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

by xeno6696 , Sonoran Desert, Monday, February 14, 2011, 03:37 (4827 days ago) @ David Turell

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.
> > 
> > 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." 
> > 
> > I don't know Davies, but his generalization here is wrong--and dangerously so. 
> > 
> > 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. 
> > 
> > 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."
> > 
> > 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.-David, -Don't be hard on yourself, you were quoting Paul Davies! The only possible error on your part was in taking him at his word; after all, physicists tend to be pretty good at math. This doesn't however, mean they're mathematicians. But I don't consider this a fault of yours.-Hawking for example has long since abandoned the idea of a "theory of everything" after having given much thought about Godel's incompleteness theorem. It is at the centerpiece of my criticism of String Theory. If String Theory is found to be complete, it will necessarily be inconsistent. -Calculus is good--by all means--but in all truth it won't get you to "real" math. (Not that calculus isn't 'real,' only that in most cases a course in calculus is targeted for engineering computations and not for abstract mathematics--ie Godel.) I would suggest this book to build the comprehension needed to tackle more abstract ideas. I can suggest others (and cheap others) beyond that, if it suits you. And if you choose to get that book, get it used... the current list price is atrocious...

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\"Why is it, Master, that ascetics fight with ascetics?\"

\"It is, brahmin, because of attachment to views, adherence to views, fixation on views, addiction to views, obsession with views, holding firmly to views that ascetics fight with ascetics.\"