"How to convince me that 2 + 2 = 3"
www.greaterwrong.com/posts/6FmqiAgS8h4EJm86s/how-to-convince-me-that-2-2-3
Hilary Putnam's Twin Earth thought experiment on conceivability vs logical possibility seems to touch on this ( www.greaterwrong.com/posts/ne6Ra62FB9ACHGSuh/heat-vs-motion):
Once we have discovered that water (in the actual world) is H2O, nothing counts as a possible world in which water isn’t H2O. In particular, if a “logically possible” statement is one that holds in some “logically possible world”, it isn’t logically possible that water isn’t H2O.
On the other hand, we can perfectly well imagine having experiences that would convince us (and that would make it rational to believe that) water isn’t H2O. In that sense, it is conceivable that water isn’t H2O. It is conceivable but it isn’t logically possible! Conceivability is no proof of logical possibility.