The Continuity and Infinity of Space According to Epicurus and Lucretius

Abstract

We must turn now to Epicurus’ conception of space, for, although from the nature of the case it is not so complicated as that of the atoms, it involves certain difficulties which cannot be disguised. The syllogistic argument by which he inferred the existence of space from the fact of motion has been discussed already:¹ we must now inquire more closely what it was that he meant by space. The mathematical conception of space as extension may be put out of court: it is impossible that Epicurus should have meant that for several reasons; (1) it would have been inconsistent with his whole attitude to the mathematical point of view, (2) it would have clashed with his theory of area as a succession of discrete minima, (3) it is sufficiently contradicted by the many synonyms which he employs to describe it, and particularly with its definition as ‘intangible existence’. Space is an ‘existence’ just as much as body, it is not mere measurement or extension: it is a ‘thing’, but a thing whose sole property is that it cannot touch or be touched, it can offer no sort of resistance to body. Here then is his answer to the difficulties of the earlier Atomists: he does not trouble himself with their subtle discussions as to whether space is ‘nothing’ (oν òν), or ‘non-existent’ (μᾐ òν); he simply affirms, with the same meaning but much closer precision, that it is an ‘intangible existence’. The conception is not abstract but concrete: it is derived from that of body by a negation of its properties.