LUDWIG WITTGENSTEIN once said that in philosophy, it is hard to work as slowly as you should. When the British philosopher Philippa Foot finally published ''Natural Goodness,'' her first and only book-length statement of her thinking, at age 80 in 2001, an editor at Oxford University Press recalled Wittgenstein's challenge. ''Well,'' he said, ''that is a problem that Philippa seems to have solved.'' Foot's philosophical voyage, her ''painfully slow journey,'' as she put it, was long in part because it was uphill. Though born into a family of privilege -- her father was a wealthy British industrialist, her mother a daughter of the U.S. president Grover Cleveland -- she was given no formal education (''I was extremely ignorant,'' she later said) and, being a woman, was not expected to go to college. Spurred on, however, by a governess who recognized her intelligence, Foot educated herself via correspondence courses and eventually attended Somerville College at Oxford. There, in the clubby, masculine atmosphere of high British learning, she cultivated friendships with a group of young female philosophers, among them Elizabeth Anscombe, who would become a prized student and editor of Wittgenstein's, and Iris Murdoch, the future novelist. (Philippa would marry one of Murdoch's former boyfriends, the historian M.R.D. Foot.) [ABSTRACT FROM PUBLISHER]