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Gödel and Leibniz

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Submitted by Richard Zach on Thu, 06/23/2005 - 9:03am

I'm re-reading Coffa's The Semantic Tradition from Kant to Carnap in preparation for my course on the Vienna Circle, and was struck by this quote on p. 14:

With his characteristic blend of genius and insanity, Leibniz had conceived of a project in which the simple constituents of concepts would be represented by prime numbers and their composition by multiplication. From the Chinese number theorem [sic] (and certein assumptions about the nature of truth) he inferred that--given this "perfect language"--could be resolved by appeal to the algorithm of division.

I wonder if Gödel was inspired by this "project" in his coding apparatus and the proof of Theorem VII in his 1931 paper on the incompleteness theorem (which is where he uses the Chinese remainder theorem to deal with arithmetical coding of sequences).


Submitted by Anonymous on Thu, 06/23/2005 - 10:13pm

I've long wondered the same thing.BTW - for an interesting history of all these approaches to language, check out Umberto Eco's <>The Search for the Perfect Language<> . It goes through the earlier moves to Leibinz such as Lullism. They all are very interesting relative to Godel though. <><><><>Posted by<><> <><>< HREF="" REL="nofollow" TITLE="clark at lextek dot com">Clark Goble<>

Submitted by Anonymous on Wed, 07/27/2005 - 4:13pm

Hmm, I think the so-called "Chinese Remainder Theorem" is just a red herring here. Leibniz, in common with a lot of 17th century logicians, had a primitive view of concepts as being made out of primitive concepts by conjunction. Hence any concept could be given uniquely by a concatenation of elementary names; hence, the appropriate bit of number theory is unique factorization. Of course, Gödel was a Leibniz fan, but I don't think we have to invoke the shade of Leibniz in connection with the incompleteness paper. By the way, Paulo Ribenboim's "Book of Prime Number Records" debunks the pseudo-history surrounding the "Chinese Remainder Theorem."  <><><><>Posted by<><> <><>< HREF="" REL="nofollow" TITLE="urquhart at cs dot toronto dot edu">Alasdair Urquhart<>