A triangle must have three sides, but that doesn't mean one exists at all. It is logically possible that nothing exists at all. Claiming the undeniability of self as a way to bridge thought and reality is not a rational argument, it is an existential one. Premises are not purely rationally defensible. There is not strictly rational way to establish rationalism.
Logic is at best a negative test for truth.
Fideism Fideism is a system of belief that places its ultimate emphasis on faith, rather than reason. If there is no purely rational or evidential way to establish Christianity, then truth rests solely on faith. Probably the most famous fideistic argument is Pascal's Wager. Either God is or he is not. If you wager he does exist and he doesn't, you haven't lost anything.