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ygert comments on Second-Order Logic: The Controversy - LessWrong
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Seems weird to think that some of the possible configurations of bits on my 1.5TB hard drive don't exist. Which ones? I hope none of the really good collections of pr0n are logically unreachable.
If that number does exist, then what about really big busy beaver numbers, like bb(2^10^13 )? They're just a series of computations on hard drive contents. And that number is so close to infinity that we might as well just step from ultrafinitism to plain old finitism.
While I am not an ultrafinitist, I believe the idea is meant to be this: It is not valid to talk about those numbers, because there is no meaningful thing you can do with those numbers that can affect the real world. Therefore, the ultrafinitists say that it is not really logical to treat these numbers as "existing" as they can not affect the real world at all, and why say that something exists if it cannot affect anything at all?