Abram,
Thanks for reply. This is presumably after the fact - can set theory
predict new branches? Which branch of maths was set theory derivable from? I
suspect that's rather like trying to derive any numeral system from a
previous one. Or like trying to derive any programming language from a
previous one- or any system of logical notation from a previous one.
Mike,
The answer here is a yes. Many new branches of mathematics have arisen
since the formalization of set theory, but most of them can be
interpreted as special branches of set theory. Moreover,
mathematicians often find this to be actually useful, not merely a
curiosity.
--Abram Demski
On Tue, Aug 26, 2008 at 12:32 PM, Mike Tintner <[EMAIL PROTECTED]>
wrote:
Valentina:In other words I'm looking for a way to mathematically define
how
the AGI will mathematically define its goals.
Holy Non-Existent Grail? Has any new branch of logic or mathematics ever
been logically or mathematically (axiomatically) derivable from any old
one? e.g. topology, Riemannian geometry, complexity theory, fractals,
free-form deformation etc etc
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