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Port-Royal Grammar
The ''Port-Royal Grammar'' (originally ''Grammaire générale et raisonnée contenant les fondemens de l'art de parler, expliqués d'une manière claire et naturelle'', "General and Rational Grammar, containing the fundamentals of the art of speaking, explained in a clear and natural manner") was a milestone in the analysis and philosophy of language. Published in 1660 by Antoine Arnauld and Claude Lancelot, it was the linguistic counterpart to the ''Port-Royal Logic'' (1662), both named after the Jansenist monastery of Port-Royal-des-Champs where their authors worked. The Port-Royal Grammar became used as a standard textbook in the study of language until the early nineteenth century, and it has been reproduced in several editions and translations. In the twentieth century, scholars including Edmund Husserl and Noam Chomsky maintained academic interest in the book. Arnauld and Lancelot's approach to language is historical, comparative, and philosophical. Discussing the essence o ...
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Philosophy Of Language
Philosophy of language refers to the philosophical study of the nature of language. It investigates the relationship between language, language users, and the world. Investigations may include inquiry into the nature of Meaning (philosophy), meaning, intentionality, reference, the constitution of sentences, concepts, learning, and thought. Gottlob Frege and Bertrand Russell were pivotal figures in analytic philosophy's "linguistic turn". These writers were followed by Ludwig Wittgenstein (''Tractatus Logico-Philosophicus''), the Vienna Circle, Logical positivism, logical positivists, and Willard Van Orman Quine. History Ancient philosophy In the West, inquiry into language stretches back to the 5th century BC with philosophers such as Socrates, Plato, Aristotle, and the Stoics. Linguistic speculation predated systematic descriptions of grammar which emerged in India and in Greece. In the dialogue ''Cratylus (dialogue), Cratylus'', Plato considered the question of whether ...
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René Descartes
René Descartes ( , ; ; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and Modern science, science. Mathematics was paramount to his method of inquiry, and he connected the previously separate fields of geometry and algebra into analytic geometry. Descartes spent much of his working life in the Dutch Republic, initially serving the Dutch States Army, and later becoming a central intellectual of the Dutch Golden Age. Although he served a Dutch Reformed Church, Protestant state and was later counted as a Deism, deist by critics, Descartes was Roman Catholicism, Roman Catholic. Many elements of Descartes's philosophy have precedents in late Aristotelianism, the Neostoicism, revived Stoicism of the 16th century, or in earlier philosophers like Augustine of Hippo, Augustine. In his natural philosophy, he differed from the Scholasticism, schools on two major point ...
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Natural Science
Natural science or empirical science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer review and reproducibility of findings are used to try to ensure the validity of scientific advances. Natural science can be divided into two main branches: list of life sciences, life science and Outline of physical science, physical science. Life science is alternatively known as biology. Physical science is subdivided into branches: physics, astronomy, Earth science and chemistry. These branches of natural science may be further divided into more specialized branches (also known as fields). As empirical sciences, natural sciences use tools from the formal sciences, such as mathematics and logic, converting information about nature into measurements that can be explained as clear statements of the "laws of science, laws of nature". Mode ...
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Humanities
Humanities are academic disciplines that study aspects of human society and culture, including Philosophy, certain fundamental questions asked by humans. During the Renaissance, the term "humanities" referred to the study of classical literature and language, as opposed to the study of religion, or "divinity". The study of the humanities was a key part of the secular curriculum in universities at the time. Today, the humanities are more frequently defined as any fields of study outside of natural sciences, social sciences, formal sciences (like mathematics), and applied sciences (or Professional development, professional training). They use methods that are primarily Critical theory, critical, speculative, or interpretative and have a significant historical element—as distinguished from the mainly Empirical method, empirical approaches of science."Humanity" 2.b, ''Oxford English Dictionary'', 3rd ed. (2003). The humanities include the academic study of philosophy, religion, histo ...
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Demarcation Problem
In philosophy of science and epistemology, the demarcation problem is the question of how to distinguish between science and non-science. It also examines the boundaries between science, pseudoscience and other products of human activity, like art and literature and beliefs.. Alternative source/ref> The debate continues after more than two millennia of dialogue among philosophers of science and Scientist, scientists in various fields. The debate has consequences for what can be termed "scientific" in topics such as education and public policy. The ancients An early attempt at demarcation can be seen in the efforts of Greek natural philosophers and medical practitioners to distinguish their methods and their accounts of nature from the mythological or mystical accounts of their predecessors and contemporaries. G. E. R. Lloyd noted that there was a sense in which the groups engaged in various forms of inquiry into nature attempt to "legitimate their own positions", laying " ...
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Predicate (mathematical Logic)
In logic, a predicate is a symbol that represents a property or a relation. For instance, in the first-order formula P(a), the symbol P is a predicate that applies to the individual constant a. Similarly, in the formula R(a,b), the symbol R is a predicate that applies to the individual constants a and b. According to Gottlob Frege, the meaning of a predicate is exactly a function from the domain of objects to the truth values "true" and "false". In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the formula R(a,b) would be true on an interpretation if the entities denoted by a and b stand in the relation denoted by R. Since predicates are non-logical symbols, they can denote different relations depending on the interpretation given to them. While first-order logic only includes predicates that apply to individual objects, other logics may allow predicates that apply to collections of objects defin ...
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Unary Operation
In mathematics, a unary operation is an operation with only one operand, i.e. a single input. This is in contrast to ''binary operations'', which use two operands. An example is any function , where is a set; the function is a unary operation on . Common notations are prefix notation (e.g. ¬, −), postfix notation (e.g. factorial ), functional notation (e.g. or ), and superscripts (e.g. transpose ). Other notations exist as well, for example, in the case of the square root, a horizontal bar extending the square root sign over the argument can indicate the extent of the argument. Examples Absolute value Obtaining the absolute value of a number is a unary operation. This function is defined as , n, = \begin n, & \mbox n\geq0 \\ -n, & \mbox n<0 \end where , n, is the absolute value of n.


Negation



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Phenomenology (philosophy)
Phenomenology is a philosophical study and movement largely associated with the early 20th century that seeks to Subjectivity_and_objectivity_(philosophy), objectively investigate the nature of subjective, consciousness, conscious experience. It attempts to describe the universal features of consciousness while avoiding assumptions about the external world, aiming to describe Phenomenon, phenomena as they appear, and to explore the meaning and significance of lived experience. This approach, while philosophical, has found many applications in qualitative research across different scientific disciplines, especially in the social sciences, humanities, Phenomenology (psychology), psychology, and cognitive science, but also in fields as diverse as health sciences, Phenomenology (architecture), architecture, and Human–computer interaction, human-computer interaction, among many others. The application of phenomenology in these fields aims to gain a deeper understanding of subjectiv ...
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Rudolf Carnap
Rudolf Carnap (; ; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism. Biography Carnap's father rose from being a poor ribbon-weaver to be the owner of a ribbon-making factory. His mother came from an academic family; her father was an educational reformer and her oldest brother was the archaeologist Wilhelm Dörpfeld. As a ten-year-old, Carnap accompanied Wilhelm Dörpfeld on an expedition to Greece. Carnap was raised in a profoundly religious Protestant family, but later became an atheist. He began his formal education at the Barmen Gymnasium (school), Gymnasium and the Gymnasium in Jena. From 1910 to 1914, he attended the University of Jena, intending to write a thesis in physics. He also intently studied Immanuel Kant's ''Critique of Pure Reason'' during a course taught by Bruno Bauch, and was one of t ...
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David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory). He adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented a collection of problems that set a course for mathematical research of the 20th century. Hilbert and his students contributed to establishing rigor and developed important tools used in modern mathematical physics. He was a cofounder of proof theory and mathematical logic. Life Early life and education Hilbert, the first of two children and only son of O ...
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Psychologism
Psychologism is a family of philosophical positions, according to which certain psychological facts, laws, or entities play a central role in grounding or explaining certain non-psychological facts, laws, or entities. The word was coined by Johann Eduard Erdmann as ''Psychologismus'', being translated into English as ''psychologism''.''Stanford Encyclopedia of Philosophy''Psychologism Definition The ''Oxford English Dictionary'' defines ''psychologism'' as: "The view or doctrine that a theory of psychology or ideas forms the basis of an account of metaphysics, epistemology, or meaning; (sometimes) spec. the explanation or derivation of mathematical or logical laws in terms of psychological facts." Psychologism in epistemology, the idea that its problems "can be solved satisfactorily by the psychological study of the development of mental processes", was argued in John Locke's '' An Essay Concerning Human Understanding'' (1690). Other forms of psychologism are logical psycholo ...
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