Under some reasonable interpretations of “objectively true,” there aren’t any outside math and possibly QFT. Under some other reasonable interpretations, lots of things are objectively true. Lots of arguments founder on this contrast.
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OK, this is great—that’s exactly what I’m calling “meta-rational judgement”! My thesis is that you always need to do that when applying rational methods, and there’s skillsets for doing that, and those tend to be neglected, and it would be good to help people learn them.
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Threading is a nightmare here. See my continuing reply. "Decision theory" isn't the adding-digits recipe, it's the more abstract idea of Peano arithmetic that helps us understand when the recipe might fail or succeed, even though applying the Peano axioms is way too laborious.
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Yes, boo to twitter threading!
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Imagine now that all you know are many recipes like this, and counting and object discrimination is as fuzzy as ever.
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You might be very skeptical of any claim about an Absolute Mathematical Truth that casts all the practical recipes as shadows, and it would certainly take some facility with abstraction just to understand the claim.
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After all, you've seen so many enthusiastic youngsters who believe Digit-Adding works absolutely every time and is the only tool you ever need in the toolbox.
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What you're being presented with isn't a replacement for your toolbox, though. It's a more abstract knowledge that governs every tool you can try to invent, even though you still need the tools because you can't use Absolute Math to get the answer, plus counting is still fuzzy.
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(I’m not sure if this tweet is the completion of a train of thought, or if you are still going?) I don’t follow (thus far). I’ve said that math is a domain of absolute truth. It’s a thing we do have, not an ideal we approximate.
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Only if you have a computer and even then you can't calculate the 100th Busy Beaver number or the leading digit of Graham's Number. It's easy to state slightly harder math questions that leave us with only guessing heuristics and no way to just Apply The Defintion of A Number.
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Right. But isn’t your point that even if we can’t implement it, decision theory is Correct? I’m agreeing that it is Correct in the sense that it’s math and math is absolutely true (or not at all).
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I'm genuinely not sure what you mean by Correct in a sense that DT could be inCorrect. DT is valid math, and it also has another key property that might not be what you mean by Correctness; it's math that governs all the tools in a certain toolbox and helps us make better tools.
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