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.