Noēsis: Plato on Exact Science

There are two places in Plato’s Dialogues in which he discusses his conception of scientific explanation: the passages on the ‘second best method’ in the Phaedo and the passages on noēsis in the Divided Line simile in Book VI of the Republic. I have written about the first of these in [1986] and I want to discuss the second of them here. The conception in question is of what we would call exact science. Some exact sciences, the so-called mathēmata, were already in existence in the fourth century BC in Greece and Plato was concerned to argue for a proper foundations for them. The reason why is part of my story of the Divided Line. The Line itself, I will argue, is a rhetorical argument for foundations. Plato was also concerned with extending the ∗Earlier versions of this paper were read in the Spring of 1997 in the Philosophy Colloquium at the University of Chicago, at the Pacific Division meeting of the APA in March, 1998, and in the Philosophy Colloquium at the University of California-Riverside in November 1998. All of these were based on a manuscript composed in 1986. An even earlier version received valuable criticisms from Henry Mendell, as did the version read at the APA. When I recently returned to the study of Plato, the hard copy of the 1986 manuscript that I found was one returned to me with comments by the late Joan Kung. Those who knew her will guess the state of the manuscript: barely a margine remained without her useful, sometimes quite critical, but always generous remarks. My paper profited very much from them. I would like to acknowledge also the valuable comments sent to me by David Glidden on the penultimate draft. Above all, I thank Howard Stein for our many years of philosophical discussion and, in particular, discussion of Plato. I can only regret his occasional lapses, brought on by an excessive and unseemly admiration for Aristotle. My account of the Line, as an argument for foundations of the exact sciences, is in substantial agreement with the excellent discussion by Nicholas White in [1976, 95-99].