Abstract

Zeno's challenge to the usual mathematical characterization of extension is still with us. Butchvarov, considering the limits of ontological analysis, writes, “I shall not explore [the decision to accept the infinite regress in which the pursuit of the analytical ideal is involved], beyond noting that the infinite divisibility of space is the reductio ad absurdum of any attempt to understand space in terms of its ultimate, simple parts.” Grünbaum states this problem, commonly known as the Measure Paradox, concisely, “[How can one conceive] of an extended continuum as an aggregate of unextended elements?”