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Certainty
Related concepts and fundamentals:Agnosticism Epistemology Presupposition Probabilityv t e Certainty is perfect knowledge that has total security from error, or the mental state of being without doubt. Objectively defined, certainty is total continuity and validity of all foundational inquiry, to the highest degree of precision. Something is certain only if no skepticism can occur
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Russell's Paradox
In the foundations of mathematics, Russell's paradox
Russell's paradox
(also known as Russell's antinomy), discovered by Bertrand Russell
Bertrand Russell
in 1901, showed that some attempted formalizations of the naïve set theory created by Georg Cantor
Georg Cantor
led to a contradiction. The same paradox had been discovered a year before by Ernst Zermelo
Ernst Zermelo
but he did not publish the idea, which remained known only to David Hilbert, Edmund Husserl, and other members of the University of Göttingen.[citation needed] According to naive set theory, any definable collection is a set. Let R be the set of all sets that are not members of themselves
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Probability Interpretations
The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical tendency of something to occur or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, mathematicians interpret the probability values of probability theory. There are two broad categories[1][2] of probability interpretations which can be called "physical" and "evidential" probabilities. Physical probabilities, which are also called objective or frequency probabilities, are associated with random physical systems such as roulette wheels, rolling dice and radioactive atoms. In such systems, a given type of event (such as a die yielding a six) tends to occur at a persistent rate, or "relative frequency", in a long run of trials. Physical probabilities either explain, or are invoked to explain, these stable frequencies
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Pyrrho
Pyrrho
Pyrrho
of Elis[1] (/ˈpɪroʊ/; Greek: Πύρρων ὁ Ἠλεῖος Pyrron ho Eleios, c. 360 – c. 270 BC) was a Greek philosopher of Classical antiquity
Classical antiquity
and is credited as being the first Greek skeptic philosopher.Contents1 Life 2 Sources on Pyrrho 3 Philosophy3.1 Pyrrhonism4 Indian influences on Pyrrho 5 Influence 6 See also 7 Notes 8 References 9 External linksLife[edit] Pyrrho
Pyrrho
of Elis
Elis
is estimated to have lived from around 365-360 BC until 275-270 BC.[2] Pyrrho
Pyrrho
was from Elis, on the Ionian Sea. Diogenes Laërtius, quoting from Apollodorus of Athens, says that Pyrrho
Pyrrho
was at first a painter, and that pictures by him were exhibited in the gymnasium at Elis
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Acatalepsia
Acatalepsy (from the Greek α̉-, privative, and καταλαμβάνειν, to seize), in philosophy, is incomprehensibleness, or the impossibility of comprehending or conceiving a thing.[1] Acatalepsy is the incomprehensibility of all things. It is the antithesis of the Stoic doctrine of katalepsis or Apprehension.[2] According to the Stoics, katalepsis was true perception, but to the Pyrrhonists and Academic Skeptics, all perceptions were acataleptic, i.e. bore no conformity to the objects perceived, or, if they did bear any conformity, it could never be known.[2] For the Academic Skeptics acatalepsy meant that human knowledge never amounts to certainty, but only to probability.[3] For the Pyrrhonists it meant that knowledge was limited to the appearances (phantasiai) and the pathē
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Ibn Rushd
Ibn Rushd (Arabic: ابن رشد‎; full name Arabic: أبو الوليد محمد ابن احمد ابن رشد‎, translit. ʾAbū l-Walīd Muḥammad Ibn ʾAḥmad Ibn Rushd; 14 April 1126 – 10 December 1198), often Latinized as Averroes (/əˈvɛroʊˌiːz/), was a medieval Andalusian Arab polymath. He wrote on logic, Aristotelian and Islamic philosophy, Islamic theology, the Maliki school of Islamic jurisprudence, psychology, political theory, the theory of Andalusian classical music, geography, mathematics, as well as the medieval sciences of medicine, astronomy, physics, and celestial mechanics. Ibn Rushd was born in Córdoba, Al Andalus (present-day Spain), and died at Marrakesh in present-day Morocco
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Descartes
René Descartes
René Descartes
(/ˈdeɪˌkɑːrt/;[9] French: [ʁəne dekaʁt]; Latinized: Renatus Cartesius; adjectival form: "Cartesian";[10] 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist. Dubbed the father of modern western philosophy, much of subsequent Western philosophy
Western philosophy
is a response to his writings,[11][12] which are studied closely to this day. A native of the Kingdom of France, he spent about 20 years (1629–49) of his life in the Dutch Republic
Dutch Republic
after serving for a while in the Dutch States Army of Maurice of Nassau, Prince of Orange
Prince of Orange
and the Stadtholder
Stadtholder
of the United Provinces
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Meditations On First Philosophy
Meditations on First Philosophy[1] (subtitled In which the existence of God and the immortality of the soul are demonstrated) is a philosophical treatise by René Descartes
René Descartes
first published in 1641 (in Latin). The French translation (by the Duke of Luynes with Descartes' supervision) was published in 1647 as Méditations Métaphysiques. The original Latin title is Meditationes de prima philosophia, in qua Dei existentia et animæ immortalitas demonstratur. The title may contain a misreading by the printer, mistaking animae immortalitas for animae immaterialitas, as suspected already by A. Baillet.[2] The book is made up of six meditations, in which Descartes first discards all belief in things that are not absolutely certain, and then tries to establish what can be known for sure
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Cogito, Ergo Sum
Cogito ergo sum[a] is a Latin philosophical proposition by René Descartes usually translated into English as "I think, therefore I am". The phrase originally appeared in French as je pense, donc je suis in his Discourse on the Method, so as to reach a wider audience than Latin would have allowed.[1] It appeared in Latin in his later Principles of Philosophy. As Descartes explained, "we cannot doubt of our existence while we doubt...." A fuller form, penned by Antoine Léonard Thomas, aptly captures Descartes’s intent: dubito, ergo cogito, ergo sum ("I doubt, therefore I think, therefore I am").[b] The concept is also sometimes known as the cogito.[2] This proposition became a fundamental element of Western philosophy, as it purported to form a secure foundation for knowledge in the face of radical doubt
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Context (language Use)
In semiotics, linguistics, sociology and anthropology, context refers to those objects or entities which surround a focal event, in these disciplines typically a communicative event, of some kind. Context is "a frame that surrounds the event and provides resources for its appropriate interpretation".[1]:2–3 It is thus a relativistic concept, only definable with respect to some focal event, not independently.Contents1 In linguistics 2 In linguistic anthropology 3 Contextual variables 4 See also 5 ReferencesIn linguistics[edit] Verbal context refers to the text or speech surrounding an expression (word, sentence, or speech act). Verbal context influences the way an expression is understood; hence the norm of not citing people out of context
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Anti-foundationalism
Anti-foundationalism (also called nonfoundationalism) is any philosophy which rejects a foundationalist approach. An anti-foundationalist is one who does not believe that there is some fundamental belief or principle which is the basic ground or foundation of inquiry and knowledge.[1]Contents1 Anti-essentialism 2 Totalisation and legitimation 3 Hope and fear 4 Criticism 5 Anti-foundationalists 6 See also 7 References 8 Further reading 9 External linksAnti-essentialism[edit] Anti-foundationalists use logical or historical or genealogical attacks on foundational concepts (see especially Nietzsche and Foucault), often coupled with alternative methods for justifying and forwarding intellectual inquiry, such as the pragmatic subordination of knowledge to practical action.[2] Foucault dismissed the search for a return to origins as Platonic essentialism, preferring to stress the contingent nature of human practices.[3] Anti-foundationalists oppose metaphysical methods
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Inductive Reasoning
Inductive reasoning
Inductive reasoning
(as opposed to deductive reasoning or abductive reasoning) is a method of reasoning in which the premises are viewed as supplying strong evidence for the truth of the conclusion. While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument may be probable, based upon the evidence given.[1] Many dictionaries define inductive reasoning as the derivation of general principles from specific observations, though some sources disagree with this usage.[2] The philosophical definition of inductive reasoning is more nuanced than simple progression from particular/individual instances to broader generalizations. Rather, the premises of an inductive logical argument indicate some degree of support (inductive probability) for the conclusion but do not entail it; that is, they suggest truth but do not ensure it
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Philosophy Of Statistics
The philosophy of statistics involves the meaning, justification, utility, use and abuse of statistics and its methodology, and ethical and epistemological issues involved in the consideration of choice and interpretation of data and methods of statistics.[1]Foundations of statistics involves issues in theoretical statistics, its goals and optimization methods to meet these goals, parametric assumptions or lack thereof considered in nonparametric statistics, model selection for the underlying probability distribution, and interpretation of the meaning of inferences made using statistics, related to the philosophy of probability and the philosophy of science. Discussion of the selection of the goals and the meaning of optimization, in foundations of statistics, are the subject of the philosophy of statistics
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Foundationalism
Foundationalism concerns philosophical theories of knowledge resting upon justified belief, or some secure foundation of certainty such as a conclusion inferred from a basis of sound premises.[1] Its main rival is coherentism, whereby a body of knowledge, not requiring a secure foundation, can be established by the interlocking strength of its components, like a puzzle solved without prior certainty that each small region was solved correctly.[1] Identifying the alternatives as either circular reasoning or infinite regress, and thus exhibiting the regress problem, Aristotle
Aristotle
made foundationalism his own clear choice, positing basic beliefs underpinning others.[2] Descartes, the most famed foundationalist, discovered a foundation in the fact of his own existence and in the "clear and distinct" ideas of reason,[1][2] whereas Locke found a foundation in experience
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Lawrence M. Krauss
Lawrence Maxwell Krauss (born May 27, 1954) is an American-Canadian theoretical physicist and cosmologist who is Foundation Professor of the School of Earth and Space Exploration at Arizona State University, and director of its Origins Project.[2] He is an advocate of the public understanding of science, of public policy based on sound empirical data, of scientific skepticism and of science education, and works to reduce the influence of what he regards as superstition and religious dogma in popular culture.[3] Krauss is the author of several bestselling books, including The Physics
Physics
of Star Trek (1995) and
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Rudolf Carnap
Rudolf Carnap
Rudolf Carnap
(/ˈkɑːrnæp/;[7] German: [ˈkaɐ̯naːp]; May 18, 1891 – September 14, 1970) was a German-born philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle
Vienna Circle
and an advocate of logical positivism. He is considered "one of the giants among twentieth-century philosophers."[8]Contents1 Life and work 2 Logical syntax2.1 The purpose of logical syntax3 Rejection of metaphysics3.1 The function of logical analysis4 Primary source materials 5 Selected publications 6 Filmography 7 See also 8 References 9 Sources 10 Further reading 11 External linksLife and work[edit]Carnap's birthplace in WuppertalCarnap's father had risen from the status of a poor ribbon-weaver to become the owner of a ribbon-making factory
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