My discussion of analogies in Greek and Chinese ethics has already brought to light first just how extensively they were used, secondly how warnings about their deceptiveness can be found in both Greek and Chinese writers, and thirdly that exceptionally, in Greece, Aristotle attempted an analysis of analogical argument explaining under what conditions it can be considered valid, namely where there is a complete induction of all the particular cases falling under a genus. That sets the agenda for this chapter where I focus on heuristics. There are some authoritative analyses of the use of analogies and models in modern science, notably the classic essay by Hesse on their role in the development of thermodynamics (Hesse 1963). One particularly fruitful area for the exploration of analogies has been the use of computers to model complex cognitive processes, where the strengths of the positive analogies have been such as to make problematic the question of whether we are dealing with ‘mere’ analogies. Does the computer have a mind, or does it just behave in ways that resemble one – the issue at the heart of controversies over Artificial Intelligence (e.g. Searle 1984, Haugeland 1985, Crane 1995), where the role of analogy in computational reasoning has been much studied (e.g. Kedar-Cabelli 1988, Burstein 1988, Holyoak and Thagard 1989)? Here, however, the chief topic I shall address relates to the ancient antecedents of the heuristic role or roles of analogies. One of my strategic aims, in these studies, is to examine the strengths and weaknesses of recurrent Western methodological preoccupations, in particular the insistence, in certain contexts at least, on strict deductive demonstration. Accordingly I shall, in this chapter, pay special attention to both the positive and the negative evaluations of analogy in heuristics that we find not just in ancient Greece, but also in ancient China and further afield.

Let me first outline the structure of my discussion. The first section will concentrate on mathematics and consider how the apprehension of similarities and the appeal to perceptible diagrams figure in a variety of contexts, and serve different purposes, in both China and Greece. One of the principal aims of early Chinese mathematics, at least to judge from remarks in Liu Hui in the third century ce, is to establish the common features that link different members of the same class of mathematical objects and, further, to develop procedures that can be applied to different fields of mathematical studies, allowing the subject to grow by extrapolation. Liu Hui considers this to be research into the guiding principles of mathematics and he expresses no reservations on the matter.