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In this article, Lucas maintains the falseness of Mechanism - the attempt to explain minds as machines - by means of Incompleteness Theorem of Gödel. Gödel’s theorem shows that in any system consistent and adequate for simple arithmetic there are formulae which cannot be proved in the system but that human minds can recognize as true; Lucas points out in his turn that Gödel’s theorem applies to machines because a machine is the concrete instantiation of a formal system: therefore, for (...) |
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In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, Godel’s Proof by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy (...) |
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Winner of the Wolf Prize for his contribution to our understanding of the universe, Penrose takes on the question of whether artificial intelligence will ever ... |
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Karl Raimund Poppers (1902-1994) Hauptwerk, die Logik der Forschung (1934), gilt als Grundlagenwerk des kritischen Rationalismus. Der kritische Rationalismus zeigt, warum unser Wissen fehlbar ist und versteht den Erkenntnisfortschritt als Resultat von Hypothesenbildung und -widerlegung. Der Sammelband orientiert sich an der Gliederung der Logik der Forschung. Seine Beiträge kommentieren die jeweiligen Themen nach aktueller Forschungslage. |
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The essay analyses the importance and the limits of Evolutionary Epistemology . Firstly, the history of EE is shortly described - especially its history in the last century. Secondly, its main arguments are reproduced. Thirdly, the points are treated in which EE really signifies a progress in comparison with traditional epistemology. Fourthly, however, it is shown that it does not solve at all the central problem of epistemology - the validity claim of knowledge. Only a broader philosophical framework - that (...) |
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Gödei's Theorem seems to me to prove that Mechanism is false, that is, that minds cannot be explained as machines. So also has it seemed to many other people: almost every mathematical logician I have put the matter to has confessed to similar thoughts, but has felt reluctant to commit himself definitely until he could see the whole argument set out, with all objections fully stated and properly met. This I attempt to do. |
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A young scientist and mathematician explores the mystery and complexity of human thought processes from an interdisciplinary point of view. |
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The essay analyses the importance and the limits of Evolutionary Epistemology (EE). Firstly, the history of EE is shortly described — especially its history in the last century. Secondly, its main arguments are reproduced. Thirdly, the points are treated in which EE really signifies a progress in comparison with traditional epistemology. Fourthly, however, it is shown that it does not solve at all the central problem of epistemology — the validity claim of knowledge. Only a broader philosophical framework — that (...) |
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The law of gravitation, an example of physical law The relation of mathematics to physics The great conservation principles Symmetry in physical law The distinction of past and future Probability and uncertainty: the quantum mechanical view of nature Seeking new laws. |
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Skeptiker aller Schattierungen nicht gern zur Kenntnis, daft sie ihren Standpunkt nicht beweisen konnen. Eine solche komplexe Feststellung provoziert geradezu das emporte Aufbegehren: "Dies kann doch unmoglich dein letztes Wort sein. Irgendeine Losung in der einen oder anderen Richtung muB es doch geben!" Dazu kann ich nur sagen: "Diese,Losung' hast du jederzeit in der Hand: Entscheide dich!" Hier trage ich allerdings an einer gewissen, bei man chen Lesern entstandenen Begriffsverwirrung vermutlich selbst Schuld. Obwohl es mir schien, daB aus dem jeweiligen (...) |
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