more ignorant logic speculation

[gusl]

So, 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?

Comments

[gustavolacerda.livejournal.com]

here's the correct link: http://en.wikipedia.org/wiki/Presburger_arithmetic

[bram.livejournal.com]

Thanks. I had never heard of this before. By making your system weaker you get around Godel's theorem but, well, you make your system weaker.