Gordon Rugg cracked the 400-year-old mystery of the Voynich manuscript

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It's a dream of mine to become a sort of rationality consultant for scientists!


Scientific Method Man

Gordon Rugg cracked the 400-year-old mystery of the Voynich manuscript. Next up: everything from Alzheimer's to the origins of the universe.

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blegging for logic help

Since I'm supposed to know something about logic once I graduate, I'm trying some self-study and talking to people who know more than me. All this extra-curricular.

Any help clarifying my ideas is very welcome!


Here are some notes:

ZFC talks about sets
PA talks about numbers
you can code PA into ZFC
Goodstein theorem is undecidable in PA
Goodstein theorem is provable in ZFC


Is there a relationship between the Undecidability of FOL and Gödel's incompleteness?


Are these the same meaning of "complete"?
complete: all tautologies are provable
complete: all consistent things have a model


What can one conclude from "FOL is complete but not decidable"?



What's the relationship between:

calculus
logic
theory
?

logic = calculus + semantics?

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I really should be ashamed of myself, but it really seems I can't learn from a static book (possibly because I don't have the patience!). But I have an open mind: perhaps I just haven't found the right book.

more ignorant logic speculation

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?