Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

258 notes on the concept of the infiniteenclosure, the simple and eternal fixity and fullness of the whole, the eternal actualityof all possibilities.2. For pre-Socratic thought as a whole, however – if indeed any general categorizationis possible here – the “infinite” is conceived principally as the antinomy oforder, and as therefore both unthinkable and dangerous. For Anaximander the a[peironis a kind of eternal and limitless (although perhaps in some sense spherical) elementalplenum from which the finite and bounded cosmos has been extracted and againstwhich the cosmic order is continuously preserved. For Empedocles, also, the universeis a kind of small, fragile, local island of order amidst the boundless flux of materialbeing, a sort of city liberated and walled off from chaos. For the Pythagoreansit is pevra” – born of number – that subdues the limitless and gives dimensions (andthereby existence) to finite things. At this point, however, the distinction between themetaphysical and the mathematical infinite has not been clearly drawn. The finite isset off against the infinite, but almost entirely in the fashion of a stable concrete objectset off against an unstable and fluid, but nonetheless material, “first element.” ThePythagorean mysticism of number is still not the abstract Aristotelian metaphysics ofform, or of the actual and the potential.3. For Plato – and, really, for the entire classical philosophical tradition of Greece,including Stoicism – the infinite was solely a negative concept. Words like a[peiron,ajperivlhpton, ajovriston, and so forth, were more or less entirely opprobrious in connotation;they were used to designate that which was “indefinite” or “indeterminate” and,hence, “irrational” or “unthinkable.” The infinite is that which lacks form, that whichreflects no ei\do” and receives the impress of no morfhv. As such, it is pure deficiency.Hence, Plato would never have called the Good beyond being “infinite.” Aristotle’sontology was entirely concerned with finite substances (a category that included evenGod, the supreme substance) and had no room for anything like a concept of “infinitebeing.”4. Of the entirety of classical Greek thought, from Plato onward, it may fairly be saidthat this “Platonic” (or perhaps “Pythagorean”) prejudice remains constant: the highestvalue and the only ground of rational meaning is intelligibility, and so the highestgood can never be conceived as lacking rational limit. Only that which possesseseidetic dimensions and boundaries is thinkable; all else is chaos, formlessness, pureirrationality, and therefore malign. One sees this not only in Plato’s epistemology, but inhis cosmology. In the Philebus, for example, the universe is considered as the productof four primordial forces: limit, the limitless, the mixture of these two, and the firstcause of this mixture; the infinite in itself is an aboriginal tumult of oppositions – suchas the dry and the moist or the hot and the cold – that can come to constitute a livingworld only when it is brought under the governance of number and harmony. In theTimaeus, it is only in imposing the limiting proportions of distinct ideas on chaos thatthe demiurge brings about a world.5. Stoic metaphysics, needless to say, is a tradition unto itself, and although therewas a constant cross-pollination of Platonic, Aristotelian, and Stoic thought over thecenturies before and after the rise of Christianity in the Empire, whatever distinctiveconcept of the infinite one might ascribe to Stoicism surely cannot be said to be “idealist”in its guiding premises. Nevertheless, the model of reality peculiar to Stoicism