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60 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
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The story of the 13 colonies.
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
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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
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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
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
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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
Su un errore di Gödel By Giuseppe Ragunì
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Lo scopo fondamentale dell'articolo è correggere un grave errore di interpretazione di un inesatto commento di Gödel al congresso di Königsberg del 1930. Malgrado la scorrettezza di... More > Gödel sia assolutamente veniale, la sua erronea lettura ha prodotto e continua a produrre frutti nefasti, come l'applicabilità dei Teoremi d'incompletezza all'Aritmetica del secondo ordine full e la deducibilità, mediante essi, dell'incompletezza semantica di questo linguaggio. I primi tre paragrafi servono da introduzione e se ne approfitta sia per definire i linguaggi intrinsecamente semantici sia per evidenziare il fatto che una Teoria non formale può essere semanticamente completa pur impiegando un linguaggio semanticamente incompleto. Infine si propone un'interpretazione alternativa per l'infelice osservazione di Gödel.< Less