Those are fascinating historical notes, indeed. Thanks for posting them. (01)
Pat (02)
On Jan 25, 2012, at 5:37 PM, John F. Sowa wrote: (03)
> Pat,
>
> I completely agree with what you and Chris said, but I just wanted
> to mention some interesting sources of inspiration.
>
>> 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.
>
> 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.
>
> 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.
>
> 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.
>
> 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.
>
> John
>
>
>
>
>
>
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