I'm afraid I'll have to defer to u on this
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I call that "orthodox computationalist". In 100 years, the "Reals" will strike people the way angels dancing on the head of a pin do now!
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Do you believe in the naturals, or algebraic/elementary numbers?
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I haven't slept well since I realized that we just accept proofs over the reals in statistics and ML without checking to see if they work on computable numbers. Paper related: https://arxiv.org/abs/1005.3014
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If you don’t buy the reals your only option is Extremely Strong. Power set of the naturals is the same as the reals.
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The computably enumerable subset of the power set of naturals is intermediate
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