Abstract
This volume contains essays by 13 up-and-coming researchers in the philosophy of mathematics, who have been invited to write on what they take to be the right philosophical account of mathematics, examining along the way where they think the philosophy of mathematics is and ought to be going. As one might expect, a rich and diverse picture emerges. Some broader tendencies can nevertheless be detected: there is increasing attention to the practice, language, and psychology of mathematics, a move to reassess the orthodoxy, as well as inspiration from philosophical logic.