By Dugald Stewart
This Elibron Classics publication is a facsimile reprint of a 1816 variation by means of Archibald Constable & Co., Edinburgh.
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Additional info for Elements of the Philosophy of the Human Mind:
Example 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.