The strange and challenging stretch of dialectic with which Plato’s Sophist begins and ends has confused and frustrated readers for generations, and despite receiving a fair amount of attention, there is no consensus regarding even basic issues concerning this method. Here I offer a new account of bifurcatory division as neither joke nor naïve method, but instead a valuable, propaedeutic method that Plato offers to us readers as a means of embarking upon the kind of mental gymnastics that will stretch (...) us properly in preparation for further, more challenging dialectical work. Considering several interpretive issues, I argue that bifurcatory division is a process of collective inquiry into the common through which an account, both definitional and taxonomical, is discovered. Depending on the level of understanding exhibited by the inquirers, this account may or may not allow for noetic understanding of the object in the deepest sense. (shrink)

In Archytas of Tarentum, Carl Huffman reconstructs Archytas’ theory of definition by linking definitions to the mathematical study of ratios and proportions. This paper considers whether and how Archytas used definitions and whether he possessed a theory of definition. Our evidence does not support the claim that Archytas has a theory of definition, and his approach to the science of harmonics suggests that he relied on analogies and proportions in the practice of inquiry. We understand sounds and other entities by (...) placing them in a network of relations governed by mathematical proportions. Although he does not seem to have formulated definitions of sound, Archytas pursued inquiry into motion and rest by formulating definitions in such a way that they fit into a larger network of causal explanations. (shrink)