
Gödel, Grammar, Go – The Limits of Rules and Facts - pshaw
https://billwadge.wordpress.com/2017/04/18/godel-grammar-go-the-limits-of-rules-and-facts/
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cirgue
This post contains a cursory discussion of Gödel's incompleteness theorem and
a promise to deliver on the title in a subsequent post.

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adrianratnapala
Yes, this has all the hallmarks of the light intro post.

But it has the important take-away that is claiming (and I agree) that we
shouldn't be too worried about the fact that some things can't be proven
within formal systems. We have what amounts to a huge body of empirical
experience that roots our confidence in many things, including set theory.

Indeed we have no real way of giving our stamp of approval to a formal system
except by our intuitions about what reason is, as modified by our life
experience. And even the innate intuitions are the product of biological
evolution, which is another kind of empirical testing process.

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ccvannorman
The one time a blogger writes content that actually has me glued to the page,
is the one time the blog is actually too short instead of way too long.

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mmalone
I'm curious... is it really true that an inconsistency would invalidate all
proofs? Wouldn't this only affect non-constructive proofs (i.e., proofs that
rely on the law of the excluded middle)? According to Wikipedia intuitionists
also accept the principle of explosion... but it's not just an automatic
result, is it? You'd need some proof or assumption that contradiction implies
everything. Right?

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ainar-g
In case you are wondering, it has nothing to do with the Go programming
language.

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pmontra
It doesn't have anything to do with go, the game, either. Not yet. The part
about games is for the next post which according to the author is very soon.
Incompleteness of posts...

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thecity2
Can we prove this post is incomplete though?

