Rationally proving rationality

[Magicthighs]

‎"...Even rationality is grounded in a leap of intutition. There is no way to rationally prove that rationallity is a good way to look at the world. We intue it - that it is very helpful. And as we know, according to Pascal, the end point of rationallity is to demonstrate the limits to rationality."

Please define rationality.

Rationality - the state or quality of being rational.
Rational - Having or exercising reason.

Okay so far, if that's what you're intending rationality to mean.

Reason - the mental powers concerned with forming conclusions, judgments, or inferences [based upon observations].

Seems like you just went to dictionary.com and tacked "[based upon observations]" at the end of entry 3. Problem is, even by tacking on that bit, you're including reasons like "the voices told me to do it" and "I saw it in a vision". Even creationists base their claims on observations.

All you're saying here is that rationality means the state of using your mind to form conclusions, judgments or inferences [based on observations]. Do you know of any other ways to form conclusions, judgments or inferences?