Artículos con la etiqueta ‘metamatemática’

Uncertainty, incompleteness, chance, and design

Por • 30 ene, 2013 • Category: Filosofía

The 20th century has revealed two important limitations of scientific knowledge. On the one hand, the combination of Poincar\’e’s nonlinear dynamics and Heisenberg’s uncertainty principle leads to a world picture where physical reality is, in many respects, intrinsically undetermined. On the other hand, G\»odel’s incompleteness theorems reveal us the existence of mathematical truths that cannot be demonstrated. More recently, Chaitin has proved that, from the incompleteness theorems, it follows that the random character of a given mathematical sequence cannot be proved in general (it is ‘undecidable’). I reflect here on the consequences derived from the indeterminacy of the future and the undecidability of randomness, concluding that the question of the presence or absence of finality in nature is fundamentally outside the scope of the scientific method.



Análisis metamatemático de los números reales

Por • 20 dic, 2012 • Category: Opinion

Postulemos la existencia ideal del conjunto N de todos los números naturales, y, consiguientemente, postulemos que razonar sobre el conjunto N no nos lleva a la contradicción; es fundamental la cuestión siguiente: ¿Se infiere de esa hipótesis la existencia ideal del conjunto potencial {0,1}N, y, por consiguiente, su consistencia lógica?. Sería muy arriesgado, y dejarse engañar por el signo, contestar afirmativamente. […]