By Jesus Mosterin, Roberto Torretti
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Extra resources for Diccionario de Logica y Filosofia de la Ciencia
Sample text
Para ello, cada uno debe administrar sus estima ciones según la regla de condicionaUxación cuya versión más simple ilustra mos enseguida. Según el bayesianismo, un agente racional X asigna a cada proposición Q la probabilidad p(0 ; la función p se ajusta a los principios del cálculo de r k g b a b i u d a d e s (de modo que p(-i0 = 1 - p{0 ), pero, por lo demás, es completamente arbitraria. Si p{//) y p(/fl/7) sort las probabilidades que X asigna respectivamente a la hipótesis H y al resultado experimental E bajo el supuesto de que H sea verdadera, entonces, según el teorema de Ba yes, la probabilidad de //, dada la verdad de E, es La regla de condicional ización prescribe que, al conocer la verdad de E, el agente X reemplace la función p por la función p', definida por p'(//) = \>(H\E) para cada hipótesis H.
Consiste dicho conflicto en la posibilidad de demostrar tesis contradictorias concernientes a (i) la duración y extensión finitas o infinitas de! Universo, (¡i) la divisibilidad finita o infinita de la materia, (iii) el determinismo y la li bertad y (iv) la contingencia o necesidad del acontecer. El propio Kánt inicia la práctica de llamar antinomias a cada uno de estos pares de tesis contra dictorias. Ella da lugar más tarde al uso generalizado de antinomia para de signar cualquier contradicción reputada fundamental e insuperable, y espe cialmente las surgidas en la teoría de conjuntos a fines del siglo xix, aunque en este diccionario se ha preferido llamarlas paradojas, conforme al uso pre valeciente hoy ( / paradoja dp, B urau -Borti, paradoja dp.
Entre los dos, Gödel y Cohen demostraron que el axioma ele elección es independiente de los otros axiomas. Por tanto, po demos aceptarlo o rechazarlo sin peligro de caer en contradicciones. Si ac tualmente la mayoría de los matemáticos lo aceptan, ello se debe sobre todo a su notable fecundidad. No solo es imprescindible para desarrollar la teoría de los cardinales transfinitos, sino que encuentra también múltiples aplica ciones en el álgebra, la topología y la teoría de la medida. axioma de cxtensionaíidad (A.