(May I propose a Philosophy-part in this forum, to prevent me and other laymen from poisoning the Theory part? I sure have a lot of wonderings about this.)
I concur, a philosophy part would be a great addition to this forum.
As far as I understand the logical foundations of mathematics, as outlined in
Principia Mathematica, self-reference (and thereby paradoxes) is avoided by having a hierarchical structure of statements. That is, until Gödels incompleteness theorems proved otherwise. Douglas Hofstadter discusses this at length in his books "I am a Strange Loop" and "Gödel, Escher, Bach". These books are good if you have some basic philosophy training and can stand the pompous writing style of the author. No mathematics above high school level is needed to follow the arguments.
Having said that, I am still convinced that mathematics is the only way to truly communicate objective truths about the nature of nature between pepole. It is just that it becomes a little strange when self-reference and infinities are involved.
Sorry for drifting off topic.
January 05, 2007, 04:19:43 AM
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