Husserl, Carnap y los conceptos de completud en lógica
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Husserl, Carnap y los conceptos de completud en lógica

Husserl, Carnap y los conceptos de completud en lógica


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About the Book

En lógica, la completud indica tanto maximalidad como suficiencia. Por un lado, es la propiedad de las teorías tan fuertes que prueban o refutan cualquier sentencia de su lenguaje. Por otro lado, la completud es una propiedad de las lógicas cuya relación de deducibilidad coincide con la de consecuencia lógica. A principios de la década de 1930, estas propiedades fueron claramente delimitadas por Gödel y Tarski. Sin embargo, hasta unos pocos años antes, el significado del término "completud" era bastante más ambiguo.


Fraenkel y Carnap intentaron resolver esta ambigüedad y distinguieron tres nociones de completud: categoricidad, no bifurcabilidad y decidibilidad. En este sentido, Carnap afirmaba haber demostrado la equivalencia de estas tres nociones. Su estudio es esencial para entender la historia del concepto (o los conceptos) de completud. Recientemente, basándose en ensayos de Hill y Majer, Da Silva, Hartimo y Centrone defienden el papel de la Doppelvortrag de Husserl en el desarrollo de esta historia. Ellos argumentan que las nociones de "teoría relativamente definida" y "teoría absolutamente definida", que se introducen para solucionar los problemas asociados a la ampliación de nuestros sistemas numéricos, pueden interpretarse como "teoría completa" (Da Silva) o "teoría categórica" (Hartimo).


La tesis de este libro es que las intuiciones que subyacen a las ideas de categoricidad, no bifurcabilidad y decidibilidad también están detrás del concepto de "teoría absolutamente definida" de Husserl. Es decir, una teoría absolutamente definida tiene un único modelo, no admite proposiciones independientes y decide la verdad o falsedad de cualquier proposición que se formule en su lenguaje. Para apoyar dicha tesis, se ofrece evidencia textual de la Doppelvortrag, comparándose este texto con los trabajos de Huntington y de Veblen (parecidos a las investigaciones de Husserl, sus artículos fueron publicados a principios del siglo XX) y se muestra que Fraenkel y Carnap citaban a Husserl cuando explican el concepto de decidibilidad.


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Product Details
  • ISBN-13: 9781848903807
  • Publisher: College Publications
  • Publisher Imprint: College Publications
  • Height: 234 mm
  • No of Pages: 232
  • Spine Width: 12 mm
  • Width: 156 mm
  • ISBN-10: 1848903804
  • Publisher Date: 21 Sep 2022
  • Binding: Paperback
  • Language: Spanish
  • Returnable: N
  • Weight: 381 gr


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