to his wifes affair with their childrens tutor, both were early advocates of birth control at a time when this was considered scandalous. Lord Amberley was an atheist and his atheism was evident when he asked the philosopher John Stuart Mill to act as Russells secular godfather, Mill died the year after Russells birth, but his writings had a great effect on Russells life. His paternal grandfather, the Earl Russell, had asked twice by Queen Victoria to form a government. The Russells had been prominent in England for several centuries before this, coming to power, Lady Amberley was the daughter of Lord and Lady Stanley of Alderley. Russell often feared the ridicule of his grandmother, one of the campaigners for education of women. Russell had two siblings, brother Frank, and sister Rachel, in June 1874 Russells mother died of diphtheria, followed shortly by Rachels death. In January 1876, his father died of bronchitis following a period of depression. Frank and Bertrand were placed in the care of their staunchly Victorian paternal grandparents and his grandfather, former Prime Minister Earl Russell, died in 1878, and was remembered by Russell as a kindly old man in a wheelchair. His grandmother, the Countess Russell, was the dominant family figure for the rest of Russells childhood, the countess was from a Scottish Presbyterian family, and successfully petitioned the Court of Chancery to set aside a provision in Amberleys will requiring the children to be raised as agnostics. Her favourite Bible verse, Thou shalt not follow a multitude to do evil, the atmosphere at Pembroke Lodge was one of frequent prayer, emotional repression, and formality, Frank reacted to this with open rebellion, but the young Bertrand learned to hide his feelings
14.
Philosophical Investigations
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He alleges that the problems are traceable to a set of related assumptions about the nature of language, which themselves presuppose a particular conception of the essence of language. In this picture of language we find the roots of the following idea and this meaning is correlated with the word. It is the object for which the word stands, Philosophical Investigations was not ready for publication when Wittgenstein died in 1951. G. E. M. Anscombe translated Wittgensteins manuscript into English, there are two popular English editions, both translated by Anscombe, Prentice Hall,1999 Blackwell Publishers,2001. This edition includes the original German text in addition to the English translation, the text is divided into two parts, consisting of what Wittgenstein calls, in the preface, Bemerkungen, translated by Anscombe as remarks. In the first part, these remarks are more than a paragraph long and are numbered sequentially. In the second part, the remarks are longer and numbered using Roman numerals, in the index, remarks from the first part are referenced by their number rather than page, however, references from the second part are cited by page number. The comparatively unusual nature of the part is due to the fact that it comprises notes that Wittgenstein may have intended to re-incorporate into the first part. Subsequent to his death it was published as a Part II in the first, second, in standard references, a small letter following a page, section, or proposition number indicates a paragraph. Philosophical Investigations is unique in its approach to philosophy, the following is an excerpt from the first entry in the book that exemplifies this method. think of the following use of language, I send someone shopping. Well, I assume that he acts as I have described, explanations come to an end somewhere. —But what is the meaning of the word five. No such thing was in here, only how the word five is used. This example is typical of the books style and we can see each of the steps in Wittgensteins method, The reader is presented with a thought experiment, someone is sent shopping with an order on a slip. Wittgenstein supplies the response of an imagined interlocutor and he usually puts these statements in quotes to distinguish them from his own, But how does he know where and how he is to look up the word red and what he is to do with the word five. Or Wittgenstein may indicate such a response by beginning with a dash, as he does before the question above. Wittgenstein shows why the reaction was misguided, No such thing was in question here. Similarly, Wittgenstein often uses the device of framing many of the remarks as a dialogue between himself and a disputant, for example, Remark 258 proposes a thought experiment in which a certain sensation is associated with the sign S written in a calendar. Through such thought experiments, Wittgenstein attempts to get the reader to come to certain difficult philosophical conclusions independently, the Investigations deals largely with the difficulties of language and meaning
15.
Truth function
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In logic, a truth function is a function that accepts truth values as input and produces a truth value as output, i. e. the input and output are all truth values. On the contrary, modal logic is non-truth-functional, a logical connective is truth-functional if the truth-value of a compound sentence is a function of the truth-value of its sub-sentences. A class of connectives is truth-functional if each of its members is, some connectives of a natural language, such as English, are not truth-functional. Connectives of the form x believes that, are typical examples of connectives that are not truth-functional. In both cases, each component sentence is false, but each compound sentence formed by prefixing the phrase Mary believes that differs in truth-value and that is, the truth-value of a sentence of the form Mary believes that. Is not determined solely by the truth-value of its component sentence, the class of classical logic connectives used in the construction of formulas is truth-functional. Their values for various truth-values as argument are usually given by truth tables, truth-functional propositional calculus is a formal system whose formulae may be interpreted as either true or false. In two-valued logic, there are sixteen possible truth functions, also called Boolean functions, truth and falsehood is denoted as 1 and 0 in the following truth tables, respectively, for sake of brevity. Because a function may be expressed as a composition, a logical calculus does not need to have dedicated symbols for all of the above-mentioned functions to be functionally complete. This is expressed in a propositional calculus as logical equivalence of certain compound statements, for example, classical logic has ¬P ∨ Q equivalent to P → Q. The conditional operator → is therefore not necessary for a logical system if ¬ and ∨ are already in use. A minimal set of operators that can express every statement expressible in the propositional calculus is called a minimal functionally complete set, a minimally complete set of operators is achieved by NAND alone and NOR alone. The following are the minimal functionally complete sets of operators whose arities do not exceed 2, some truth functions possess properties which may be expressed in the theorems containing the corresponding connective. Commutativity, The operands of the connective may be swapped without affecting the truth-value of the expression, distributivity, A connective denoted by · distributes over another connective denoted by +, if a · = + for all operands a, b, c. Idempotence, Whenever the operands of the operation are the same, in other words, the operation is both truth-preserving and falsehood-preserving. Absorption, A pair of connectives ∧, ∨ satisfies the law if a ∧ = a for all operands a, b. A set of functions is functionally complete if and only if for each of the following five properties it contains at least one member lacking it, monotonic. Bn ∈ such that a1 ≤ b1, a2 ≤ b2, affine, Each variable always makes a difference in the truth-value of the operation or it never makes a difference
16.
Platonic form
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As universals were considered by Plato to be ideal forms, this stance is ambiguously also called Platonic idealism. Platos Forms include numbers and geometrical figures, making them a theory of realism, they also include the Form of the Good. Plato expounded his own articulation of realism regarding the existence of universals in his dialogue The Republic and elsewhere, notably in the Phaedo, the Phaedrus, the Meno and the Parmenides. In Platonic realism, universals do not exist in the way that physical objects exist. More modern versions of the seek to avoid applying potentially misleading descriptions to universals. Instead, such versions maintain that it is meaningless to apply the categories of space, regardless of their description, Platonic realism holds that universals do exist in a broad, abstract sense, although not at any spatial or temporal distance from peoples bodies. Thus, people see or otherwise come into sensory contact with universals. Theories of universals, including Platonic realism, are challenged to satisfy certain constraints on theories of universals, Platonic realism satisfies one of those constraints, in that it is a theory of what general terms refer to. Forms are ideal in supplying meaning to referents for general terms and that is, to understand terms such as wikt, Applehood and redness, Platonic realism says that they refer to forms. Some contemporary linguistic philosophers construe Platonism to mean the proposition that universals exist independently of particulars, similarly, a form of modern Platonism is found in the predominant philosophy of mathematics, especially regarding the foundations of mathematics. The Platonic interpretation of this includes the thesis that mathematics is discovered rather than created. Platos interpretation of universals is linked to his Theory of Forms in which he uses both the terms εἶδος and ἰδέα to describe his theory, Forms are mind independent abstract objects or paradigms of which particular objects and the properties and relations present in them are copies. Form is inherent in the particulars and these are said to participate in the form, classically idea has been translated as idea, but secondary literature now typically employs the term form to avoid confusion with the English word connoting thought. Platonic form can be illustrated by contrasting a material triangle with an ideal triangle, the Platonic form is the ideal triangle — a figure with perfectly drawn lines whose angles add to 180 degrees. Any form of triangle that we experience will be a representation of the ideal triangle. Regardless of how precise your measuring and drawing tools you will never be able to recreate this perfect shape, even drawn to the point where our senses cannot perceive a defect, in its essence the shape will still be imperfect, forever unable to match the ideal triangle. Some versions of Platonic realism, like that of Proclus, regard Platos forms as thoughts in the mind of God, most consider forms not to be mental entities at all. In Platonic realism, forms are related to particulars in that a particular is regarded as a copy of its form, for example, a particular apple is said to be a copy of the form of applehood and the apples redness is an instance of the form of Redness
17.
Plato
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Plato was a philosopher in Classical Greece and the founder of the Academy in Athens, the first institution of higher learning in the Western world. He is widely considered the most pivotal figure in the development of philosophy, unlike nearly all of his philosophical contemporaries, Platos entire work is believed to have survived intact for over 2,400 years. Along with his teacher, Socrates, and his most famous student, Aristotle, Plato laid the foundations of Western philosophy. Alfred North Whitehead once noted, the safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato. In addition to being a figure for Western science, philosophy. Friedrich Nietzsche, amongst other scholars, called Christianity, Platonism for the people, Plato was the innovator of the written dialogue and dialectic forms in philosophy, which originate with him. He was not the first thinker or writer to whom the word “philosopher” should be applied, few other authors in the history of Western philosophy approximate him in depth and range, perhaps only Aristotle, Aquinas and Kant would be generally agreed to be of the same rank. Due to a lack of surviving accounts, little is known about Platos early life, the philosopher came from one of the wealthiest and most politically active families in Athens. Ancient sources describe him as a bright though modest boy who excelled in his studies, the exact time and place of Platos birth are unknown, but it is certain that he belonged to an aristocratic and influential family. Based on ancient sources, most modern scholars believe that he was born in Athens or Aegina between 429 and 423 BCE. According to a tradition, reported by Diogenes Laertius, Ariston traced his descent from the king of Athens, Codrus. Platos mother was Perictione, whose family boasted of a relationship with the famous Athenian lawmaker, besides Plato himself, Ariston and Perictione had three other children, these were two sons, Adeimantus and Glaucon, and a daughter Potone, the mother of Speusippus. The brothers Adeimantus and Glaucon are mentioned in the Republic as sons of Ariston, and presumably brothers of Plato, but in a scenario in the Memorabilia, Xenophon confused the issue by presenting a Glaucon much younger than Plato. Then, at twenty-eight, Hermodorus says, went to Euclides in Megara, as Debra Nails argues, The text itself gives no reason to infer that Plato left immediately for Megara and implies the very opposite. Thus, Nails dates Platos birth to 424/423, another legend related that, when Plato was an infant, bees settled on his lips while he was sleeping, an augury of the sweetness of style in which he would discourse about philosophy. Ariston appears to have died in Platos childhood, although the dating of his death is difficult. Perictione then married Pyrilampes, her mothers brother, who had served many times as an ambassador to the Persian court and was a friend of Pericles, Pyrilampes had a son from a previous marriage, Demus, who was famous for his beauty. Perictione gave birth to Pyrilampes second son, Antiphon, the half-brother of Plato and these and other references suggest a considerable amount of family pride and enable us to reconstruct Platos family tree
18.
Aristotle
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Aristotle was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidice, on the northern periphery of Classical Greece. His father, Nicomachus, died when Aristotle was a child, at seventeen or eighteen years of age, he joined Platos Academy in Athens and remained there until the age of thirty-seven. Shortly after Plato died, Aristotle left Athens and, at the request of Philip II of Macedon, teaching Alexander the Great gave Aristotle many opportunities and an abundance of supplies. He established a library in the Lyceum which aided in the production of many of his hundreds of books and he believed all peoples concepts and all of their knowledge was ultimately based on perception. Aristotles views on natural sciences represent the groundwork underlying many of his works, Aristotles views on physical science profoundly shaped medieval scholarship. Their influence extended from Late Antiquity and the Early Middle Ages into the Renaissance, some of Aristotles zoological observations, such as on the hectocotyl arm of the octopus, were not confirmed or refuted until the 19th century. His works contain the earliest known study of logic, which was incorporated in the late 19th century into modern formal logic. Aristotle was well known among medieval Muslim intellectuals and revered as The First Teacher and his ethics, though always influential, gained renewed interest with the modern advent of virtue ethics. All aspects of Aristotles philosophy continue to be the object of academic study today. Though Aristotle wrote many elegant treatises and dialogues – Cicero described his style as a river of gold – it is thought that only around a third of his original output has survived. Aristotle, whose means the best purpose, was born in 384 BC in Stagira, Chalcidice. His father Nicomachus was the physician to King Amyntas of Macedon. Aristotle was orphaned at a young age, although there is little information on Aristotles childhood, he probably spent some time within the Macedonian palace, making his first connections with the Macedonian monarchy. At the age of seventeen or eighteen, Aristotle moved to Athens to continue his education at Platos Academy and he remained there for nearly twenty years before leaving Athens in 348/47 BC. Aristotle then accompanied Xenocrates to the court of his friend Hermias of Atarneus in Asia Minor, there, he traveled with Theophrastus to the island of Lesbos, where together they researched the botany and zoology of the island. Aristotle married Pythias, either Hermiass adoptive daughter or niece and she bore him a daughter, whom they also named Pythias. Soon after Hermias death, Aristotle was invited by Philip II of Macedon to become the tutor to his son Alexander in 343 BC, Aristotle was appointed as the head of the royal academy of Macedon. During that time he gave not only to Alexander
19.
Heraclitus
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Heraclitus of Ephesus was a pre-Socratic Greek philosopher, and a native of the city of Ephesus, then part of the Persian Empire. Little is known about his life and education, but he regarded himself as self-taught. Heraclitus was famous for his insistence on ever-present change as being the essence of the universe, as stated in the famous saying. This position was complemented by his commitment to a unity of opposites in the world, stating that the path up and down are one. Through these doctrines Heraclitus characterized all existing entities by pairs of contrary properties and this, along with his cryptic utterance that all entities come to be in accordance with this Logos has been the subject of numerous interpretations. Diogenes said that Heraclitus flourished in the 69th Olympiad, 504–501 BC, All the rest of the evidence — the people Heraclitus is said to have known, or the people who were familiar with his work — confirms the floruit. His dates of birth and death are based on a span of 60 years. Heraclitus was born to a family in Ephesus, in the Persian Empire, in what is now called present-day Efes. His father was named either Blosôn or Herakôn, how much power the king had is another question. Ephesus had been part of the Persian Empire since 547 and was ruled by a satrap, two extant letters between Heraclitus and Darius I, quoted by Diogenes, are undoubtedly later forgeries. With regard to education, Diogenes says that Heraclitus was wondrous from childhood, Diogenes relates that Sotion said he was a hearer of Xenophanes, which contradicts Heraclitus statement that he had taught himself by questioning himself. Burnet states in any case that, Xenophanes left Ionia before Herakleitos was born. Diogenes relates that as a boy Heraclitus had said he knew nothing and his statement that he heard no one but questioned himself, can be placed alongside his statement that the things that can be seen, heard and learned are what I prize the most. Diogenes relates that Heraclitus had an opinion of human affairs. He believed that Hesiod and Pythagoras lacked understanding though learned and that Homer, laws needed to be defended as though they were city walls. Timon is said to have called him a mob-reviler, Heraclitus hated the Athenians and his fellow Ephesians, wishing the latter wealth in punishment for their wicked ways. Says Diogenes, Finally, he became a hater of his kind, making his diet of grass and herbs. Heraclitus life as a philosopher was interrupted by dropsy, the physicians he consulted were unable to prescribe a cure
20.
Qi
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In traditional Chinese culture, qì or chi is an active principle forming part of any living thing. Qi literally translates as breath, air, or gas, and figuratively as material energy, life force, Qi is the central underlying principle in traditional Chinese medicine and martial arts. Some elements of the concept of qi can be found in the energy when used in the context of various esoteric forms of spirituality. Notions in the West of energeia, élan vital, or vitalism are purported to be similar, despite widespread belief in the reality of qi, it is a non-scientific, unverifiable concept. The logograph 氣 is read with two Chinese pronunciations, the usual qì 氣 air, vital energy and the rare archaic xì 氣 to present food, pronunciations of 氣 in Sino-Xenic borrowings include, Japanese language ki, Korean language gi, and Vietnamese language khi. Reconstructions of the Middle Chinese pronunciation of 氣, standardized to IPA transcription, include, /kʰe̯iH/, /kʰĭəiH/, /kʰiəiH/, /kʰɨjH/, reconstructions of the Old Chinese pronunciation of 氣, standardized to IPA transcription, include, /*kʰɯds/, and /*C. qʰəp-s/. In addition, qì 炁 is an uncommon character especially used in writing Daoist talismans, historically, the word qì was generally written as 气 until the Han dynasty, when it was replaced by the 氣 graph clarified with mǐ 米 rice indicating steam. These oracle, bronze, and seal scripts graphs for qì 气 air, breath, etc. were anciently used as a loan character to write qǐ 乞 plead for, beg, ask. The regular script character qì 氣 is unusual because qì 气 is both the air radical and the phonetic, with mǐ 米 rice semantically indicating steam, vapor. This qì 气 air/gas radical, which was used in a few native Chinese characters like yīnyūn 氤氲 thick mist/smoke, was used to create new scientific characters for gaseous chemical elements. Some examples are based on pronunciations in European languages, fú 氟 fluorine and nǎi 氖 neon, others are based on semantics, qīng 氫 hydrogen and lǜ 氯 chlorine. Qi was an early Chinese loanword in English, romanized as, ki in Church Romanization in the century, chi in Wade–Giles in the mid-19th century. An early form of the idea comes from the writings of the Chinese philosopher Mencius, historically, the Huangdi Neijing/The Yellow Emperors Classic of Medicine is credited with first establishing the pathways through which qi circulates in the human body. The ancient Chinese described it as life force and they believed qi permeated everything and linked their surroundings together. They likened it to the flow of energy around and through the body, forming a cohesive, by understanding its rhythm and flow they believed they could guide exercises and treatments to provide stability and longevity. Although the concept of qi has been important within many Chinese philosophies, until China came into contact with Western scientific and philosophical ideas, they had not categorized all things in terms of matter and energy. Qi and li were fundamental categories similar to matter and energy, yuán qì is a notion of innate or pre-natal qi to distinguish it from acquired qi that a person may develop over the course of their lifetime. The earliest texts that speak of qi give some indications of how the concept developed, the philosopher Mo Di used the word qi to refer to noxious vapors that would in due time arise from a corpse were it not buried at a sufficient depth
21.
Immanuel Kant
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Immanuel Kant was a German philosopher who is considered a central figure in modern philosophy. Kant took himself to have effected a Copernican revolution in philosophy and his beliefs continue to have a major influence on contemporary philosophy, especially the fields of metaphysics, epistemology, ethics, political theory, and aesthetics. Politically, Kant was one of the earliest exponents of the idea that peace could be secured through universal democracy. He believed that this will be the outcome of universal history. Kant wanted to put an end to an era of futile and speculative theories of human experience, Kant argued that our experiences are structured by necessary features of our minds. In his view, the shapes and structures experience so that, on an abstract level. Among other things, Kant believed that the concepts of space and time are integral to all human experience, as are our concepts of cause, Kant published other important works on ethics, religion, law, aesthetics, astronomy, and history. These included the Critique of Practical Reason, the Metaphysics of Morals, which dealt with ethics, and the Critique of Judgment, Immanuel Kant was born in 1724 in Königsberg, Prussia. His mother, Anna Regina Reuter, was born in Königsberg to a father from Nuremberg. His father, Johann Georg Kant, was a German harness maker from Memel, Immanuel Kant believed that his paternal grandfather Hans Kant was of Scottish origin. Kant was the fourth of nine children, baptized Emanuel, he changed his name to Immanuel after learning Hebrew. Young Kant was a solid, albeit unspectacular, student and he was brought up in a Pietist household that stressed religious devotion, humility, and a literal interpretation of the Bible. His education was strict, punitive and disciplinary, and focused on Latin and religious instruction over mathematics, despite his religious upbringing and maintaining a belief in God, Kant was skeptical of religion in later life, various commentators have labelled him agnostic. Common myths about Kants personal mannerisms are listed, explained, and refuted in Goldthwaits introduction to his translation of Observations on the Feeling of the Beautiful and Sublime. It is often held that Kant lived a strict and disciplined life. He never married, but seemed to have a social life — he was a popular teacher. He had a circle of friends whom he met, among them Joseph Green. A common myth is that Kant never traveled more than 16 kilometres from Königsberg his whole life, in fact, between 1750 and 1754 he worked as a tutor in Judtschen and in Groß-Arnsdorf
22.
Logical
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Logic, originally meaning the word or what is spoken, is generally held to consist of the systematic study of the form of arguments. A valid argument is one where there is a relation of logical support between the assumptions of the argument and its conclusion. Historically, logic has been studied in philosophy and mathematics, and recently logic has been studied in science, linguistics, psychology. The concept of form is central to logic. The validity of an argument is determined by its logical form, traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic. Informal logic is the study of natural language arguments, the study of fallacies is an important branch of informal logic. Since much informal argument is not strictly speaking deductive, on some conceptions of logic, formal logic is the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as an application of a wholly abstract rule, that is. The works of Aristotle contain the earliest known study of logic. Modern formal logic follows and expands on Aristotle, in many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language, Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference. Symbolic logic is divided into two main branches, propositional logic and predicate logic. Mathematical logic is an extension of logic into other areas, in particular to the study of model theory, proof theory, set theory. Logic is generally considered formal when it analyzes and represents the form of any valid argument type, the form of an argument is displayed by representing its sentences in the formal grammar and symbolism of a logical language to make its content usable in formal inference. Simply put, formalising simply means translating English sentences into the language of logic and this is called showing the logical form of the argument. It is necessary because indicative sentences of ordinary language show a variety of form. Second, certain parts of the sentence must be replaced with schematic letters, thus, for example, the expression all Ps are Qs shows the logical form common to the sentences all men are mortals, all cats are carnivores, all Greeks are philosophers, and so on. The schema can further be condensed into the formula A, where the letter A indicates the judgement all - are -, the importance of form was recognised from ancient times
23.
Geometric
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Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer, Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes. Geometry began to see elements of mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into a form by Euclid, whose treatment, Euclids Elements. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC, islamic scientists preserved Greek ideas and expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid footing by mathematicians such as René Descartes. Since then, and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, while geometry has evolved significantly throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, contemporary geometry has many subfields, Euclidean geometry is geometry in its classical sense. The mandatory educational curriculum of the majority of nations includes the study of points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles, Euclidean geometry also has applications in computer science, crystallography, and various branches of modern mathematics. Differential geometry uses techniques of calculus and linear algebra to problems in geometry. It has applications in physics, including in general relativity, topology is the field concerned with the properties of geometric objects that are unchanged by continuous mappings. In practice, this often means dealing with large-scale properties of spaces, convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues, often using techniques of real analysis. It has close connections to convex analysis, optimization and functional analysis, algebraic geometry studies geometry through the use of multivariate polynomials and other algebraic techniques. It has applications in areas, including cryptography and string theory. Discrete geometry is concerned mainly with questions of relative position of simple objects, such as points. It shares many methods and principles with combinatorics, Geometry has applications to many fields, including art, architecture, physics, as well as to other branches of mathematics. The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia, the earliest known texts on geometry are the Egyptian Rhind Papyrus and Moscow Papyrus, the Babylonian clay tablets such as Plimpton 322. For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, later clay tablets demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiters position and motion within time-velocity space
24.
Projection (mathematics)
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In mathematics, a projection is a mapping of a set into a subset, which is equal to its square for mapping composition. The restriction to a subspace of a projection is called a projection. An everyday example of a projection is the casting of shadows onto a plane, the projection of a point is its shadow on the paper sheet. The shadow of a point on the sheet is this point itself. The shadow of a sphere is a closed disk. Originally, the notion of projection was introduced in Euclidean geometry to denote the projection of the Euclidean space of three dimensions onto a plane in it, like the shadow example. The points P such that the line CP is parallel to the plane do not have any image by the projection, the projection of the point C itself is not defined. The projection parallel to a direction D, onto a plane, see Affine space § Projection for an accurate definition, generalized to any dimension. The concept of projection in mathematics is an old one. This rudimentary idea was refined and abstracted, first in a geometric context, over time differing versions of the concept developed, but today, in a sufficiently abstract setting, we can unify these variations. In cartography, a map projection is a map of a part of the surface of the Earth onto a plane, which, in some cases, the 3D projections are also at the basis of the theory of perspective. The need for unifying the two kinds of projections and of defining the image by a projection of any point different of the center of projection are at the origin of projective geometry. However, a transformation is a bijection of a projective space. In an abstract setting we can say that a projection is a mapping of a set which is idempotent. A projection may also refer to a mapping which has a left inverse, both notions are strongly related, as follows. Let p be an idempotent map from a set A into itself, if we denote by π the map p viewed as a map from A onto B and by i the injection of B into A, then we have π. i= IdB. Conversely, π. i = IdB implies that π∘i is idempotent, a mapping that takes an element to its equivalence class under a given equivalence relation is known as the canonical projection. The evaluation map sends a function f to the value f for a fixed x, the space of functions YX can be identified with the cartesian product ∏ i ∈ X Y i, and the evaluation map is a projection map from the cartesian product
25.
Natural sciences
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Natural science is a branch of science concerned with the description, prediction, and understanding of natural phenomena, based on observational and empirical evidence. Mechanisms such as review and repeatability of findings are used to try to ensure the validity of scientific advances. Natural science can be divided into two branches, life science and physical science. Physical science is subdivided into branches, including physics, space science, chemistry and these branches of natural science may be further divided into more specialized branches. Modern natural science succeeded more classical approaches to natural philosophy, usually traced to ancient Greece, galileo, Descartes, Francis Bacon, and Newton debated the benefits of using approaches which were more mathematical and more experimental in a methodical way. Still, philosophical perspectives, conjectures, and presuppositions, often overlooked, systematic data collection, including discovery science, succeeded natural history, which emerged in the 16th century by describing and classifying plants, animals, minerals, and so on. Today, natural history suggests observational descriptions aimed at popular audiences, philosophers of science have suggested a number of criteria, including Karl Poppers controversial falsifiability criterion, to help them differentiate scientific endeavors from non-scientific ones. Validity, accuracy, and quality control, such as peer review and this field encompasses a set of disciplines that examines phenomena related to living organisms. The scale of study can range from sub-component biophysics up to complex ecologies, biology is concerned with the characteristics, classification and behaviors of organisms, as well as how species were formed and their interactions with each other and the environment. The biological fields of botany, zoology, and medicine date back to periods of civilization. However, it was not until the 19th century that became a unified science. Once scientists discovered commonalities between all living things, it was decided they were best studied as a whole, modern biology is divided into subdisciplines by the type of organism and by the scale being studied. Molecular biology is the study of the chemistry of life, while cellular biology is the examination of the cell. At a higher level, anatomy and physiology looks at the internal structures, constituting the scientific study of matter at the atomic and molecular scale, chemistry deals primarily with collections of atoms, such as gases, molecules, crystals, and metals. The composition, statistical properties, transformations and reactions of these materials are studied, chemistry also involves understanding the properties and interactions of individual atoms and molecules for use in larger-scale applications. Most chemical processes can be studied directly in a laboratory, using a series of techniques for manipulating materials, chemistry is often called the central science because of its role in connecting the other natural sciences. Early experiments in chemistry had their roots in the system of Alchemy, the science of chemistry began to develop with the work of Robert Boyle, the discoverer of gas, and Antoine Lavoisier, who developed the theory of the Conservation of mass. The success of science led to a complementary chemical industry that now plays a significant role in the world economy
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Truth tables
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In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid. A truth table has one column for each variable. Each row of the table contains one possible configuration of the input variables. See the examples below for further clarification, the Com row indicates whether an operator, op, is commutative - P op Q = Q op P. The L id row shows the operators left identities if it has any - values I such that I op Q = Q, the R id row shows the operators right identities if it has any - values I such that P op I = P. The four combinations of values for p, q, are read by row from the table above. The output function for p, q combination, can be read, by row. Key, The following table is oriented by column, rather than by row, There are four columns rather than four rows, to display the four combinations of p, q, as input. P, T T F Fq, T F T F There are 16 rows in this key, the output row for ↚ is thus 2, F F T F and the 16-row key is Logical operators can also be visualized using Venn diagrams. Logical conjunction is an operation on two values, typically the values of two propositions, that produces a value of true if both of its operands are true. The truth table for p AND q is as follows, In ordinary language terms, for all other assignments of logical values to p and to q the conjunction p ∧ q is false. The truth table for p OR q is as follows, Stated in English, if p, then p ∨ q is p, otherwise p ∨ q is q. The truth table associated with the conditional if p then q. Logical equality is an operation on two values, typically the values of two propositions, that produces a value of true if both operands are false or both operands are true. The truth table for p XNOR q is as follows, So p EQ q is true if p and q have the truth value. Exclusive disjunction is an operation on two values, typically the values of two propositions, that produces a value of true if one but not both of its operands is true. The truth table for p XOR q is as follows, For two propositions, XOR can also be written as ∨. The logical NAND is an operation on two values, typically the values of two propositions, that produces a value of false if both of its operands are true
27.
Tautology (logic)
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In logic, a tautology is a formula that is true in every possible interpretation. Philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921, a formula is satisfiable if it is true under at least one interpretation, and thus a tautology is a formula whose negation is unsatisfiable. Unsatisfiable statements, both through negation and affirmation, are known formally as contradictions, a formula that is neither a tautology nor a contradiction is said to be logically contingent. Such a formula can be either true or false based on the values assigned to its propositional variables. The double turnstile notation ⊨ S is used to indicate that S is a tautology, Tautology is sometimes symbolized by Vpq, and contradiction by Opq. Tautologies are a key concept in logic, where a tautology is defined as a propositional formula that is true under any possible Boolean valuation of its propositional variables. A key property of tautologies in propositional logic is that a method exists for testing whether a given formula is always satisfied. The definition of tautology can be extended to sentences in predicate logic, in propositional logic, there is no distinction between a tautology and a logically valid formula. The set of formulas is a proper subset of the set of logically valid sentences of predicate logic. In 1800, Immanuel Kant wrote in his book Logic, The identity of concepts in analytical judgments can be explicit or non-explicit. In the former case analytic propositions are tautological, here analytic proposition refers to an analytic truth, a statement in natural language that is true solely because of the terms involved. In 1884, Gottlob Frege proposed in his Grundlagen that a truth is analytic if it can be derived using logic. But he maintained a distinction between analytic truths and tautologies, in 1921, in his Tractatus Logico-Philosophicus, Ludwig Wittgenstein proposed that statements that can be deduced by logical deduction are tautological as well as being analytic truths. Henri Poincaré had made remarks in Science and Hypothesis in 1905. It has got to be something that has some quality, which I do not know how to define. Here logical proposition refers to a proposition that is using the laws of logic. During the 1930s, the formalization of the semantics of propositional logic in terms of truth assignments was developed, the term tautology began to be applied to those propositional formulas that are true regardless of the truth or falsity of their propositional variables. Some early books on logic used the term for any proposition that is universally valid, propositional logic begins with propositional variables, atomic units that represent concrete propositions
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Logical consequence
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Logical consequence is a fundamental concept in logic, which describes the relationship between statements that holds true when one statement logically follows from one or more statements. A valid logical argument is one in which the conclusions are entailed by the premises, the philosophical analysis of logical consequence involves the questions, In what sense does a conclusion follow from its premises. And What does it mean for a conclusion to be a consequence of premises, All of philosophical logic is meant to provide accounts of the nature of logical consequence and the nature of logical truth. Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. A sentence is said to be a consequence of a set of sentences, for a given language, if and only if. The most widely prevailing view on how to best account for logical consequence is to appeal to formality and this is to say that whether statements follow from one another logically depends on the structure or logical form of the statements without regard to the contents of that form. Syntactic accounts of logical consequence rely on schemes using inference rules, for instance, we can express the logical form of a valid argument as, All A are B. All C are A. Therefore, all C are B and this argument is formally valid, because every instance of arguments constructed using this scheme are valid. This is in contrast to an argument like Fred is Mikes brothers son, if you know that Q follows logically from P no information about the possible interpretations of P or Q will affect that knowledge. Our knowledge that Q is a consequence of P cannot be influenced by empirical knowledge. Deductively valid arguments can be known to be so without recourse to experience, however, formality alone does not guarantee that logical consequence is not influenced by empirical knowledge. So the a property of logical consequence is considered to be independent of formality. The two prevailing techniques for providing accounts of logical consequence involve expressing the concept in terms of proofs, the study of the syntactic consequence is called proof theory whereas the study of semantic consequence is called model theory. A formula A is a syntactic consequence within some formal system F S of a set Γ of formulas if there is a proof in F S of A from the set Γ. Γ ⊢ F S A Syntactic consequence does not depend on any interpretation of the formal system, or, in other words, the set of the interpretations that make all members of Γ true is a subset of the set of the interpretations that make A true. Modal accounts of logical consequence are variations on the basic idea, Γ ⊢ A is true if and only if it is necessary that if all of the elements of Γ are true. Alternatively, Γ ⊢ A is true if and only if it is impossible for all of the elements of Γ to be true, such accounts are called modal because they appeal to the modal notions of logical necessity and logical possibility. Consider the modal account in terms of the argument given as an example above, the conclusion is a logical consequence of the premises because we cant imagine a possible world where all frogs are green, Kermit is a frog, and Kermit is not green
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Logical NOR
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In boolean logic, logical nor or joint denial is a truth-functional operator which produces a result that is the negation of logical or. That is, a sentence of the form is true precisely when neither p nor q is true—i. e, when both of p and q are false. In grammar, nor is a coordinating conjunction, thus, as with its dual, the NAND operator, NOR can be used by itself, without any other logical operator, to constitute a logical formal system. It is also known as Quines dagger, the ampheck by Peirce, one way of expressing p NOR q is p ∨ q ¯, where the symbol ∨ signifies OR and the bar signifies the negation of the expression under it, in essence, simply ¬. Other ways of expressing p NOR q are Xpq, and p + q ¯, the computer used in the spacecraft that first carried humans to the moon, the Apollo Guidance Computer, was constructed entirely using NOR gates with three inputs. The NOR operation is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both operands are false. In other words, it produces a value of false if, the truth table of A NOR B is as follows, Logical NOR does not possess any of the five qualities required to be absent from at least one member of a set of functionally complete operators. Thus, the set containing only NOR suffices as a complete set, NOR has the interesting feature that all other logical operators can be expressed by interlaced NOR operations. The logical NAND operator also has this ability, the logical NOR ↓ is the negation of the disjunction, Expressed in terms of NOR ↓, the usual operators of propositional logic are
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Theorem
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In mathematics, a theorem is a statement that has been proved on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms. A theorem is a consequence of the axioms. The proof of a theorem is a logical argument for the theorem statement given in accord with the rules of a deductive system. The proof of a theorem is interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally deductive, in contrast to the notion of a scientific law, many mathematical theorems are conditional statements. In this case, the proof deduces the conclusion from conditions called hypotheses or premises, however, the conditional could be interpreted differently in certain deductive systems, depending on the meanings assigned to the derivation rules and the conditional symbol. Although they can be written in a symbolic form, for example, within the propositional calculus. In some cases, a picture alone may be sufficient to prove a theorem, because theorems lie at the core of mathematics, they are also central to its aesthetics. Theorems are often described as being trivial, or difficult, or deep and these subjective judgments vary not only from person to person, but also with time, for example, as a proof is simplified or better understood, a theorem that was once difficult may become trivial. On the other hand, a theorem may be simply stated. Fermats Last Theorem is a particularly well-known example of such a theorem, logically, many theorems are of the form of an indicative conditional, if A, then B. Such a theorem does not assert B, only that B is a consequence of A. In this case A is called the hypothesis of the theorem and B the conclusion. The theorem If n is an natural number then n/2 is a natural number is a typical example in which the hypothesis is n is an even natural number. To be proved, a theorem must be expressible as a precise, nevertheless, theorems are usually expressed in natural language rather than in a completely symbolic form, with the intention that the reader can produce a formal statement from the informal one. It is common in mathematics to choose a number of hypotheses within a given language and these hypotheses form the foundational basis of the theory and are called axioms or postulates. The field of known as proof theory studies formal languages, axioms. Some theorems are trivial, in the sense that they follow from definitions, axioms, a theorem might be simple to state and yet be deep
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Sheffer stroke
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It is also called nand or the alternative denial, since it says in effect that at least one of its operands is false. In Boolean algebra and digital electronics it is known as the NAND operation, like its dual, the NOR operator, NAND can be used by itself, without any other logical operator, to constitute a logical formal system. This property makes the NAND gate crucial to modern digital electronics, the NAND operation is a logical operation on two logical values. It produces a value of true, if — and only if — at least one of the propositions is false, the truth table of A NAND B is as follows, The stroke is named after Henry M. Because of self-duality of Boolean algebras, Sheffers axioms are equally valid for either of the NAND or NOR operations in place of the stroke. Sheffer interpreted the stroke as a sign for non-disjunction in his paper, mentioning non-conjunction only in a footnote and it was Jean Nicod who first used the stroke as a sign for non-conjunction in a paper of 1917 and which has since become current practice. Russell and Whitehead used the Sheffer stroke in the 1927 second edition of Principia Mathematica and suggested it as a replacement for the or and not operations of the first edition. Charles Sanders Peirce had discovered the functional completeness of NAND or NOR more than 30 years earlier, using the term ampheck, therefore is a functionally complete set. This can also be realized as follows, All three elements of the complete set can be constructed using only NAND. Thus the set must be complete as well. Hence any formal system including the Sheffer stroke must also include a means of indicating grouping and we shall employ to this effect. We also write p, q, r, … instead of p0, p1, Construction Rule I, For each natural number n, the symbol pn is a well-formed formula, called an atom. Construction Rule II, If X and Y are wffs, then is a wff, closure Rule, Any formulae which cannot be constructed by means of the first two Construction Rules are not wffs. The letters U, V, W, X, and Y are metavariables standing for wffs, then repeat this recursive deconstruction process to each of the subformulae. Eventually the formula should be reduced to its atoms, but if some subformula cannot be so reduced, All wffs of the form are axioms. Instances of, U ⊢ W are inference rules, since the only connective of this logic is |, the symbol | could be discarded altogether, leaving only the parentheses to group the letters. A pair of parentheses must always enclose a pair of wffs, examples of theorems in this simplified notation are. The notation can be simplified further, by letting, = ≡ U for any U and this simplification causes the need to change some rules, More than two letters are allowed within parentheses
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A priori and a posteriori
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The Latin phrases a priori and a posteriori are philosophical terms of art popularized by Immanuel Kants Critique of Pure Reason, one of the most influential works in the history of philosophy. These terms are used with respect to reasoning to distinguish necessary conclusions from first premises from conclusions based on sense observation, a posteriori knowledge or justification is dependent on experience or empirical evidence, as with most aspects of science and personal knowledge. There are many points of view on two types of knowledge, and their relationship gives rise to one of the oldest problems in modern philosophy. The terms a priori and a posteriori are primarily used as adjectives to modify the noun knowledge, however, a priori is sometimes used to modify other nouns, such as truth. Philosophers also may use apriority and aprioricity as nouns to refer to the quality of being a priori, although definitions and use of the terms have varied in the history of philosophy, they have consistently labeled two separate epistemological notions. See also the related distinctions, deductive/inductive, analytic/synthetic, necessary/contingent, the intuitive distinction between a priori and a posteriori knowledge is best seen in examples. A priori Consider the proposition, If George V reigned at least four days and this is something that one knows a priori, because it expresses a statement that one can derive by reason alone. A posteriori Compare this with the proposition expressed by the sentence and this is something that one must come to know a posteriori, because it expresses an empirical fact unknowable by reason alone. Several philosophers reacting to Kant sought to explain a priori knowledge without appealing to, as Paul Boghossian explains and that has never been described in satisfactory terms. One theory, popular among the positivists of the early 20th century, is what Boghossian calls the analytic explanation of the a priori. The distinction between analytic and synthetic propositions was first introduced by Kant, in short, proponents of this explanation claimed to have reduced a dubious metaphysical faculty of pure reason to a legitimate linguistic notion of analyticity. However, the explanation of a priori knowledge has undergone several criticisms. Most notably, Quine argued that the distinction is illegitimate. Quine states, But for all its a priori reasonableness, a boundary between analytic and synthetic statements simply has not been drawn and that there is such a distinction to be drawn at all is an unempirical dogma of empiricists, a metaphysical article of faith. While the soundness of Quines critique is highly disputed, it had an effect on the project of explaining the a priori in terms of the analytic. The metaphysical distinction between necessary and contingent truths has also related to a priori and a posteriori knowledge. A proposition that is true is one whose negation is self-contradictory. Consider the proposition that all bachelors are unmarried and its negation, the proposition that some bachelors are married, is incoherent, because the concept of being unmarried is part of the concept of being a bachelor
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Arthur Schopenhauer
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Arthur Schopenhauer was a German philosopher. He is best known for his 1818 work The World as Will and Representation, wherein he characterizes the phenomenal world as the product of a blind and his writing on aesthetics, morality, and psychology would exert important influence on thinkers and artists throughout the 19th and 20th centuries. Though his work failed to garner substantial attention during his life, Schopenhauer has had an impact across various disciplines, including philosophy, literature. When Danzig became part of Prussia in 1793, Heinrich moved to Hamburg, as early as 1799, Arthur started playing the flute. In 1805, Schopenhauers father died, possibly by suicide and he dedicated himself wholly to studies at the Gotha gymnasium in Saxe-Gotha-Altenburg, but left in disgust after seeing one of the masters lampooned. By that time, Johanna Schopenhauer had already opened her famous salon and he was also disgusted by the ease with which his mother had forgotten his fathers memory. He left to become a student at the University of Göttingen in 1809, there he studied metaphysics and psychology under Gottlob Ernst Schulze, the author of Aenesidemus, who advised him to concentrate on Plato and Immanuel Kant. In Berlin, from 1811 to 1812, he had attended lectures by the prominent post-Kantian philosopher Johann Gottlieb Fichte, Schopenhauer had a notably strained relationship with his mother Johanna. He wrote his first book, On the Fourfold Root of the Principle of Sufficient Reason and his mother informed him that the book was incomprehensible and it was unlikely that anyone would ever buy a copy. In a fit of temper Arthur Schopenhauer told her that his work would be long after the rubbish she wrote would have been totally forgotten. In fact, although they considered her novels of dubious quality and we published more and more of her son Arthurs work and today nobody remembers Johanna, but her sons works are in steady demand and contribute to Brockhaus reputation. He kept large portraits of the pair in his office in Leipzig for the edification of his new editors, in 1814, Schopenhauer began his seminal work The World as Will and Representation. He finished it in 1818 and Brockhaus published it that December, in Dresden in 1819, Schopenhauer fathered, with a servant, an illegitimate daughter who was born and died the same year. In 1820, Schopenhauer became a lecturer at the University of Berlin and he scheduled his lectures to coincide with those of the famous philosopher G. W. F. Hegel, whom Schopenhauer described as a clumsy charlatan. However, only five students turned up to Schopenhauers lectures, a late essay, On University Philosophy, expressed his resentment towards the work conducted in academies. While in Berlin, Schopenhauer was named as a defendant in a lawsuit initiated by a woman named Caroline Marquet and she asked for damages, alleging that Schopenhauer had pushed her. According to Schopenhauers court testimony, she annoyed him by raising her voice while standing right outside his door. Marquet alleged that the philosopher had assaulted and battered her after she refused to leave his doorway and her companion testified that she saw Marquet prostrate outside his apartment
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Logical atomism
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Logical atomism is a philosophical belief that originated in the early 20th century with the development of analytic philosophy. Its principal exponents were the British philosopher Bertrand Russell, the work of his Austrian-born pupil and colleague Ludwig Wittgenstein. The theory holds that the world consists of ultimate logical facts that cannot be broken down any further, having originally propounded this stance in his Tractatus Logico-Philosophicus, Wittgenstein rejected it in his later Philosophical Investigations. The name for this kind of theory was coined in 1918 by Russell in response to what he called logical holism—i. e, the belief that the world operates in such a way that no part can be known without the whole being known first. This belief is commonly called monism, and in particular, Russell were reacting to the absolute idealism dominant then in Britain and exemplified in works of F. H. Bradley, the term was first coined in a 1911 essay by Russell entitled The Basis of Realism. However, it widely known only when Russell gave a series of lectures in 1918 entitled The Philosophy of Logical Atomism. Russell was much influenced by Ludwig Wittgenstein, as an introductory note explicitly acknowledges, Russell and Moore broke themselves free from British Idealism which, for nearly 90 years, had dominated British philosophy. Russell referred to his atomistic doctrine as contrary to the tier of the people who more or less follow Hegel, the first principle of logical atomism is that the World contains facts. The facts are complex structures consisting of objects and this he defines as objects relations in terms of atomic facts is a fact, either from an object with a simple property or from different objects, in relation to each other more easily. In addition, there are judgments, which are in a relationship to the facts, according to this theory, even ordinary objects of daily life are apparently complex entities. According to Russell, words like this and that are used to denote particulars, in contrast, ordinary names such as Socrates actually are definitive descriptions. In the analysis of Plato talks with his pupils, Plato needs to be replaced with something like the man who was the teacher of Aristotle. In 1905, Russell had already criticized Alexius Meinong, whose theories led to the paradox of the existence and non-existence of fictional objects. This theory of descriptions was crucial to logical atomism, as Russell believed that language mirrored reality, Bertrand Russells theory of logical atomism consists of three interworking parts, the atomic proposition, the atomic fact, and the atomic complex. An atomic proposition, also known as a judgement, is a fundamental statement describing a single entity. Russell refers to this entity as a fact, and recognizes a range of elements within each fact that he refers to as particulars. A particular denotes a signifier such as a name, many of which may apply to an atomic fact, while a universal lends quality to these particulars, e. g. color, shape. In Russells Theory of Acquaintance, awareness of particulars and universals comes through sense data
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Theory of descriptions
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The theory of descriptions is the philosopher Bertrand Russells most significant contribution to the philosophy of language. It is also known as Russells Theory of Descriptions, in short, Russell argued that the syntactic form of descriptions is misleading, as it does not correlate their logical and/or semantic architecture. It has been argued, for example, that RTD largely underpinned Russells theory of sense-data, since the first development of the theory in Russells 1905 paper On Denoting, RTD has been hugely influential and well-received within the philosophy of language. However, it has not been without its critics, in particular, the philosophers P. F. Strawson and Keith Donnellan have given notable, well known criticisms of the theory. Such developments have themselves been criticised, and debate continues, Bertrand Russells theory of descriptions was initially put forth in his 1905 essay On Denoting, published in the journal of philosophy Mind. Phrases which denote one definite object, for example the present President of the U. S. A. We need not know which object the phrase refers to for it to be unambiguous, for example the cutest kitten is a unique individual, phrases which denote ambiguously, for example, an Aardvark. Indefinite descriptions constitute Russells third group, Descriptions most frequently appear in the standard subject-predicate form. Russell put forward his theory of descriptions to solve a number of problems in the philosophy of language, the two major problems are co-referring expressions and non-referring expressions. The problem of co-referring expressions originated primarily with Gottlob Frege as the problem of informative identities, the problem of non-referring expressions is that certain expressions that are meaningful do not truly refer to anything. For example, by any dog is annoying it is not meant that there is an individual dog, namely any dog. Thus, what Russell wants to avoid is admitting mysterious non-existent entities into his ontology, normally, propositions of the subject-predicate form are said to be true if and only if the subject is in the extension of the predicate. But, there is currently no Emperor of Kentucky, so, since the subject does not exist, it is not in the extension of either predicate. Thus, it appears that this is a case in which the law of excluded middle is violated, Russell analyses definite descriptions similarly to indefinite descriptions, except that the individual is now uniquely specified. Take as an example of a description the sentence the current Emperor of Kentucky is gray. It is instead analysed as there is one unique thing such that it is the morning star, thus, strictly speaking, the two expressions the morning star. and the evening star. Are not synonymous, so it makes sense that they cannot be substituted and this solves Gottlob Freges problem of informative identities. Since the phrase the current Emperor of Kentucky is gray is not a referring expression, the denials of such propositions are true, but in these cases the Emperor of Kentucky has a secondary occurrence
36.
Chess
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Chess is a two-player strategy board game played on a chessboard, a checkered gameboard with 64 squares arranged in an eight-by-eight grid. Chess is played by millions of people worldwide, both amateurs and professionals, each player begins the game with 16 pieces, one king, one queen, two rooks, two knights, two bishops, and eight pawns. Each of the six piece types moves differently, with the most powerful being the queen, the objective is to checkmate the opponents king by placing it under an inescapable threat of capture. To this end, a players pieces are used to attack and capture the opponents pieces, in addition to checkmate, the game can be won by voluntary resignation by the opponent, which typically occurs when too much material is lost, or if checkmate appears unavoidable. A game may result in a draw in several ways. Chess is believed to have originated in India, some time before the 7th century, chaturanga is also the likely ancestor of the Eastern strategy games xiangqi, janggi and shogi. The pieces took on their current powers in Spain in the late 15th century, the first generally recognized World Chess Champion, Wilhelm Steinitz, claimed his title in 1886. Since 1948, the World Championship has been controlled by FIDE, the international governing body. There is also a Correspondence Chess World Championship and a World Computer Chess Championship, online chess has opened amateur and professional competition to a wide and varied group of players. There are also many variants, with different rules, different pieces. FIDE awards titles to skilled players, the highest of which is grandmaster, many national chess organizations also have a title system. However, these are not recognised by FIDE, the term master may refer to a formal title or may be used more loosely for any skilled player. Until recently, chess was a sport of the International Olympic Committee. Chess was included in the 2006 and 2010 Asian Games, since the 1990s, computer analysis has contributed significantly to chess theory, particularly in the endgame. The computer IBM Deep Blue was the first machine to overcome a reigning World Chess Champion in a match when it defeated Garry Kasparov in 1997, the rise of strong computer programs that can be run on hand-held devices has led to increasing concerns about cheating during tournaments. The official rules of chess are maintained by FIDE, chesss international governing body, along with information on official chess tournaments, the rules are described in the FIDE Handbook, Laws of Chess section. Chess is played on a board of eight rows and eight columns. The colors of the 64 squares alternate and are referred to as light, the chessboard is placed with a light square at the right-hand end of the rank nearest to each player
![[\bar p,\bar\xi, N(\bar\xi)]](https://wikimedia.org/api/rest_v1/media/math/render/svg/2280fc5b18f2a18924aeac15d592429f9a30389c)
