To "bite the bullet" is to endure a painful or otherwise unpleasant situation that is seen as unavoidable. The phrase was first recorded by Rudyard Kipling in his 1891 novel The Light that Failed.
It was suggested by the movie "Bite the Bullet" that biting the bullet meant using a shell casing to cover an aching tooth, especially one that had been broken, and where a nerve is exposed. In the film, the slug was removed from the bullet, the cap was hit to expend that charge, and the casing was cut down to allow it to sit level with the other teeth.
It is often stated that 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, though evidence for biting a bullet rather than a leather strap during surgery is sparse. It has been speculated to have evolved from the British empire expression "to bite the cartridge", which dates to the Indian Rebellion of 1857, but the phrase "chew a bullet", with a similar meaning, dates to at least 1796.
A more specific meaning of the phrase is to accept unpleasant consequences of one's assumed beliefs. Sound reasoning requires its practitioner to always sustain a consistent set of beliefs. This may involve accepting a disturbing belief that is a consequence of one's currently held beliefs. It may be disturbing because it is counterintuitive or has other disturbing consequences. Given a philosopher's currently held beliefs that he or she is not prepared to give up, he or she may have to bite the bullet by accepting a particular claim offered as an extreme case or putative counterexample.