Philosophy of science

From: Zach Newton (zbnewton@mindspring.com)
Tue Oct 24 19:40:59 2000


Below is a capture of a post found on another board.

With hope for your indulgence, it seems worthy of sharing. ---------------------------------------------------------------

A little history of science lesson (specifically history of --------------------------------------------------------------- mathematics). ---------------------------------------------------------------

Back around the turn of the century, there was a belief that it would be possible to construct a "theorem machine" that would prove any proposition in mathematics true or false. The finest minds in mathematics were all in agreement.

Well, along came a 23 year old mathematician named Godel, who proved that there were statements about arithematic that could not be proved true or false, i.e. arithematic is either incomplete or inconsistent. Not only that, it could not be patched up by adding any finite number of new axioms. If this was true about something as simple as arithematic, then the whole notion of a "theorem machine" was absurd.

This was so contrary to the foundations of mathematics as understood at the time that the greatest mathematician of the time, David Hilbert, turned on Godel with a vengence that put Godel in a mental institution. Years later, Godel would come out, take a look around, shake his head "uh-uh", and go back in.

Hilbert eventually realized that Godel was right, but it was too late for Godel.

Now if something as simple as fundamental as arithematic is so different from what we believed, isn't it possible that our "understanding" of "hard science" will continue to come under fundamental change, as has been the case throughout history?

snip

Poster (elsewhere): Harry Pierson -------------------------------------------------------------------------------------------------------------------------

Zach Newton ------------------------------------------------------------------------------------------------------------------------- Z. B. Newton, III, M.D. ------------------------------------------------------------------------------------------------------------------------- Atlanta/Gyn





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