Thursday, 4 February 2010

"What Can't Logic Do--Part 2: Theoretical Responses to Ruchir Verma, Laura Niada and Sandy Singh"

1. This is in reply to the astute observations by Ruchir, Laura and Sandy to my wicked 10 claims of "What Logic Can't Do" filed as a note in my Facebook.

2. Leibniz believed that we could have a pure calculative language that would have necessary and sufficient premises for a complete description of the entire universe--the famous Mathematica Universalis (MU--or in my previous note referred to as "Moo"). The hopes for a calculative language reducible to a few logical premises called axiomatics grew in the early part of the 20th century. Problem was it was cumbersome--Russell and Whitehead in their Principia Mathematica (very unpopular which they had to privately publish and sold about 7 copies) took 157 pages of pure symbolic logic to prove a couple trivial existence relations and never got going to prove anything of any use or consequence to normal arithmetic operations. And then Kurt Godel in the 1930s with his incompleteness theorem showed how it was logically impossible (sic!) to have both a consistent set of premises and no danggling infinitudes for a simple arithmetic system. (All systems theorists -- Luhmanists should beware of their outrageous claims in light of Kurt's supreme and god-like clarity!) Logicians however grew very clever with Zermelo and later Tarski showing how an axiomatic system could be developed with powerful applications--much of our current computation goes back to them. Despite huge formal advances, however, the limitations of logic are stark. Although I personally like Leibniz' MU--I don't think it is doable within any standard interpretation of how our universe works. This does not prevent any mystical bent and encourages me to search for solutions and translations of the quotidien law and finance into group theoretic and category theoretic terms. My goal is to give "traders' talk" a voice in Platonic Heaven under risk symmetric invariance. After all, physics is the ultimate option since its reference asset is reality.

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