A Conversation for 'Principia Mathematica' by Bertrand Russell and Alfred North Whitehead

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Post 1

The Jabberwock

Russel and Whitehead claimed that it was a book that put the whole of mathematics on a totaly formal footing; using it, they claimed, mathematics would become totaly precice and it would be easy to verify if a particular result was true by checking if it obeyed the rules in the book. This was an incredibly ambitious claim, and it raised the obvious question of whether they'd got it right. This was hard to check as it is the least readable book ever written.

Eventualy, Godel showed that they had got it wrong, not by finding a mistake (as that would involve reading the book) but by proving that it was impossible to put the whole of mathematics on a totaly formal footing. If you want to know more, read 'Godel Esher Bach: An eternam Golden Braid' by Douglas Hofstadter. It's not quite suitable for reading on a beach but it is very readable for a book trying to explain a major theory in modern maths. It's also probably the funniest book about propositional calculus ever.

Presumably all the chapters after 56 were removed having been proved wrong.

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Post 2


*wanders through muttering 'very cool book, very cool book indeed'*

*wanders back through... 'Godel Escher Bach, I mean'*

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Post 3

Jim diGriz

Yes, GEB excellent book! And I love that comment, "funniest book on propositional calculus"! LOL!

Russell turns up (not unexpectedly) a lot in Ray Monk's _Ludwig Wittgenstein: The Duty of Genius_. I thoroughly recommend that book for anyone interested in understanding Wittgenstein's approach, and the source of his disagreements with Russell.

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Post 4

Jim Lynn

I'm not sure if it's the same thing as Godel's Incompleteness Theorem, but wasn't the catalogue paradox another nail in PM's coffin? The problem being related to set theory, and the fact that some sets are not representable using set theory. I think that was the first thing with which Russell was presented that told him the endeavour was futile.

BTW, *very* good page on Godel's here: http://www.miskatonic.org/godel.html

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