How To Use Godel In A Sentence
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Graham Priest, a very very clever logician, has done some work on reformulating an arithmetic using paraconsistent logics to allow for the Godel paradox to be solved within the system.
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“[T] he formation within geological time of a human body,” Kurt Gödel remarked in conversation with Hao Wang, “by the laws of physics (or any other laws of similar nature), starting from a random distribution of elementary particles and the field, is as unlikely as the separation by chance of the atmosphere into its components.”
Think Progress » Poll: Large Number Of Texans Doubt The Theory Of Evolution, Believe In Human-Dinosaur Coexistence
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Godel made an analogy between optical illusions in the physical world and antinomies like Russell's paradox in the mathematical realm.
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Soon it dawned on a few insightful souls, Gödel foremost among them, that this way of looking at things opened up a brand-new branch of mathematics — namely, metamathematics.
Incompatible Arrows, III: Lewis Carroll
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Gödel proved inductively that every primitive recursive function can be simply represented in first-order number theory.
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Moreover, the whole point of Godel is that any (consistent, and moderately strong) first order system has true but unprovable statements.
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The Godel Incompleteness Theorem applies only to formal logic systems axiomatized in a certain way.
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Given that we are quoting Godel, I assumed that we were sticking to standard binary logic systems.
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By operationalizing Godel and set theory, Badiou's rationalism makes no concessions at all to the worldly or to the empirical.
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By operationalizing Godel and set theory, Badiou's rationalism makes no concessions at all to the worldly or to the empirical.
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There is a theorem proved by Kurt Godel in 1931, which is the Incompleteness Theorem for mathematics.
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Furthermore, Godel proved that any mathematical system of proofs must be either incomplete (not able to determine the truth or falsehood of certain statements) or contradictory.
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Fraenkel, von Neumann, Bernays and Gödel are all important figures in this development.
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He also examined the consistency of certain propositions in Gödel's system of axiomatic set theory.
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Moreover, whilst Peano arithmetic is axiomatizable, there is a particular model of Peano arithmetic, whose theory is typically referred to as Number theory, which Godel demonstrated to be undecidable and non-axiomatizable.
Archive 2009-06-01
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And in this smooth manner he eased Gödel into conversation.
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Godel showed that in any formal system adequate for number theory there is an undecidable formula, that is, a formula such that neither it nor its negation can be proved.
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In 1934 Gödel gave a series of lectures at Princeton entitled On undecidable propositions of formal mathematical systems.
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Moreover, whilst Peano arithmetic is axiomatizable, there is a particular model of Peano arithmetic, whose theory is typically referred to as Number theory, which Godel demonstrated to be undecidable and non-axiomatizable.
Archive 2009-06-01
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Was Godel correct "that the formation within geological times of a human body by the laws of physics (or any other law of a similar nature) starting from a random distribution of the elementary particles and the field, is about as unlikely as the separation by chance of the atmosphere into its components?
2009 November - Telic Thoughts
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According to name drop 1, name drop 2 bogus reference 1 and bogus reference 2 embrace the Godellian Quantum bijective ontological entanglement love dynamic resulting from entanglement with holographic universe.
New Scientist - Online News
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Gödel showed, in 1940, that the Axiom of Choice cannot be disproved using the other axioms of set theory.
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The present paper points out the universal sense of the theory of Godel that there is widely the winding of meaning in the system of vocabulary.
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There is a theorem proved by Kurt Godel in 1931, which is the Incompleteness Theorem for mathematics.
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Recall that, for Godel, mathematical intuition represents some sort of relationship between humans and the non-physical, mathematical realm.
