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Sewing-Machine comments on How to Convince Me That 2 + 2 = 3 - Less Wrong

53 Post author: Eliezer_Yudkowsky 27 September 2007 11:00PM

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Comment author: [deleted] 14 September 2011 06:08:07AM *  2 points [-]

Maybe "earplugs do not model PA," not the other way around? (Edit: just saw this excellent clarification.)

Number-handling is an older science than Peano arithmetic, and especially older than model theory. The numbers 2 and 3 would "exist" even if PA were shown to have no models. At least, the notation 2 and 3 would still be relevant to things that really exist.

It is very easily verified that 2 + 2 does not equal 3, but not effortlessly verified. It takes a positive amount of effort to verify it, and there is a positive amount risk of having made a mistake while doing so.