Anaxagoras, the thoroughgoing infinitist

Abstract

In the analysis of Anaxagoras’ physics in view of the relation between his teachings on multitude and heterogeneity, two central questions emerge: 1) How can the structure of the universe considered purely mereo-topologically help us explain that at the first cosmic stage no qualitative difference is manifest in spite of the fact that the entire qualitative heterogeneity is supposedly already present there? 2) How can heterogeneity become manifest at the second stage, resulting from the noûs intervention, if according to fragment B 6 such a possibility requires the existence of “the smallest”, while according to the general principle stated in fragment B 3 there is not “the smallest” but always only “a smaller”? This paper showcases the perplexity of these two questions but deals only with the former. The answer follows from Anaxagoras’ being a thoroughgoing infinitist in the way in which no Greek physicist was: the principle of space isotropy operative in geometry is extended to physics as well. So any two parts of the original mixture are similar to each other not only in view of the smaller-larger relation but also because each contains everything that the other one contains. This in effect means that at the stage of maximal possible heterogeneity each part of any part contains infinitely many heterogeneous parts of any kind whatsoever. So, neither can there be homogeneous parts in view of any qualitative property, nor can there be predominance in quantity of parts of any kind that would make some property manifest.