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Nick_Tarleton 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: Nick_Tarleton 28 September 2007 10:05:28PM 0 points [-]

I draw the line at P AND ~P, though: just unthinkable.

I've heard religious people profess beliefs of this nature. I don't think they actually believe it, but I don't think it's pure belief-in-belief either; I see it as an attempt to explain a deeply unusual subjective experience in poorly suited language. (Which is not to say I think any statements like that are metaphysically true or anything.)

I do think there's something to "a priori" besides a mere semantic stopsign, though. I could model physically possible worlds with different contents, or logically possible worlds with different physics, but I can't imagine how I could model (as opposed to loosely imagine) a universe where 2+2=3. Eliezer, would you hold that such a world is actually constructable and modelable in addition to imaginable? Do you think "necessary" and "contingent" or "logically possible"/"impossible" are semantic stopsigns too?