Una introducción magistral a la vida y pensamiento del hombre que transformó para siempre nuestra concepción de las matemáticas. Se considera a Kurt Gödel el lógico más importante desde Aristóteles. Su monumental teorema de la incompletitud demuestra que en cualquier sistema formal de aritmética existen proposiciones verdaderas que, sin embargo, no pueden demostrarse. Este resultado creó una conmoción mucho más allá de las matemáticas, poniendo en duda nuestra concepción de la naturaleza y la mente. Rebecca Goldstein, novelista y filósofa, explica la visión filosófica que inspira las matemáticas de Gödel, y revela el error en las interpretaciones de su teorema por parte de los pensamientos filosóficos entonces en boga, desde el positivismo al postmodernismo. Irónicamente, tanto Gödel como su íntimo amigo y colega en Princeton, Einstein, se sentían exiliados intelectuales justo cuando sus trabajos eran aclamados como los más importantes del siglo XX. Para Gödel esta sensación de aislamiento tuvo unas consecuencias trágicas. Este libro, lúcido y accesible, permite al lector comprender el teorema de Gödel, dando vida al mismo tiempo a este genio excéntrico y torturado y a su mundo. “En su libro penetrante, accesible y magníficamente escrito, Rebecca Goldstein no sólo explora el trabajo de uno de los más grandes matemáticos, sino también la relación de la mente humana con el mundo que la rodea.” Alan Lightman, autor de Einstein's Dreams. Traducción de Víctor Úbeda Fernández
A portrait of the eminent twentieth-century mathematician discusses his theorem of incompleteness, relationships with such contemporaries as Albert Einstein, and untimely death as a result of mental instability and self-starvation.
Now, in the first book for a general audience on this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life.
An introduction to the work of the mathematical logician Kurt Godel, which guides the reader through his Theorem of Undecidability and his theories on the completeness of logic, the incompleteness of numbers and the consistency of the axiom ...
... Marilyn vos, 290 Scepticism, Rules, and Language (Hacker and Gordon), 327 Schindler, Oskar, 312 Schopenhauer, Arthur, 49, 253 Schrödinger, Erwin, 228,233,283 Schwartz, Stephen, 324 Schweitzer, Albert, 307 spirituality, 105,108, 112, ...
First Published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.
The inhabitants of the Platonic mathematical world are to be simply those mathematical entities or assertions whose meanings and validity are indeed objective and unambiguous. Moreover, as we shall see, the arguments that I give will, ...
This shows that Hilbert's proposal to prove just the simple consistency of a formal system S, if one should succeed in it, would not rule out there being in S false theorems — like ~xIIR(x, q) in PK* if PK is simply consistent. Godel ...
Frege’s book, translated in its entirety, begins the present volume. The emergence of two new fields, set theory and foundations of mathematics, on the borders of logic, mathematics, and philosophy, is depicted by the texts that follow.
This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics.
From his famous Incompleteness Theorem, which shook the foundations of mathematical truth, to his perilous escape from Nazi Vienna, this book weaves together his creative genius, mental illness, and idealism in the face of adversity.