Welcome to European Tribune. It's gone a bit quiet around here these days, but it's still going.
Look, this is like telling me that Set Theory doesn't work and bringing up Frege as an example.

As you know, the internal consistency of a logical system complex enough to contain the arithmetic of natural numbers [without tautology] cannot be proved from within the system. That is, the internal consistency of any theory of the logic of numbers cannot be proved without appeal to external principles.

Russel and Whitehead did their work on the definition of number 30 years before this fact was discoverd by Gödel. Not only Russell's philosophical approach to the logic of Mathematics, but also David Hilbert's were shattered by Gödel, Turing, Post [hey, I can even quote a Russian mathematician here] and others in teh 1930's and 40's.

I don't know what you mean by tautology.

Now, if you think that the fact that mathematics is based on unproven principles is a new insight, I suggest you take a look at Euclid and Aristotle, for whom it was clear already 2000+ years ago that axioms and postulates were accepted without proof and were not ashamed of it.

Those whom the Gods wish to destroy They first make mad. — Euripides

by Carrie (migeru at eurotrib dot com) on Sat Sep 16th, 2006 at 09:25:40 AM EST
[ Parent ]

Others have rated this comment as follows:

Nomad 4


Occasional Series