It _would_ be self-contradictory *if* I followed your chain of logic, but I don’t.
Faith in a system built on self-doubt is still this:
Faith in a system.
What the system is constructed of does not matter. It’s still a system one has faith in.
Science does not take well to questioning itself by the way tongue emoticon It only questions things that can be questioned within the limiting parameters of acceptability utilizing solely the methodologies acceptable within science and no other.
Trusting a system based on trust.
Trusting a system based on distrust.
Both cases are trusting a system.