As his title suggests, Black focuses on the Achilles paradox (though he also has something to say about the Dichotomy). The paper is divided into a couple dozen short sections that can be collected into three groups.
• Sections 1-8 (pp. 67-72) offer a survey of responses to the Achilles. There is little that goes beyond Salmon and Russell, but Black’s presentation is exceptionally clear.
• The heart of Black’s paper is a series of arguments in §§9-21 (pp. 72-79) concerning what he calls “infinity machines.” In these, he tries to recast the paradox into a genuine paradox regarding the completion of infinite tasks.
• His last two sections (§§22-23 on pp. 79-81) discuss the significance of the problems he takes himself to have found with the idea of infinite tasks. Although he presents it very quickly, you should spend some time thinking about his association of infinity with our mathematical description of reality (as opposed to reality itself). This issue provides one of the closest ties between discussions of the paradoxes and questions about the nature of time.