Chorology: On Beginning in Plato's Timaeus

Remembrance of the City

1 Remembrance of the City R E C E P T I O N One, two, three— One takes this as the beginning, these three words, the words one, two, three. Reading them from the point where the inscription begins, reading them at the beginning of its ¤rst line, one takes them as the beginning, sets them down as the beginning, takes them to be set down as the beginning in the manner of a hypothesis (in the Greek sense), vowing to remember in all that follows the need to circle back upon them. Proclus marked their appropriateness, marked it with a word that could be taken to signal from afar the very heart of the matter to be put in question in the dialogue: “Suitably [e¥kítwV], therefore, the discourse at its beginning proceeds through numbers and uses numbers as things numbered .”1 Suitably, ¤ttingly, as an image (e¥k»n) is suited or ¤tted to image its original, its paradigm. The ¤rst three words of the Timaeus bespeak the dialogue as a whole. These three words, the words one, two, three, enact an operation that will be repeated at several decisive junctures and in several basic articulations in and of the dialogue. For with these words Socrates is counting; he is counting off the persons who, as he counts, are receiving him as their guest. Hence, these opening words do not just express the ¤rst three positive integers but also enact a counting. Indeed, as Jacob Klein has shown,2 the Greek understanding of number is intrinsically as well as lin1 . Proclus, In Platonis Timaeum Commentaria, ed. E. Diehl (Amsterdam: Verlag Adolf M. Hakkert, 1965), 1:16. 2. Jacob Klein, Greek Mathematical Thought and the Origin of Algebra, trans. Eva Brann (Cambridge: MIT Press, 1968), 46–60. 8 CHOROLOGY guistically linked to counting. The link is posed by the linguistic connection. The verb åriqmèw means primarily: to count out, to count off, a number of things. The word that is uttered last in counting off a number of things is the number (the counting number: åriqmíV) of these things. Number signi¤es, therefore, a de¤nite number of de¤nite things. Thus, the intentionality is quite different from that which would set numbers over against things and submit such detached numbers to operations carried out quite apart from things and the link to things. For the Greeks the intentionality is rather one by which a number intends things insofar as they are present in this number. A sentence from Aristotle is explicit: “And a number, whatever it may be, is always of something, for example, of parts of ¤re, or of parts of earth, or of units” (Mtp. Ν 1092b19–21). Thus it is that one is not regarded as a number: only what can be counted, a number of things, is a number, the smallest of which is therefore two. On the other hand, this basic intentionality does not preclude a transition— the very transition ventured in the Platonic dialogues—to a level at which the things counted would no longer be sensibly presented things, the level of theoretical arithmetic where number becomes a number of pure units, a number of ones—still, however, a number of something.3 Thus counting, one, two, three, Socrates marks a beginning by setting forth, in the strict sense, not three numbers but only one, the (counting) number three. It is this number and the counting numbered by it that will be decisively repeated throughout the Timaeus. Socrates is being received by three persons, Timaeus, Critias, and Hermocrates . Since Hermocrates presents no speech but only a single remark enjoining Critias to speak, there are in fact three speakers in the dialogue. Counting them off by name in the order in which they present their speeches, Socrates, Critias, Timaeus, one notices that it is the third that is the major speaker, at least assuming that what is actually presented has precedence over a brief remembrance of an earlier speech and a mere anticipation of a speech promised for later. Timaeus’ speech, which is several times the length of the other speeches, is itself divided into three distinct speeches, the transitions marked by explicit interruptions in the discourse (at 47e and 69a). This counting, one, two, three, will be repeated many times in the course of the Timaeus, and each time it will be imperative to circumscribe precisely what is being counted. In a sense everything will hinge on the third...