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The Lesson Of Frege

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Posted by Harvey on May 10, 2002 19:26:57 UTC

I want to reply, but I have limited time. So, phrases can come out incorrect. But, I'm the kind of person that makes mistakes and see no loss of face in correcting them. I think we become stronger by not only be admitting to our mistakes, but trying to see them so that we can correct them.

One inspirational story of this sort (on the more dramatic side) is when Gottlob Frege finished his logical analysis of mathematics showing that it can be derived from a rudimentary form of set theory. Betrand Russell, as a young unheard of logician, heard of Frege's manuscript and read it. He wrote the famous Frege and told him that there was a self-referent paradox that defeated his Axiom V. Frege was distraught as his manuscript was going into publication. He mentioned the paradox (later to be called Russell's paradox) and said that there could be no greater shake-up to a scientist than to find a fundamental error in one's theory right at the time of publication. Nevertheless, he said he thought that the study of logic and mathematics would benefit from this paradox finding. Which, of course, is what happened. The period that followed was a whole analysis of paradoxes and their effects on formal systems (e.g., mathematics). I suppose it even cumulated with Gödel's discoveries. Frege, what a great philosopher and logician and insightful person he was.

I digress...

Warm regards, Harv

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