The need for historical research on the Presocratics' continuum in Aristotle

This chapter demonstrates how the lines in Phys. III 1, 200b16–18 present several enigmatic statements. They introduce the need to study motion and infinity through the concept of the continuum and also provide the definition of the continuum as that which is divisible to infinity. However, 1) Aristotle does not use the concept of continuity to discuss the motion; 2) it is unclear what he means when he says that ‘in the continuum, the infinite appears first’, as it is not clear why he uses ‘appears’ or in what sense he means ‘first’; and 3) he attributes the definition of the continuum to other philosophers who, however, ‘often’, but evidently not ‘always’, used infinity to define the continuum—as if a definition could lack one of its defining terms. The discussion of these claims of Aristotle, in which we attempt to trace their origins to both physicists and mathematicians, demonstrates the necessity of investigating the Presocratic concept of the continuum as an indispensable step before studying Aristotle’s continuum.