Lee_B comments on How to Convince Me That 2 + 2 = 3 - Less Wrong
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I concede (a little)!
In a previous Overcoming Bias post we learned that people sometimes believe the conjunction of events R and Q is more probable than event Q alone. Thus people can believe simple and strictly illogical things, and so I shouldn't throw around the word "unthinkable."
If I stretch my imagination, I can just maybe imagine this sort of logical blunder with small integers.
I draw the line at P AND ~P, though: just unthinkable.