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61 results for "godel"
On a Gödel's misjudgment By Giuseppe Raguní
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The fundamental aim of the paper is to correct an harmful way to interpret a Gödel's erroneous remark at the Congress of Königsberg in 1930. Despite the Gödel's fault is rather venial,... More > its misreading has produced and continues to produce dangerous fruits, as to apply the incompleteness Theorems to the full second-order Arithmetic and to deduce the semantic incompleteness of its language by these same Theorems. The first three paragraphs are introductory and serve to define the languages inherently semantic and its properties, to discuss the consequences of the expression order used in a language and some question about the semantic completeness: in particular is highlighted the fact that a non-formal theory may be semantically complete despite using a language semantically incomplete. Finally, an alternative interpretation of the Gödel's unfortunate comment is proposed.< Less
Lucky 13 By Ethan Godel
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The story of the 13 colonies.
Lucky 13 By Ethan Godel
eBook (PDF): $5.00
The story of the 13 colonies.
Gödel Versus Wittgenstein By Mike Hockney
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Perhaps nothing has been more misinterpreted than Gödel’s incompleteness theorems. Stephen Hawking, adopting the popular misconception, said, “Thus mathematics is either... More > inconsistent, or incomplete. The smart money is on incomplete.” If mathematics is tautology, as Wittgenstein said, mathematics cannot be inconsistent and/or incomplete, and so Gödel’s work cannot be about mathematics. If mathematics is not tautological, mathematics is mired in inconsistency and/or incompleteness, just as Stephen Hawking said, hence is unreliable. If mathematics is non-ontological, it cannot say anything about reality. If mathematics is ontological, it’s the only thing that can say anything true about reality. There can’t be a world where math is a bit true and a bit false. Either the world is wholly mathematical – in which case math and not science is how we must study the world – or the world isn’t mathematical at all, in which case it’s absurd for science to use math.< Less
The Gödel's legacy: revisiting the Logic By giuseppe raguní
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ABSTRACT: Some common fallacies about fundamental themes of Logic are exposed: the First and Second incompleteness Theorem interpretations, Chaitin’s various superficialities and the usual... More > classification of the axiomatic Theories in function of its language order. KEYWORDS: Incompleteness, undecidability, semantic completeness, categoricity, randomness, Chaitin's constant, first and second order languages, consistency.< Less
The Godel Incompleteness Theorem: Is it a True Theorem? By Lloyd Miller
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Essay. Non-technical. Expresses and explains the controversial viewpoint that the apparently established theorem is not really a true theorem. The author is particularly interested in the present... More > consensus of opinion, whether everyone who has any interest and understanding of the theorem, really agrees, based on his own understanding, that it is a true theorem, as is the case with real mathematics. Or is it that, in this case, which is sometimes called metamathematics, mathematicians just go along with it, or let it slide, based on what they're told to believe? Who decides the issue?< Less
The Godel Incompleteness Theorem: Is It a True Theorem? By Lloyd Miller
eBook (ePub): $2.99
Essay. Non-technical. Expresses and explains the controversial viewpoint that the apparently established theorem is not really a true theorem. The author is particularly interested in the present... More > consensus of opinion, whether everyone who has any interest and understanding of the theorem, really agrees, based on his own understanding, that it is a true theorem, as is the case with real mathematics. Or is it that, in this case, which is sometimes called metamathematics, mathematicians just go along with it, or let it slide, based on what they're told to believe Who decides the issue< Less
La proposizione di Gödel By Francesca Guidi
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Dal 1931 ad oggi, i teoremi di incompletezza di Gödel continuano ad affascinare. Più che mai attuali, essi sono invocati, a torto o a ragione, nei dibattuti temi dell'intelligenza... More > artificiale, attizzando le speranze tanto di chi crede nella costruibilità di una mente meccanica, che di chi la nega. Famosi autori infatti, come Penrose (Ombre della mente) e Hofstadter (Gödel, Escher, Bach) rivisitano i teoremi oggi, e con opposti intenti.Tuttavia di fronte alla infinita diatriba così innescata, lo schivo Gödel sarebbe forse più sconcertato che soddisfatto.Tuttavia di fronte alla infinita diatriba così innescata, lo schivo Gödel sarebbe forse più sconcertato che soddisfatto.< Less
La proposizione di Gödel By Francesca Guidi
eBook (PDF): $1.64
Dal 1931 ad oggi, i teoremi di incompletezza di Gödel continuano ad affascinare. Più che mai attuali, essi sono invocati, a torto o a ragione, nei dibattuti temi dell'intelligenza... More > artificiale, attizzando le speranze tanto di chi crede nella costruibilità di una mente meccanica, che di chi la nega. Famosi autori infatti, come Penrose (Ombre della mente) e Hofstadter (Gödel, Escher, Bach) rivisitano i teoremi oggi, e con opposti intenti.Tuttavia di fronte alla infinita diatriba così innescata, lo schivo Gödel sarebbe forse più sconcertato che soddisfatto.Tuttavia di fronte alla infinita diatriba così innescata, lo schivo Gödel sarebbe forse più sconcertato che soddisfatto.< Less
Fathoming Gödel: An Examination of Kurt Gödel's 1931 Paper: On Formally Undecidable Propositions of Principia Mathematica and Related Systems 1 By James Spinosa
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A short e-book with a very long title Fathoming Gödel: an Examination of Kurt Gödel’s 1931 Paper: On Formally Undeciable Propositions of Principia Mathematica and Related Systems 1. ... More > The title of my e-book includes the title of Kurt Gödel’s 1931 paper, and the title of his 1931 paper includes the title of Bertrand Russell and Alfred North Whitehead’s monumental work Principia Mathematica, the title of which harkens back to Isaac Newton’s Philosophiae Naturalis Principia Mathematica. I remember in high school someone lent me Ernest Nagel and James R. Newman’s book Gödel’s Proof published in 1958. At the time I was quite impressed and thought that if I kept studying assiduously I would one day understand the complex mathematics present in that text. It seems that Gödel’s proofs have had an aura of mystery around them for quite sometime. In high school I believed that Gödel had discovered something profound about the nature of reality and about the limits of human understanding. Now I think he is a fraud.< Less