Science vs. Religion: (Chapter One) (Humans)

by David Turell , Monday, February 14, 2011, 00:58 (4827 days ago) @ xeno6696

I have only just begun, but right away I wanted to clarify something. On pg 15, where you reference Godel's theorem, I need to correct what it seems Paul Davies was suggesting. Of course I'm correcting him once-removed.
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> The line is thus: "Godel's Theorem (1931) is proof that not evetything can be explained: he conclusively demonstrated "that mathematical statements existed for which no systematic procedure could determine whether they are true or false." 
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> I don't know Davies, but his generalization here is wrong--and dangerously so. 
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> Godel's incompleteness theorems (there are two, the second makes the first stronger) states that for every set of theorems obtained from an axiomatic system using the natural numbers there will be one theorem that is true, but it will not be derivable from any theorem in the set. 
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> In his own words: "For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent."
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> In plain terms, no formal axiomatic theory can be both consistent and complete.-We are dealing with my very incomplete math background. I've recently bought a calculus course to put on my computer and study.