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A basic probability question

by shminux 1 min read23rd Aug 20193 comments

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From the logical induction paper https://intelligence.org/files/LogicalInductionAbridged.pdf:

Let φ stand for the claim that the 87,653rd digit of π is a 7. If this claim is true, then (1 + 1 = 2) ⇒ φ. I don't understand the second sentence at all, any help appreciated.

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is true iff one of (i) is false or (ii) is true. Therefore, if is some true sentence, for any . Here, is .