To "bite the bullet" is to accept the consequences of a hard choice. It is derived historically from the practice of having a patient clench a bullet in his or her teeth as a way to cope with the extreme pain of a surgical procedure without anesthetic.
In philosophy, a major goal is to always sustain a consistent set of beliefs using sound reasoning. Often this will involve accepting a belief that is a disturbing truth. It may be disturbing because it is counterintuitive or has other disturbing consequences. Given a philosopher's previously held beliefs he or she may have to bite the bullet by accepting a particular claim offered as an extreme case or counterexample.