I'd argue one actually can do that, especially rationality in the precise technical sense of the word I'm using. Cox's theorem derives probability theory from ordinary logic under very minimalistic assumptions; utility maximisation is provably optimal as an economic and behavioural strategy; the universal prior is a provably optimal formalism of the Occam's razor; etc.

Furthermore and perhaps more importantly, rationality is empirically justified: probability theory as "the logic of science", the demonstrable detrimental effects of cognitive biases on prediction- and decision-making, etc.