but I figure it is so esoteric that not many people will be harmed, and also that it will probably fizzle out in a decade or so.
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Replying to @Meaningness
There's the Wildberger sorts who want to just throw out all the uncomputable stuff, but there is a more reasonable position where you...
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Replying to @ReferentOfSelf @Meaningness
realize that we don't really have an understanding what the relation between this uncomputable stuff has to reality, but that we can...
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Replying to @ReferentOfSelf @Meaningness
actually go and figure stuff out. On the other hand, there is the fact that restricting yourself like this actually gives you more useful...
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Replying to @ReferentOfSelf @Meaningness
stuff. There is less of a translation from theory to application. As for the proof verification stuff, that's all about the fact that...
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Replying to @ReferentOfSelf @Meaningness
proofs are getting so big and intricate that human verification is becoming unreliable. See eg. https://www.ias.edu/ideas/2014/voevodsky-origins …
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Replying to @ReferentOfSelf @Meaningness
There is also the idea of closing the gap between mathematics and programming, which also gets into this proof verification stuff
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Replying to @ReferentOfSelf @Meaningness
For me, it's not clear what a classical proof using AC actually means and it frustrates me that no one seems to be trying to understand this
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Oh, right. Well… lots of people tried to understand that for a long time, and didn’t get very far, so here we are :)
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Replying to @Meaningness
Curry-Howard-Lambek correspondence is new in comparison. Need to translate AC to more concrete computational principles.
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