the thing which originally caused me to believe X was learning Y
because I believe X, I ended up convinced of Y
things which caused me to believe X also caused me to believe Y
… and in all three cases, Y might be a “crux”, since changing my belief about Y would also lead me to change my belief about X as the update propagates. Yet the cases are really quite different:
first case: if I changed my belief about Y, then my original reason for believing X would be gone, so it would make sense to change my belief about X
second case: if the falsehood of Y is really strong evidence for the falsehood of X, then changing my mind on Y could make me change my mind on X, but I’d also end up really confused because whatever evidence which originally made me believe X would still be there.
third case: falsehood of Y is evidence that my underlying beliefs are somehow wrong, but I still have no idea where the mistake is.
Seems like there’s a big difference between:
the thing which originally caused me to believe X was learning Y
because I believe X, I ended up convinced of Y
things which caused me to believe X also caused me to believe Y
… and in all three cases, Y might be a “crux”, since changing my belief about Y would also lead me to change my belief about X as the update propagates. Yet the cases are really quite different:
first case: if I changed my belief about Y, then my original reason for believing X would be gone, so it would make sense to change my belief about X
second case: if the falsehood of Y is really strong evidence for the falsehood of X, then changing my mind on Y could make me change my mind on X, but I’d also end up really confused because whatever evidence which originally made me believe X would still be there.
third case: falsehood of Y is evidence that my underlying beliefs are somehow wrong, but I still have no idea where the mistake is.
This is not really a response, but it is related: A Taxonomy of Cruxes.