Comments on: GĂ¶del’s Theorem’s Philosophical Implications
https://abstractnonsense.wordpress.com/2006/10/19/godels-theorems-philosophical-implications/
Mathematics, liberal politics, and rants about the news of the daySat, 08 Mar 2014 08:42:58 +0000
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By: Brian Coyle
https://abstractnonsense.wordpress.com/2006/10/19/godels-theorems-philosophical-implications/#comment-122697
Sat, 08 Mar 2014 08:42:58 +0000http://abstractnonsense.wordpress.com/2006/10/19/godels-theorems-philosophical-implications/#comment-122697Eight years later, I came across this. Perhaps the author has disappeared. Still, I think something has been missed. Godel’s proof was really a disproof. He showed what could not be asserted. This was, indeed, all the he could do, because, like the system he analyzed, his analysis was on the same plane as what he analyzed. I use the word plane descriptively, but not without reason. The Romans codified Aristotle’s logic in the word explanation, meaning ex-planus, or apart from the plane. Achieving what today we call theory requires a meta-level perspective. But math is unique among sciences, because its reality isn’t concrete. We use the terms inference and evaluation just as physical and social sciences do, but in reference to ideas, not objects, organisms, or processes. Einstein could explain gravity by discovering a new dimension to perceive from. Darwin’s meta-level was also a new way to view time. Explanation that leads to deep theory has this component, which challenges the mathematician. It’s fair to say Stephen Wolfram’s algorithms, and indeed the IT mathematics of Group, Category, and Proof theory, may be meta-level explanations. Set theory wasn’t, which is why Godel matters. Did that stop set theory’s use? No, but it limits is wider applicability.
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