We discuss the philosophical status of the statement that (9n – 1) is divisible by 8 for various sizes of the number n. We argue that even this simple problem reveals deep tensions between truth and verification. Using Gillies's empiricist classification of theories into levels, we propose that statements in arithmetic should be classified into three different levels depending on the sizes of the numbers involved. We conclude by discussing the relationship between the real number system and the physical continuum.

A moving cultural biography of abolitionist martyr John Brown, by one of the most important African-American intellectuals of the twentieth century. In the history of slavery and its legacy, John Brown looms large as a hero whose deeds partly precipitated the Civil War. As Frederick Douglass wrote: "When John Brown stretched forth his arm... the clash of arms was at hand." DuBois's biography brings Brown stirringly to life and is a neglected classic.

We describe in some detail how to build an infinite computing machine within a continuous Newtonian universe. The relevance of our construction to the Church-Turing thesis and the Platonist-Intuitionist debate about the nature of mathematics is also discussed.

Housed in one volume for the first time are several of the seminal essays on Du Bois's contributions to sociology and critical social theory: from DuBois as inventor of the sociology of race to Du Bois as the first sociologist of American religion; from Du Bois as a pioneer of urban and rural sociology to Du Bois as innovator of the sociology of gender and culture; and finally from Du Bois as groundbreaking sociologist of education and cultural criminologist to Du (...) Bois as critic of the disciplinary decadence of the discipline of sociology. Unlike any other anthology or critical reader on Du Bois, this new volume offers an excellent overview of the critical commentary on arguably one of the most imaginative and innovative, perceptive and prolific founders of the discipline of sociology. (shrink)