The articles collected in this volume of Science in Context have as their common theme the history of early science. The reader will note the great diversity of the subjects dealt with in this volume, and also some strong commonalities. In our view, this tension between diversity and commonality is central to the historiography of early science, and may represent an important value of this study. To see this, let us first consider the papers in sequence.

Argument

If visual inspection of corpses was central to the development of anatomy in modern Europe, one may ask which of the senses was important for the emergence of the predominant currents of scholarly medical knowledge and practice in third- and second-century B.C.E. China? This article argues that it was tactile perception prompted by a tactile exploration of living bodies. The evidence, derived from a close reading of the Mawangdui medical manuscripts, the 105th chapter of the Records of the Historian (Shi ji), and selected passages from the Huang Di's Inner Canon (Huang Di nei jing), points to three important trends: first, the tactile exploration of the extremities led to a rich vocabulary of compound words for pain (tong) as localized in specific body parts; second, the tactile exploration of the mai (vessels/pulses) gave rise to an even richer vocabulary on qualities of touch in pulse diagnostics; and third, the tactile exploration of the abdomen led to the assessment of the quality of the internal viscera (zang) with words that generally were used for describing the tactile quality of skin and flesh. This finding may appear surprising in the light of later developments during the dynastic history of Chinese medicine where tactile exploration of abdomen and extremities would appear unseemly. The author suggests that extensive tactile explorations of the body were possible before Confucius' teachings became a predominant aspect of state ideology.

Argument

This paper is detective work. I aim to show that the brilliant Pythagorean mathematician Archytas of Tarentum was the founder of ancient Greek mathematical optics. The evidence is indirect. (1) A fragment of Aristotle preserved in Iamblichus is one of two doxographical notices to mention Pythagorean work in optics. (2) Apuleius credits Archytas with a theory of visual rays which saves the principle that the angle of reflection is equal to the angle of incidence. I argue that the source from which Apuleius got this information was the Catoptrics of Archimedes, the genuineness of which I defend against Knorr's hypothesis that it is the Euclidean Catoptrics, which had been misattributed to Archimedes. (3) The omission of optics from the mathematical curriculum in Plato's Republic, and the Timaeus' wholly physical account of mirror-images, can be explained as polemical, for it is well attested that optics was practiced in the Academy. The reason Plato does not mention optics is that he objected to Archytas using mathematics to understand the physical world rather than to transcend it.

Argument

Aristotle's colleague Theophrastus wrote a number of short works on natural historical subjects. They have proved something of a challenge to modern critics. In his Metaphysics, Theophrastus had warned of the dangers in expecting consistent evidence of purpose-directed activity throughout all levels of the natural world. Taken too far, he argued, this expectation carries with it a risk of destroying the prestige of explanation altogether. In the short works – such as On Stones – he appears to be taking his own warning very seriously. So much so that there is little obvious sign to the modern eye of any philosophically inspired taxonomical principle behind the organization of the material presented. Yet taxonomy (of a sort) there is. If Plato had advocated a hard-line teleology in which all natural phenomena worthy of mention and study could be understood in terms of their emulation of the Forms, both Aristotle and Theophrastus allowed several species of teleological impulse. One type drives an organism to be the best it possibly can be, but another drives it to serve the interests of man in the best way it can. The two impulses occasionally collide, but at the “lower” levels of creation where purpose-directed activity pure and simple is often less than evident, we can often find organisms and even inanimate matter serving the interest of human users. This species of anthropocentric teleology provides a justification – and a potential taxonomical framework – for much of Theophrastus' investigation into the more intractable reaches of the natural world, and offers a glimpse of the developing mind-set of the Lyceum in the generations after Aristotle.

Argument

How well does Aristotle's abstract definition of nature in the Physics cope with some significant agricultural facts? Are its implications in tension with the workings of artificial teleology? How Aristotle might categorize domesticated plants is problematic: they are neither obviously natural nor obviously artificial. That artificial things generally retain an intrinsic source of change does not help us to settle the status of “living quasi-artefacts.” A survey of Theophrastus reveals that many agricultural techniques go against nature, rather than collaborating with it; and, moving from the practical to the theoretical, the Mechanica might suggest a scientific program at odds with the Aristotelian tradition of passive observation. Reflection on the Historia Animalium exposes difficulties in specifying natural and artificial environments which exacerbate the puzzle, and reinforce the rationale for Aristotelians to adopt an active stance when investigating nature. The Aristotelian olive remains mysterious.

Argument

The term “universal” is ambiguous; it can indicate either what actually exists in several instances, or what can so exist, even if it is actually exemplified in only one instance. The former sense implies the latter, but not vice versa. It is suggested that form for Aristotle is universal in the latter sense, including what is part of the nature of a species but not individual accidents due to the matter, and that this may help to explain a problematic passage in Metaphysics Z 15. Analysis of passages in Metaphysics Z 8 may however suggest that form as universal in the former sense exists only as a potentiality. The claim that form includes only specific, not individual features has implications for Aristotle's theory of heredity; more generally, his theory of form reflects the tensions between Platonist and non-Platonist elements in his thought and his methods of enquiry.

Argument

The influence of Galen on the subsequent interpretation of the history of ancient medicine has been substantial. This paper explores the consequences of adopting a non-Galenic perspective in two different areas of research. It argues that Galen's own career, and his own views of the ideal physician, cannot be taken as typical of most ancient medical practitioners; and that the theory of the four humors, blood, bile, black bile, and phlegm, did not become a universal standard until after Galen. That theory was merely one of several variations on the theme of body fluids, and entered Greek medicine relatively late. Hippocratic contemporaries of Galen accepted it alongside other theories from the Corpus, e.g. Diseases I, that modern scholars have viewed as incompatible.

Argument

This paper argues that there was a shift in China in the nature, and use, of geometrical figures between around the beginning of the Common Era and the third century. Moreover, I suggest that the emphasis mathematicians in ancient China placed on generality as a guiding theoretical value may account for this shift. To make this point, I first give a new interpretation of a text often discussed, which is part of the opening section of The Gnomon of the Zhou (first century B.C.E. or C.E.). This interpretation suggests that the argument presented in this text for establishing the so-called “Pythagorean theorem” is based upon a certain kind of drawing. Secondly, I contrast this passage with Chinese texts from the third century on the same topic, but relying on a completely different type of drawing. What commands the difference in the kinds of drawing is that the latter drawings are “more general” than the former, in a sense to be made explicit. This paper hence aims at making a contribution to the study of geometrical figures in ancient China.

Commenting on one of the latter figures, one of the authors of the third century, Liu Hui, describes how various algorithms emerge out of the same transformation of one particular figure. His remarks provide grounds for commenting on the link between the general and the particular, in relation to figures and how algorithms rely on them, as the issue was perceived by the practitioners themselves.

The particular figure in question and its transformation are exactly what we find in the Meno, though in relation to a different mathematical issue. The link of that very figure to the one that is perceived as its “generalization” for several algorithms, including the so-called “Pythagorean theorem,” is made not only in Liu Hui, but also by Thabit ibn Qurra (ninth century C.E.), in a letter where he explicitly addresses the purpose of generalizing the reasoning of the Meno. This parallel offers an appropriate basis to highlight differences in terms of conception and use of figures.

Argument

While undeniably more restricted in many respects than the history of modern science (both in that the evidence is lacunose and because the science itself is more elementary) the comparative inquiry into ancient investigations may, from another point of view, be said to be far richer. We can open up the question of why science should have taken such different forms in different ancient civilizations. How did the ancient investigators come to define the problems, and the methods to tackle them, in the ways they did? A history of pre-modern science provides access to ancient aims, values, and ideologies in a distinctive fashion, differing from other areas of ancient thought in that “reality” – as the ancients themselves understood it in different ways – could and did act as a check on their speculations.