Lets say some ones declared mental, from there we are able to work out the level of abstraction this person is away from reality.
Another potential use.
Psych wards could be numbered by the level of Cuil and the patients treated accordingly.
Professions of the mind could benefit, "Patient X is X Cuils, treatment X has proven to have a X Cuil deduction."
Treatments could be categorized by the level of deduction for a certain level of Cuil.
Crude ideas, hopefully helpful.