Named after George Boole - British mathematician (1815-1864).
Boole is a lunar crater that lies along the northwestern limb , to the northwest of the crater Gerard. The crater formation is nearly circular, however, with a wide inner wall that has been worn and rounded due to subsequent impacts. To the north is the crater Cremona, and to the southwest are Paneth and Smoluchowski. (wikipedia entry)
A crater is a circular depression likely created by an impact event. On the Moon they are named after deceased scientists, polar explorers, astronauts or cosmonauts.