1.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times

2.
Philosophy of science
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Philosophy of science is a branch of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of theories. This discipline overlaps with metaphysics, ontology, and epistemology, for example, in addition to these general questions about science as a whole, philosophers of science consider problems that apply to particular sciences. Some philosophers of science also use contemporary results in science to reach conclusions about philosophy itself, Karl Popper and Charles Sanders Pierce moved on from positivism to establish a modern set of standards for scientific methodology. Subsequently, the coherentist approach to science, in which a theory is validated if it makes sense of observations as part of a coherent whole, became prominent due to W. V. Quine and others. Some thinkers such as Stephen Jay Gould seek to ground science in axiomatic assumptions, another approach to thinking about science involves studying how knowledge is created from a sociological perspective, an approach represented by scholars like David Bloor and Barry Barnes. Finally, a tradition in continental philosophy approaches science from the perspective of an analysis of human experience. Philosophies of the particular sciences range from questions about the nature of time raised by Einsteins general relativity, a central theme is whether one scientific discipline can be reduced to the terms of another. That is, can chemistry be reduced to physics, or can sociology be reduced to individual psychology, the general questions of philosophy of science also arise with greater specificity in some particular sciences. For instance, the question of the validity of scientific reasoning is seen in a different guise in the foundations of statistics, the question of what counts as science and what should be excluded arises as a life-or-death matter in the philosophy of medicine. Distinguishing between science and non-science is referred to as the demarcation problem, for example, should psychoanalysis be considered science. How about so-called creation science, the multiverse hypothesis, or macroeconomics. Karl Popper called this the question in the philosophy of science. However, no unified account of the problem has won acceptance among philosophers, Martin Gardner has argued for the use of a Potter Stewart standard for recognizing pseudoscience. Early attempts by the logical positivists grounded science in observation while non-science was non-observational, Popper argued that the central property of science is falsifiability. That is, every genuinely scientific claim is capable of being proven false, a closely related question is what counts as a good scientific explanation. In addition to providing predictions about events, society often takes scientific theories to provide explanations for events that occur regularly or have already occurred. One early and influential theory of scientific explanation is the deductive-nomological model and it says that a successful scientific explanation must deduce the occurrence of the phenomena in question from a scientific law

3.
Germany
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Germany, officially the Federal Republic of Germany, is a federal parliamentary republic in central-western Europe. It includes 16 constituent states, covers an area of 357,021 square kilometres, with about 82 million inhabitants, Germany is the most populous member state of the European Union. After the United States, it is the second most popular destination in the world. Germanys capital and largest metropolis is Berlin, while its largest conurbation is the Ruhr, other major cities include Hamburg, Munich, Cologne, Frankfurt, Stuttgart, Düsseldorf and Leipzig. Various Germanic tribes have inhabited the northern parts of modern Germany since classical antiquity, a region named Germania was documented before 100 AD. During the Migration Period the Germanic tribes expanded southward, beginning in the 10th century, German territories formed a central part of the Holy Roman Empire. During the 16th century, northern German regions became the centre of the Protestant Reformation, in 1871, Germany became a nation state when most of the German states unified into the Prussian-dominated German Empire. After World War I and the German Revolution of 1918–1919, the Empire was replaced by the parliamentary Weimar Republic, the establishment of the national socialist dictatorship in 1933 led to World War II and the Holocaust. After a period of Allied occupation, two German states were founded, the Federal Republic of Germany and the German Democratic Republic, in 1990, the country was reunified. In the 21st century, Germany is a power and has the worlds fourth-largest economy by nominal GDP. As a global leader in industrial and technological sectors, it is both the worlds third-largest exporter and importer of goods. Germany is a country with a very high standard of living sustained by a skilled. It upholds a social security and universal health system, environmental protection. Germany was a member of the European Economic Community in 1957. It is part of the Schengen Area, and became a co-founder of the Eurozone in 1999, Germany is a member of the United Nations, NATO, the G8, the G20, and the OECD. The national military expenditure is the 9th highest in the world, the English word Germany derives from the Latin Germania, which came into use after Julius Caesar adopted it for the peoples east of the Rhine. This in turn descends from Proto-Germanic *þiudiskaz popular, derived from *þeudō, descended from Proto-Indo-European *tewtéh₂- people, the discovery of the Mauer 1 mandible shows that ancient humans were present in Germany at least 600,000 years ago. The oldest complete hunting weapons found anywhere in the world were discovered in a mine in Schöningen where three 380, 000-year-old wooden javelins were unearthed

4.
Historiography
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Historiography is the study of the methods of historians in developing history as an academic discipline, and by extension is any body of historical work on a particular subject. The historiography of a specific topic covers how historians have studied that topic using particular sources, techniques, beginning in the nineteenth century, with the ascent of academic history, there developed a body of historiographic literature. The extent to which historians are influenced by their own groups, in 2007, of 5,723 faculty in the departments of history at British universities,1,644 identified themselves with social history and 1,425 identified themselves with political history. In the early period, the term historiography meant the writing of history. In that sense certain official historians were given the title Historiographer Royal in Sweden, England, the Scottish post is still in existence. Understanding the past appears to be a human need. What constitutes history is a philosophical question, the earliest chronologies date back to Mesopotamia and ancient Egypt, though no historical writers in these early civilizations were known by name. For the purposes of article, history is taken to mean written history recorded in a narrative format for the purpose of informing future generations about events. Before writing, there was only oral history or oral tradition, in China, the earliest history was recorded in oracle bone script which was deciphered and may date back to around late 2nd millennium BCE. The Zuo Zhuan, attributed to Zuo Qiuming in the 5th century BCE, is the earliest written of narrative history in the world, the Classic of History is one of the Five Classics of Chinese classic texts and one of the earliest narratives of China. It is traditionally attributed to Confucius, zhan Guo Ce was a renowned ancient Chinese historical compilation of sporadic materials on the Warring States period compiled between the 3rd and 1st centuries BCE. Sima Qian was the first in China to lay the groundwork for professional historical writing and his written work was the Shiji, a monumental lifelong achievement in literature. His work influenced every subsequent author of history in China, including the prestigious Ban family of the Eastern Han Dynasty era, traditional Chinese historiography describes history in terms of dynastic cycles. In this view, each new dynasty is founded by a morally righteous founder, over time, the dynasty becomes morally corrupt and dissolute. Eventually, the dynasty becomes so weak as to allow its replacement by a new dynasty, the tradition of Korean historiography was established with the Samguk Sagi, a history of Korea from its allegedly earliest times. It was compiled by Goryeo court historian Kim Busik after its commission by King Injong of Goryeo. It was completed in 1145 and relied not only on earlier Chinese histories for source material, the latter work is now lost. The earliest works of history produced in Japan were the Rikkokushi, the first of these works were the Nihon Shoki, compiled by Prince Toneri in 720

5.
Stephen Hawking
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Hawking was the first to set forth a theory of cosmology explained by a union of the general theory of relativity and quantum mechanics. He is a supporter of the many-worlds interpretation of quantum mechanics. In 2002, Hawking was ranked number 25 in the BBCs poll of the 100 Greatest Britons, Hawking has a rare early-onset, slow-progressing form of amyotrophic lateral sclerosis that has gradually paralysed him over the decades. He now communicates using a single cheek muscle attached to a speech-generating device, Hawking was born on 8 January 1942 in Oxford, England to Frank and Isobel Hawking. Despite their families financial constraints, both attended the University of Oxford, where Frank read medicine and Isobel read Philosophy. The two met shortly after the beginning of the Second World War at a research institute where Isobel was working as a secretary. They lived in Highgate, but, as London was being bombed in those years, Hawking has two younger sisters, Philippa and Mary, and an adopted brother, Edward. In 1950, when Hawkings father became head of the division of parasitology at the National Institute for Medical Research, Hawking and his moved to St Albans. In St Albans, the family were considered intelligent and somewhat eccentric. They lived an existence in a large, cluttered, and poorly maintained house. During one of Hawkings fathers frequent absences working in Africa, the rest of the family spent four months in Majorca visiting his mothers friend Beryl and her husband, Hawking began his schooling at the Byron House School in Highgate, London. He later blamed its progressive methods for his failure to learn to read while at the school, in St Albans, the eight-year-old Hawking attended St Albans High School for Girls for a few months. At that time, younger boys could attend one of the houses, the family placed a high value on education. Hawkings father wanted his son to attend the well-regarded Westminster School and his family could not afford the school fees without the financial aid of a scholarship, so Hawking remained at St Albans. From 1958 on, with the help of the mathematics teacher Dikran Tahta, they built a computer from clock parts, although at school Hawking was known as Einstein, Hawking was not initially successful academically. With time, he began to show aptitude for scientific subjects and, inspired by Tahta. Hawkings father advised him to medicine, concerned that there were few jobs for mathematics graduates. He wanted Hawking to attend University College, Oxford, his own alma mater, as it was not possible to read mathematics there at the time, Hawking decided to study physics and chemistry

6.
David Hilbert
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David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th, Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis, Hilbert adopted and warmly defended Georg Cantors set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems set the course for much of the mathematical research of the 20th century. Hilbert and his students contributed significantly to establishing rigor and developed important tools used in mathematical physics. Hilbert is known as one of the founders of theory and mathematical logic. In late 1872, Hilbert entered the Friedrichskolleg Gymnasium, but, after a period, he transferred to. Upon graduation, in autumn 1880, Hilbert enrolled at the University of Königsberg, in early 1882, Hermann Minkowski, returned to Königsberg and entered the university. Hilbert knew his luck when he saw it, in spite of his fathers disapproval, he soon became friends with the shy, gifted Minkowski. In 1884, Adolf Hurwitz arrived from Göttingen as an Extraordinarius, Hilbert obtained his doctorate in 1885, with a dissertation, written under Ferdinand von Lindemann, titled Über invariante Eigenschaften spezieller binärer Formen, insbesondere der Kugelfunktionen. Hilbert remained at the University of Königsberg as a Privatdozent from 1886 to 1895, in 1895, as a result of intervention on his behalf by Felix Klein, he obtained the position of Professor of Mathematics at the University of Göttingen. During the Klein and Hilbert years, Göttingen became the preeminent institution in the mathematical world and he remained there for the rest of his life. Among Hilberts students were Hermann Weyl, chess champion Emanuel Lasker, Ernst Zermelo, john von Neumann was his assistant. At the University of Göttingen, Hilbert was surrounded by a circle of some of the most important mathematicians of the 20th century, such as Emmy Noether. Between 1902 and 1939 Hilbert was editor of the Mathematische Annalen, good, he did not have enough imagination to become a mathematician. Hilbert lived to see the Nazis purge many of the prominent faculty members at University of Göttingen in 1933 and those forced out included Hermann Weyl, Emmy Noether and Edmund Landau. One who had to leave Germany, Paul Bernays, had collaborated with Hilbert in mathematical logic and this was a sequel to the Hilbert-Ackermann book Principles of Mathematical Logic from 1928. Hermann Weyls successor was Helmut Hasse, about a year later, Hilbert attended a banquet and was seated next to the new Minister of Education, Bernhard Rust

7.
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

8.
Metamathematics
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Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories, emphasis on metamathematics owes itself to David Hilberts attempt to secure the foundations of mathematics in the early part of the 20th Century. Metamathematics provides a mathematical technique for investigating a great variety of foundation problems for mathematics. An important feature of metamathematics is its emphasis on differentiating between reasoning from inside a system and from outside a system, an informal illustration of this is categorizing the proposition 2+2=4 as belonging to mathematics while categorizing the proposition 2+2=4 is valid as belonging to metamathematics. Something similar can be said around the well-known Russells paradox, Metamathematics was intimately connected to mathematical logic, so that the early histories of the two fields, during the late 19th and early 20th centuries, largely overlap. More recently, mathematical logic has often included the study of new pure mathematics, such as set theory, recursion theory and pure model theory, serious metamathematical reflection began with the work of Gottlob Frege, especially his Begriffsschrift. David Hilbert was the first to invoke the term metamathematics with regularity, in his hands, it meant something akin to contemporary proof theory, in which finitary methods are used to study various axiomatized mathematical theorems. Today, metalogic and metamathematics are largely synonymous with each other, the discovery of hyperbolic geometry had important philosophical consequences for Metamathematics. Before its discovery there was just one geometry and mathematics, the idea that another geometry existed was considered improbable, the uproar of the Boeotians came and went, and gave an impetus to metamathematics and great improvements in mathematical rigour, analytical philosophy and logic. Begriffsschrift is a book on logic by Gottlob Frege, published in 1879, Begriffsschrift is usually translated as concept writing or concept notation, the full title of the book identifies it as a formula language, modeled on that of arithmetic, of pure thought. Freges motivation for developing his formal approach to logic resembled Leibnizs motivation for his calculus ratiocinator, Frege went on to employ his logical calculus in his research on the foundations of mathematics, carried out over the next quarter century. As such, this project is of great importance in the history of mathematics and philosophy. One of the inspirations and motivations for PM was the earlier work of Gottlob Frege on logic. PM sought to avoid this problem by ruling out the creation of arbitrary sets. This was achieved by replacing the notion of a set with notion of a hierarchy of sets of different types. Contemporary mathematics, however, avoids paradoxes such as Russells in less unwieldy ways, gödels completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic. It makes a link between model theory that deals with what is true in different models, and proof theory that studies what can be formally proven in particular formal systems. More formally, the theorem says that if a formula is logically valid then there is a finite deduction of the formula

9.
Linguistics
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Linguistics is the scientific study of language, and involves an analysis of language form, language meaning, and language in context. Linguists traditionally analyse human language by observing an interplay between sound and meaning, phonetics is the study of speech and non-speech sounds, and delves into their acoustic and articulatory properties. While the study of semantics typically concerns itself with truth conditions, Grammar is a system of rules which governs the production and use of utterances in a given language. These rules apply to sound as well as meaning, and include componential sub-sets of rules, such as those pertaining to phonology, morphology, modern theories that deal with the principles of grammar are largely based within Noam Chomskys ideological school of generative grammar. In the early 20th century, Ferdinand de Saussure distinguished between the notions of langue and parole in his formulation of structural linguistics. According to him, parole is the utterance of speech, whereas langue refers to an abstract phenomenon that theoretically defines the principles. This distinction resembles the one made by Noam Chomsky between competence and performance in his theory of transformative or generative grammar. According to Chomsky, competence is an innate capacity and potential for language, while performance is the specific way in which it is used by individuals, groups. The study of parole is the domain of sociolinguistics, the sub-discipline that comprises the study of a system of linguistic facets within a certain speech community. Discourse analysis further examines the structure of texts and conversations emerging out of a speech communitys usage of language, Stylistics also involves the study of written, signed, or spoken discourse through varying speech communities, genres, and editorial or narrative formats in the mass media. In the 1960s, Jacques Derrida, for instance, further distinguished between speech and writing, by proposing that language be studied as a linguistic medium of communication in itself. Palaeography is therefore the discipline that studies the evolution of scripts in language. Linguistics also deals with the social, cultural, historical and political factors that influence language, through which linguistic, research on language through the sub-branches of historical and evolutionary linguistics also focus on how languages change and grow, particularly over an extended period of time. Language documentation combines anthropological inquiry with linguistic inquiry, in order to describe languages, lexicography involves the documentation of words that form a vocabulary. Such a documentation of a vocabulary from a particular language is usually compiled in a dictionary. Computational linguistics is concerned with the statistical or rule-based modeling of natural language from a computational perspective, specific knowledge of language is applied by speakers during the act of translation and interpretation, as well as in language education – the teaching of a second or foreign language. Policy makers work with governments to implement new plans in education, related areas of study also includes the disciplines of semiotics, literary criticism, translation, and speech-language pathology. Before the 20th century, the philology, first attested in 1716, was commonly used to refer to the science of language

10.
Robert T. Craig
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Robert T. Craig was on the 1988 founding board of the journal Research on Language and Social Interaction, a position he continues to hold. From 1991 to 1993 Craig was the editor of the International Communication Association journal Communication Theory which has been in continuous publication since 1991. He is currently the editor for the ICA Handbook series, in 2009 Craig was elected as a Lifetime Fellow for the International Communication Association, an organization he was president for in 2004–2005. That work has since translated into French and Russian. In 1995 Robert T. Craig and Karen Tracy published Grounded Practical Theory and this was an attempt by Craig and Tracy to create a methodological model using discourse analysis which will guide the development and assessment of normative theories. This neglect of normative theories limits the usefulness of communication studies. Grounded practical theory is an approach based on Craigs notion of communication as a practical, rather than scientific. The goal of communication as a discipline is to develop normative theories to guide practice. Based on this argument, GPT was developed as a methodologically grounded means of theorizing communication practices, GPT involves reconstructing communicative practices, redescribing those practices in less context-specific terms, and identifying implicit principles which guide the practice. Generally a GPT study begins by looking for troubles or dilemmas endemic to situated interaction and this constitutes the “problem level” and the “grounded” component of the GPT approach. Then, problems are reconstructed concretely and abstractly and matched with the techniques which participants employ for dealing with those problems and this constitutes the “technical level” and is an important part of the theorizing process. Finally, the ideals and standards shaping the practice and how to manage its problems, a methodological approach which is explicitly guided by GPT is action implicative discourse analysis. In 1999 Craig wrote a landmark article Communication Theory as a Field which expanded the conversation regarding disciplinary identity in the field of communication, at that time, communication theory textbooks had little to no agreement on how to present the field or what theories to include in their textbooks. This article has become the foundational framework for four different textbooks to introduce the field of communication. In this article Craig proposes a vision for communication theory that takes a step toward unifying this rather disparate field. In this deliberative process theorists would engage in dialog about the implications of communication theories. In the end Craig proposes seven different traditions of Communication Theory, Craig proposes that these seven suggested traditions of communication theory have emerged through research into communication, and each one has their own way of understanding communication. These seven traditions are, Rhetorical, views communication as the art of discourse