THE MATHEMATICAL COSMOLOGY of PLATO's TIMAEUS Introduction

THE MATHEMATICAL COSMOLOGY OF PLATO’S TIMAEUS [419] Introduction In this paper I argue that Plato’s Timaeus should be understood in light of the purportedly Socratic ‘autobiography’ in Phaedo 96–100, even though the Apology claims that Socrates took little or no interest in cosmological speculation. Extant reports (Met. 987b1–3) about Socrates’ philosophical activity also testify to his lack of interest in mathematics and in physics, while the early ‘Socratic’ dialogues consistently con ne him to pursuing moral questions by means of his famous elenctic method. By contrast, the Meno presents a ‘Socrates’ who uses mathematical diagrams to teach a slave boy something about geometry, so as to illustrate and defend a theory of recollection which can hardly be attributed to the historical Socrates. Finally the Phaedo, which develops a more elaborate version of this theory, the so- called ‘autobiography’ of Socrates, tells about an early interest in cosmological speculation which he gave up in disappointment because it failed to answer his questions. This inconsistency in the representation of Socrates I see as a clear hint that in the Meno and Phaedo Plato is self-consciously going beyond his mentor by introducing the hypothetical method of mathematics, combined with a metaphysical and epistemological theory of recollection. Furthermore, I claim that the so-called ‘autobiographical’ passage in the Phaedo can be treated as Plato’s own path to the cosmological theory which is developed fully in the Timaeus. Since this cosmology is narrated by a Pythagorean from Sicily in the sort of ‘long speech’ which Socrates deplored, it is quite clear that Plato has abandoned any pretence of merely expanding the ideas of his mentor. Yet Socrates does appear as a minor character at the | [420] beginning of the Timaeus dialogue where its project is explicitly connected with that of the Republic, although it is clear that, with the possible exception of Book I, the Republic is not a typical Socratic dialogue nor does it expound the political ideas of Socrates. Still one can read the whole dialogue as a response to the Socratic problem about how virtue is to be acquired, which is underlined by his paradoxical claim that no one does wrong knowingly. In order to examine the thesis that virtue is knowledge, Plato constructs an ideal polis with its distinct classes, each of which displays a distinctive virtue that is inculcated by a diferent curriculum of education. Thus, in general, it is plausible to read the Republic as a ‘thought-experiment’ by 154 history of mathematics means of which the deeper (i. e. Platonic) meaning of the Socratic dictum that virtue is knowledge is grounded in an ideal political order. Similarly, I think that the Timaeus can be interpreted as a parallel construction of an intelligible cosmology which is a necessary presupposition for the sort of teleological explanation that the ‘Socrates’ of the Phaedo seeks in his purported autobiography. Now that I have given a general overview of my interpretive approach, let me try to make it more plausible with reference to Plato’s texts. I. The Demand for Teleological Explanation At Phaedo 96a Socrates narrates his so-called ‘autobiography’ with reference to the question of Cebes about whether human souls are really indestructible and immortal and not just long lasting. Socrates admits that this is a very di cult question whose discussion demands an account of the causes of generation and corruption in general. It is within this dialogical context that Socrates recounts his supposed intellectual experience as a younger man when he had a remarkable enthusiasm for the kind of wisdom called natural science (περὶ φύσεως ἱστορίαν) (96a7–8). His enthusiasm was motivated by his belief that it would be magni cent (ὑπερήφανος)1 to know the reasons for everything, e.g. why a thing comes into being (διὰ τί γίγνεται), why it perishes (διὰ τί ἀπό υται), and why it exists (διὰ τί ἔστι). Socrates gives a sample of the typical questions posed by natural philosophers: Do living creatures develop when putrefaction develops from the conjunction of the hot and the cold? (Archelaus) Do we think with our blood, or with air, or with re? (Anaximenes, Heraclitus, Empedocles) Or is thought due to something else, namely, the brain providing sensation which gives rise to memory and judgment, and ultimately to knowledge? (Alcmaeon) Further questions ask about how things perish, and about what goes on in the heavens and the earth. According to Socrates, his lack of success with these questions convinced him that he had no gift for such inquiry because, instead of learning something new, he became totally confused about what he thought that 1 Since it is derived from the verb ὑπερηφανέω (which is ambiguous between ‘being conspicuous’ and ‘being arrogant’), this adjective may contain an implied critique of the arrogant claims of the physiologoi, especially as these were transmitted and used to support the pretentious claims of sophists like Gorgias. In view of later passages, however, it may be seriously intended in praise of the search for nal causes..

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