Or, as a (former) doctor, I love telling my engineer friends:

Intuition can't be formalized.

Part of the reason simply being the "system level" thinking that has to be developed, practiced and honed by any doctor worth his/her salt. And when you think of it, even with our current understanding of the human organism and the phenomenon called life, we are primarily working using 'heuristics', barely glimpsing the ultra-complex jigsaw that makes everything tick. Someday, when the ken of this knowledge is complete, we may be able to formalize the logic, albeit, the 'computer' it runs on, may well be as complex as our own brains!