I think the type of mental training Ralph - and he can certainly correct me if I am mistaken - means might be more along the lines of spiritual training; that is, training designed to improve or test a trainees spirit (hence Taekwon-Do's tenet "Baekjul Boolgool," or Indomitable Spirit). It's not so much a matter of deductive reasoning so much as developing willpower. The type of training that's been discussed (lots of fitness requirements during a test or to even enter a school as a student) would seem to be similar to the Japanese concept of "Shugyo." Shugyo is intense physical and mental training designed to push the student to his limits and so improve his spirit or character. While I'm not a fan of fitness tests as part of a rank test per se, I think the practice of shugyo certainly has a place within martial arts and know some schools that set aside a couple of specific dan level tests as shugyo-type experiences.
Ultimately, such austere training will become something that a student takes upon themselves and will largely (though not exclusively) be something that is done alone and only periodically, perhaps to mark a special date such as an anniversary of training. Because of the intensity of the training, both physical and mental, it really isn't something that is done day in and day out.
Pax,
Chris