more ignorant logic speculation
Oct. 19th, 2004 08:54 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
guslSo, I've been thinking, how significan't should Gödel's Incompleteness be anyway? It seems those example sentences are always pretty contrived, whereas I only really care about "concrete" statements.
Give me an example of a concrete-looking undecidable statement in number theory.
Should we replace the ideal of static axiomatization with a dynamic one? Can there be an algorithmic way of picking new axioms? Would this create a logic on its own, which also suffers from Gödel's Incompleteness?
Chaitin views Gödel's incompleteness as an information-theoretic necessity.
Does the undecidability of FOL imply that there are no bounds on proof size?
Give me an example of a concrete-looking undecidable statement in number theory.
Should we replace the ideal of static axiomatization with a dynamic one? Can there be an algorithmic way of picking new axioms? Would this create a logic on its own, which also suffers from Gödel's Incompleteness?
Chaitin views Gödel's incompleteness as an information-theoretic necessity.
Does the undecidability of FOL imply that there are no bounds on proof size?
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(no subject)
Date: 2004-10-23 11:31 am (UTC)My hope is that there exists a decidable arithmetic which can express statements of the form of the Goldbach Conjecture.