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To: Gib Bogle who wrote (13802)	6/18/2006 11:31:19 PM
From: E. Charters	Respond to of 78421

He was mad, but his logic was sound. It forms the basis for much of what mathematicians don't do today and how the sciences now approach their justification of axioms and theories. In short he changed the course of all logical thought, science and philososphy. Not bad for a madman. Before Godel, many mathematicians were labouring to form a system of axioms that would justify all mathematical thinking and theorems. Before Godel, mathematicians and scientists thought that systems could be self justifying, or the elements of their consistency could all be found. Godel proved that only if the systems were consistent could we never find all the axioms that formed the basis for the system. In other words all thinking must be incomplete. This infinitude of systems does indeed point at god, as surely as water flows downhill. That some think his synthetic proofs are weak, or inconsistent shows that they do not understand the very basis of Godel's thought, in that any system is either inconsistent or incomplete, but not both. Most of the arguments Godel use a priori logical patterns to dispute his assumptions. In my opinion they miss the point and anyway miss the power of the positivity principle. There is no weak starting point to the logic. It is quite acceptable. The positivity matters are hard to understand. Godel's proof of God, so to speak, is not weak. His theory of incompleteness, so far unassailable, is based on similar kinds of seemingly trivial examples. But the paradoxes that Godel used are far from trivial when you get to the heart of them. They form the essence of the fundamental paradox of incompleteness. Like the all knowing machine that cannot confirm a statment that it will not not confirm a statement. There is not getting around them synthetically. The arguments against Godel's proof are somewhat complex but they are based on argument against the assumptions, as, in the Anselm proof, Anselm's assertion that those of faith would enter heaven, is disputable. This however is not the weakness of the logic, or the proof. The difficulty lies in understanding Godel's positivity property and accepting what the nature of a godhead must be. But what Godel proved is accepting that nature, then this thing exists. If one does not accept that nature it is tantamount to denying reason, or the idea of a god at the outset, which "we are not asked to do". One cannot define or "be sure of" the nature of god, then set out to prove that nature must exist, that much I grant. But something strange is afoot in a logical system that must be proved outside of logic. They must (be true), but is truth logical? Godel hinted at its inherence in thought outside provability. If that is true, then true things must exist outside thought. What are they true to? I leave it to you. EC<:-}