BFI /BFI/ , n. See brute force and ignorance. Also encountered in the variants BFMI, brute force and massive ignorance and BFBI brute force and bloody ignorance. In some parts of the U.S. this abbreviation was probably reinforced by a company called Browning-Ferris Industries in the waste-management business; a large BFI logo in white-on-blue could be seen on the sides of garbage trucks.