Janet Sisson

In his 'Moral Theory' Plato developed and justified views on the best way for humans to live, and to set up and regulate societies in the light of their understanding of their own needs and limitations. These views are presented in his dialogues. The study of the influence of mathematics on Plato's dialogues, and hence on his moral theory, is not a matter of tracing the effects of contemporary mathematics on particular arguments or styles of argument. The dialogues are stimulants to thought, not presentations of finished theses in a dialectical dress. The introduction of mathematical ideas into the dialogues is to be explained on educational grounds, as contributing to philosophical understanding. Mathematics provided a number of techniques of problem solution, and an abstract world in which the problems of argument in terms of general ideas could themselves be more readily studied and arguments now considered metaphysical could be formulated and discussed. Further the working methods of mathematicians provided an example of how intensive discussion could lead, although sometimes by a lengthy route, to real increases in understanding. Mathematics provided extensions to the language and practice of discussion, rather than a simple model for an improved discourse or an ideal ontology. All these aspects appear in Plato's treatment of moral, social and political issues. ;In the dialogues readers are instructed in how to inquire into philosophical questions while having some chance of securing answers that are more than the result of unfounded preference. Plato uses techniques of investigation drawn from the successful research of mathematicians. Ancient researchers would seek definitions of suitable objects. They would try out various hypotheses. They might classify the objects necessary for their inquiry in ways that depend upon what would later be called their 'essential connections' with one another. Each genuine inquiry might be thought to discover the logos underlying the beliefs upon which decisions in particular spheres, solutions to particular problems, depend. Plato's dialogues provide an introduction to these elements of philosophical thinking, a way of grasping the mathemata known to those doing new work, but mathemata that are modes of inquiry, and not collections of facts or of supposed truths