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Mathematics Expert - Theory Help Required

Need help with the 'theories'

     
7:36 pm on Apr 18, 2003 (gmt 0)

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Hi all.

Well, Ive taken a short break from a dinner party to ask this question:

My friend tells me that there is some inconsistency in mathmatical theory, though she cant' give me a good example.

I thought 1+1=2 and all maths was basically that 'with knobs on'?

So, if there are theoretical inconsistencies or differences of opinion, would someone be kind enough to 'rough it out' for a non scientist?

Many thanks.... ;)

Nick

8:02 pm on Apr 18, 2003 (gmt 0)

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Gödel's theorem...

It's not quite easy to grasp. I recommend the excellent book "Gödel, Escher, Bach - an Eternal Golden Braid" by Douglas Hofstadter.

It is not really about "1+1=2"; it basically says that it's not possible to have a system that is both complete and consistent.

8:04 pm on Apr 18, 2003 (gmt 0)

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There is no such thing as 'mathematical theory' per se. There are mathematical theories of 'something' e.g. the mathematical theory of knots or the mathematical theory of networks etc., etc. So I am afraid your friend’s statement, as you quoted it, is meaningless :(


9:03 pm on Apr 18, 2003 (gmt 0)

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One way to express this is that it's possible to form a statement that cannot be either proved or disproved. Even though the statement is not ambiguous -- it has a "truth value" of either true or false -- its truth or falsehood still can't be proved within the system. Now that's quite an unexpected result.

I just finished Stephen Wolfram's recent book "A New Kind of Science" -- highly recommended. He gets into this area of completeness and consistency with some real intensity - and introduces some remarkable insights that he feels will change the way we do science altogether, and he just might be right.

The book can appear foreboding at nearly 1200 pages, but it is written in common English, and not formal math. Amazing diagrams.

10:22 pm on Apr 18, 2003 (gmt 0)

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OK, you wanted an example and I'll give you a tortoise [geocities.com]'s opinion. (Just found it! Thank you for your suggestion... I had looked for it before, not finding it and forgetting about it)
10:28 pm on Apr 18, 2003 (gmt 0)

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Try this on the Study of Inconsistencies in Mathematics [plato.stanford.edu]

And may the Lord have mercy on your soul ;)

9:08 pm on Apr 19, 2003 (gmt 0)

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the key thing is that 1+1=2 is arithmetic...and by and large mathematicians don't do arithmetic...they send that to engineers since it's far too applicable to the real world to be of any possible interest to a mathematician

what mathematicians like is asking why 1+1=2 and how you might go about making it be something else...which, of course, lends itself beautifully to inconsistency, argument, and TV documentaries...all the things that make the world of academia go round