Illogically nested beliefs

[bunny]

Amongst my beliefs are the following positions:

theism - dualism - platonism

The path to each of them was unrelated, yet I suspect that the ones to the left would disappear if the ones to the right shifted. Ie if I was persuaded of materialism, I expect I would go back to being an atheist. If formalism was established (or similar) then I expect both the others would disappear shortly thereafter. This is despite the fact that they dont seem to logically rely on each other (although they're probably correlated). Anyone know if there a name for this phenomenon/fallacy?