Pat, (01)
I completely agree with what you and Chris said, but I just wanted
to mention some interesting sources of inspiration. (02)
> What Goedel did pioneer, and which was highly original, was how
> to encode any formalism into arithmetic, using the Chinese Remainder
> theorem. In hindsight, one might call that an ingenious piece of
> prime-number hacking. (03)
I also agree that his encoding of logic was a highly original and
valuable contribution that stimulated many later techniques for
encoding formal notations in arithmetic. (04)
But I'd like to mention that Gödel explicitly said that Leibniz
was his favorite philosopher. And it was Leibniz who invented
the use of prime numbers for encoding and reasoning about
Aristotle's categories. That was probably one of the sources
for G's inspiration. (05)
Another point: Leibniz had also studied Chinese characters and
the 64 hexagrams of the I Ching, which uses patterns of 6 straight
and broken lines. That encoding led him to invent binary arithmetic. (06)
That is one reason why I like to dig into some of the musty old tomes.
There are often little nuggets of forgotten lore that can suggest
novel ways of interpreting current theories and technology. (07)
John (08)
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