new issues in the history of ancient science

New Issues in the Historyof Ancient ScienceG.E.R. Lloyd

The history of science, as we all know, took some time to break free fromthe positivist programme of its founding fathers. During the twentiethcentury, in one field after another, it rapidly became the case thatscientists themselves needed to study no more than the last fifteen totwenty years of their subject to provide enough grounding to get on withthe job. Where history of science had been undertaken by Whewell, 1837to demonstrate progress, later advocates of the discipline still repeatedlyused the language of breakthroughs. Herbert Butterfield, who was oneof the prime movers in setting up the Department of History andPhilosophy of Science in Cambridge,1 made much change of the 'scien-tific revolution' — a handy rubric for his university political purposes,but open to the objection that whatever we make of the work of Coperni-cus, Galileo, Kepler and the rest, intellectual changes should never havebeen compared implicitly with political revolutions. There was nostorming of the Bastille, no arrival at the Finland Station. Even Kuhn'slifelong commitment to incommensurability strikes me as overly preoc-cupied with moments of radical change.21 shall have more to say aboutincommensurability later.

I trust I may take it for granted that all serious historians of sciencetoday have learnt the lessons of our immediate past and are alive to thetwin dangers of anachronism and teleology. We cannot reprimand the

1 This has been the subject of two recent articles by A.-K. Mayer, 2000; 2004.

2 See Kuhn's posthumously published autobiographical interview in Kühn, 2000.

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10 G.E.R. Lloyd

ancients for not being modem: we cannot blame them for not even tryingto be modem.

I take those points to be agreed, and those are not the new issues Iwant to discuss in this paper. My starting-point is a different desidera-tum, namely the need to be ecumenical, not in the sense that we assumethat early science is the same across the world, but rather — quite to thecontrary — that we should pay attention to the differences in earlyscience in different cultures. The need is to be genuinely comparative. Itis not enough, I would say, to stick to one's own backyard, as Hellenistssay, or as students of Mesopotamia, or Egypt, or India, or China, and tobe content with our analyses of how theory and practice changed, andone thing led to another, or at any rate was superseded by another, inour own chosen culture. We have to find out, as best we can, difficultthough it is, what happened elsewhere, since it is only if we do so, that wecan test our own ideas about why things turned out in the way they didin our primary target culture. I take it that we are all tempted, from timeto time, to assume that developments more or less had to occur in theway they did occur in the culture we are used to — that the kind ofdialectic we are used to in Greece is inevitable, where continuum theoriesbattle it out with atomist ones, arguments for the eternity of the cosmoswith those for its creation and so on. But even a superficial acquaintancewith other cultures should be enough to disabuse us of that.

Most of my paper will be devoted to elaborating those points andexplaining why I think ecumenical history of science, as 1 wish torecommend it, is the way ahead. But let me first identify some of thephilosophical issues that it brings in its wake. They are not new, for sure,but they gain added urgency when we pay attention to the diversity ofscientific traditions across the world. Let me highlight two especially,the problem of whether any of this is science in the first place, and theissue of how or even whether comparison is possible.

One objection might go like this. If we find a variety of different waysof going about astronomy, or harmonics, or anatomy, how can they allbe science? Indeed perhaps none of them is. Surely, this objection wouldcontinue, the problems that science must tackle are given by the data,and the way they must be tackled is laid down by what the scientists callscientific method. So if we find radically different ways of defining thesubject and setting about its investigation, this is a sure sign that some— or maybe even all — are failing one or other test of scientificity.

Then the second problem follows that up. If we find radical differ-ences in what counts as 'astronomy', say, in different cultures, on whatbasis can we make any comparisons between them ·— and indeed



Neu; issues in the History of Ancient Science 11

between any of them and what we today call 'astronomy'? The analo-gous problem is evidently far greater if we take the example of 'physics'.All history is evaluative, but on what basis can we make evaluations,without slipping into the anachronism and teleology that I have alreadycondemned?

I shall be returning to these problems at the end, but let me say straightaway that I have a good deal of sympathy with those who take the hardline and limit 'science' to what has been recognised as such only sinceabout the mid-nineteenth century.3 Certainly the institutions in whichscientific research is nowadays conducted, the research laboratories, aretotally different from anything that existed before the nineteenth cen-tury, and that makes a profound difference. Yet the hard-liner facesproblems too. What are we to call the systematic investigation of eclipsecycles, and the discovery of their regularities leading to confidence intheir prediction and explanation, other than 'science'? To the argumentthat there cannot be any doubt about what science should study, sincethat is given unequivocally by the data, the counter (which I shallelaborate in due course) is that the data are always multidimensional.As for the argument that there is a, indeed the, scientific method, I takeit that most people nowadays agree that while some such may still betaught in schools, as an ideal, that is merely a pedagogic device. If youtake today's scientists as your yardstick, and eavesdrop their conversa-tions in the laboratory, let alone in the coffee room, you will find thatthere is wide diversity in how they set about their work and none of ithas very much to do with the hypothetico-deductive experimentalmethod taught in schools.

Then to allude briefly, at this stage, to the incommensurability prob-lem, what the hard line on that leaves out of account is that there are stillpoints of contact even between radically divergent ways of under-standing the subject-matter. My claim is that those ways do indeed differ,and that we cannot take what the study of the heavens (for instance)should comprise for granted. But to revert to my previous example ofeclipses, even though the interest in their investigation developed indifferent ways in Babylonia, in China and in Greece, we can still talk ofthem as investigations of eclipses. Indeed using Tuckerman's Tables,

3 Cunningham and Wilson, 1993, offer a particularly trenchant statement of theproblems. Brought to you by | University of Haifa

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12 G.E.R. Lloyd

1962,1964, for example, we can even say what there was for the ancientsto observe, predict or explain, if they chose to do so, that is to say whateclipses would, in principle, have been visible at different times atdifferent locations on the earth. The styles of inquiry (as I shall call them,after Crombie and Hacking4) differ, but what there was to be inquiredinto contains certain common elements, even though, as I said, theproblems are not fully determined by the given data.

So much by way of philosophical preliminaries. But now to someconcrete exemplifications. Let me begin with 'mathematics', where Isuppose that our expectations of cross-cultural uniformity are at theirhighest. Two and two make four wherever in the world you are and atwhatever period in time. That is perfectly true: but aims and interests inmathematical research do vary. Let me introduce you to some aspects ofthe Chinese investigation of numbers (shu). First, what is the evidence?There are two major mathematical classics dating from some hundredyears either side of the millennium, the Zhoubi suanjing and the Jiuzhangsuanshu (both appear in Qian Baocong, 1963, the standard edition bywhich I cite them). The first is conventionally translated the 'ArithmeticClassic of the Zhou Gnomon', the second is sometimes rendered the'Nine Chapters of the Arithmetical Art', but in both cases more thanarithmetic is involved.

The Nine Chapters, for instance, deal with subjects such as field meas-urement, the calculation of the volumes of pyramids, prisms and the like,as well as with the addition and multiplication of fractions, the solutionto equations with multiple unknowns, the extraction of cube roots andso on. The problems are invariably expressed in concrete terms: the textdeals with the construction of city-walls, trenches, moats, canals, the fairdistribution of taxes across different populations, the conversion ofquantities of grain of different types and much else besides. But weshould not be fooled. The answer given to a problem in V 5 about thenumber of labourers needed to dig a trench with particular dimensionsis 7 plus 42773064th of a labourer. That shows that the interest is in theexact solution to the equation rather than in the materialities of thesituation. Nor would the problem discussed in VIII 9, of weighing

4 Crombie used the notion of styles of scientific thinking some time before thepublication of his three-volume magnum opus in 1994. Hacking, 1992, explainswhat his own use of the term 'styles of scientific reasoning' shares with and how itdiffers from Crombie's. Cf also Lloyd, 2004, Chapter 7.Brought to you by | University of Haifa


New Issues in the History of Ancient Science 13

swallows and sparrows, ever occur in real life, even though strictlyanalogous ones certainly might.5

Then in addition to the two Han classics, since 1983 we now have aneven earlier text found in a tomb sealed in 186 BCE, which throws lighton the antecedents of the Nine Chapters in particular. This is the Suan-shushu (Book of the Calculation of shu/numbers).6 Here too we havediscussions of multiplying and dividing fractions, calculating taxes andinterest, determining areas and volumes. But a comparison between itand the Nine Chapters shows both that the latter tackles more complexcases and that it is more systematic in its presentation. Indeed it allowsus to conjecture that systematicity is one of its aims — a point that hasoften been missed in the past.

Points made in the earliest commentator on the Nine Chapters, Liu Hui,writing in the third century CE, are valuable here since they can tell usabout the nature of the systematization sought. The Nine Chapters use acouple of terms, tang (second tone) and tong" (first tone) in a number ofdifferent chapters, dealing, for example, with the manipulation of frac-tions, rectangular arrays, the solution to linear equations and so on. Thefirst tang1 means something like 'equalize', the second 'to bring intocommunication'. Liu Hui brings into play a third term, qi, homogenize.But where the Nine Chapters had left the links between different proce-dures implicit, Liu Hui now defines each of the key terms and points outthat the solutions to the problems depend on the same procedures ineach case.

Thus in I 9, 96.1, he writes: 'Every time denominators multiply anumerator that does not correspond to them, we call this qi, homogenize.Multiplying with one another the set of denominators, we call this long1,equalize.' 'Multiplying to disaggregate, simplifying to unite, homoge-nizing and equalizing to make them communicate [the other tong"], howcan these not be the guiding principles, gangji, of suan (calculation,"mathematics")' (96.3-4).

5 The text discusses how to calculate the weight of each type of bird, given first thetotal weight of five sparrows and six swallows and secondly that each groupbalances when one bird is transferred from each group to the other.

6 Cullen, 2004, offers a translation and commentary with a text based on the Zhangji-ashan han mu zhu jian edition, 2001, Beijing. Brought to you by | University of Haifa


14 G.E.R. Lloyd

The Nine Chapters collect, chapter by chapter, problems of a certaintype, calling for the application of similar techniques, procedures, algo-rithms. There is a greater unity within each chapter than there wasbetween the various more loosely grouped problems in the earlier text,the Suanshushu: that is one point where the Nine Chapters advances insystematicity. But there is a second level of systematization or unificationbetween the chapters, provided by what Liu Hui calls the recurrent'guiding principles'.

As is clear from the Preface Liu Hui wrote for his Commentary, hesees the aim as being to find and show the connections between thedifferent areas of mathematics. The unity is a matter of seeing that thesame procedures work across the board. The other great mathematicalclassic from the Han period, the Zhoubi, shows that this is no merelyisolated, idiosyncratic ambition (on Liu Hui's part), for it too identifiesthe goal as finding the methods that can be applied in different contexts.7

If, asked about one thing, one gives a category that is applicable to amyriad others, then one is said to know the Way (the Dao).

To those brought up on Greek mathematics, Chinese work may seemvery strange. It is obvious that Chinese mathematics is innocent of anydrive towards axiomatisation. Euclid's project, of deducing more or lessthe whole of mathematics as it was known, from a limited number ofindemonstrable primary principles, is totally foreign to the interests ofour extant classical Chinese texts, foreign indeed to the whole of Chinesemathematics down to the arrival of the Jesuits in the sixteenth century,with whom, for the first time, a vocabulary to cope with the notion of'axiomatics' is introduced. But while classical Chinese mathematics doesnot aim at demonstration in the axiomatic-deductive mode, it is a disas-ter to dismiss it, as has been done so often, as merely interested inpracticalities.

That is doubly mistaken. First, there is plenty of evidence of Chineseinvestigations of theoretical and abstract issues. My favourite exampleis the attack on the problem of the value of pi. This was by way ofinscribing increasingly many-sided regular polygons (much as in Ar-chimedes, though in On the Dimension of the Circle, 1232-42, Heiberg-Sta-

Thus the Zhoubi suanjing states that one should seek methods that are 'conciselyworded but of broad application' (24.12ff) and again 'similar methods in compari-son with one another.' The ability to 'distinguish categories in order to unitecategories' is, precisely, what differentiates stupid and intelligent scholars (25.5).Brought to you by | University of Haifa



matis, he uses circumscribed as well as inscribed polygons to give upperand lower bounds for the value). For practical purposes a value of 3 or3 1/7 is perfectly adequate (and such values were often used). But thecommentary tradition on the Nine Chapters engages in the calculation ofthe area of inscribed polygons with 192 sides, and even 3072-sided onesare contemplated. By Zhao Youqin's day, in the thirteenth century, weare up to 16,384-sided ones.8

But the second, more fundamental, flaw in representing Chinesemathematics as just practical in orientation is that it neglects those signsof an interest in systematicity that I reviewed. It is rather that the natureof that interest differs from that of the Euclidean tradition. Liu Hui, theZhoubi and the Nine Chapters do not attempt to deduce the whole ofsuanshu from primary principles. Rather they sought to establish the linksbetween different categories of problems, disengaging the same basicprinciples exhibited in different particular cases and showing that theirrange of applicability was not limited just to them. The movement is notdeductive, but analogical: the concern is not with axiomatic demonstra-tion, but with extrapolation.

Let me add as a coda to this discussion of mathematics, that we donot, of course, have to go to China to appreciate its possible diversity.We have only to remember the different agenda and methods of Hero,Diophantus, Porphyry, lamblichus and Proclus to recognize the diver-sity within the different traditions of Greek mathematike.9 But maybe thedistinctive Chinese contribution to ecumenical history of mathematics isthe focus on finding the guiding principles that link procedures acrossdifferent problems and enable the subject to grow by their extension toothers.

Let me now review briefly a number of other fields, before I attemptto assess the implications. We are used to recognizing quite a differencebetween Greek phusike and modem 'physics'. There is very little inAristotle's treatise on ta phusika that a modern physicist would acknow-ledge to belong to his subject (let alone to make an essential contributionto it). Phusis, as is well known, covers the whole of nature, both inanimateand more especially animate beings. Periphuseos historia looks as if it doesquite well as the Greeks' own — actors' — category for the investigation

8 See Volkov, 1997.

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of the whole of nature, though we must remember that phusis is oftennormative as much as descriptive. In Aristotle, humans are 'the mostright-sided' of animals, and our 'up' is directed at what is naturally 'up','right' and 'up' being defined in terms of the archai of movement andgrowth respectively.10 So humans are the norm by which other animalsare judged. When Aristotle says that humans are by nature, phusei,political animals, he has left the domain of what we call natural science,for what we call sociology.

But if we have some problems with how Greek phusike maps on to'physics' or 'biology' or 'natural science' more generally, we are poten-tially in for a far greater shock when we turn to China. In China there isno single concept that is equivalent to phusis or to 'nature' as such at all.11

In different contexts the Chinese discuss 'heaven', tian, or 'heaven-and-earth', tiandi, or the myriad things, wanwu: or they investigate whathappens spontaneously (without human intervention, naturally in thatsense) for which their term is ziran; or they study the patterns of things,li, or their innate characteristics, for which they have two terms. First ;zng,a term used initially of refined rice, and so of things' 'essences' thoughnot in any Aristotelian sense, and secondly xing, though when that isused of water and of humans in the Lüshi Chunqiu the former is said tobe purity, the latter longevity.12 And of course they investigate change,especially those associated with the interactions of yin and yang, and withthe five phases, wuxing. The latter, however, are not elements in theGreek sense of the ultimate building blocks of physical substances, butrather, precisely, the phases in the transformations in cycles of change.

Yet while the Chinese show plenty of interest in a wide range ofgeneral and particular problems, where we might use the term 'nature'in our translations of their ideas, they had no single term — and nounitary concept — that equates with ours or with Greek phusis (but thenthat may not be so surprising, if we reflect on the polyvalence that bothphusis and 'nature' display).

10 See 1A 706al9f and PA 656alOff especially.

11 Cf Lloyd, 1996, 6ff.

12 'The true nature (xing) of water is to be clear . The true nature (xing again) of manis to live to an old age' (Lushi chuncjiu 12, Knoblock and Riegel, 2000, 64-5).Brought to you by | University of Haifa



Now five phase theory (in this like Greek studies peri phuseos) wassome time in the making. But once in place — at around the turn of themillennium — it provided a common framework within which verydifferent types of phenomena and modes of change could be describedand so comprehended. The five phases are named fire, earth, metal,water, wood, but these are not substances, so much as processes. Watermeans soaking downwards: fire means flaming upwards, as one classictext puts it.13 What they are interested in is not an analysis of theconstitution of water, fire and the rest, but their interactions, whatdestroys what and what generates what.

If we probe further, more differences come to light. In Greek thoughtthe boundaries between phusike and mathematike were contested. Radi-cally different views were proposed as to what mathematike was about,with Plato locating 'mathematical intermediates' between Forms andperceptible particulars, and Aristotle insisting that what the mathema-tician studies is the mathematical properties of physical objects. In China,in the bibliographical treatise in the Hanshu (30), both the study of theheavens (tianwen) and five phase theory (wuxing) were considered sub-divisions of shushu (numbers and methods).14 There was no question ofany controversy about when or under what conditions 'physics' couldbe tackled 'mathematically' — no problem over category boundaries:investigators got on with finding the numbers in things (in the move-ments of the heavenly bodies, or in the cycles of the phases) as and whenthis suggested itself as possible and relevant. There was, to be sure, someoveroptimistic finding of relevance where there was none, but then thesame can be said of Greece.

Again unlike in Greece, the five phases do not postulate any radicalgulf between a hidden underlying reality and the surface appearances,let alone between an intelligible and a perceptible world. Five phasetheory is not dependent on an epistemology in which reason is pittedagainst perception or where the evidence of the senses is challenged inthe name of a more reliable criterion of the truth. The Dao may be hardto fathom, but it is not located on the far side of an epistemological or

13 This comes from the Hong Fan (Great Plan) section of the Documents (ShangshuChapter 32) discussed by Graham, 1989,326. Cf Nylan, 2001,139-42.

14 See Kalinowski, forthcoming, and contrast Harper, 1999.Brought to you by | University of HaifaAuthenticated | 142.58.101.27


18 G.E.R. Lloyd

metaphysical gulf. Besides, the important thing is not to know it, so muchas to embody it.

Of course generalizing about Chinese thought on change is asfoolhardy as doing so about Greek phusike, but let me recapitulate themain contrast. While most Greeks focused on elements and essences— and where Aristotle's ideal was causal accounts demonstrated insyllogisms with the causes as the middle terms — the Chinese concen-trate rather on the associations between things that govern the trans-formations they undergo. They are concerned with what interacts orresonates with what. True, many of the associations they postulatedare pretty fanciful — but then the same can certainly be said of manyproposed Greek causal accounts. Besides, it was the Chinese who firstspotted, for example, the directionality of the magnetized compassneedle, even though how they got there — via Han divination tech-niques — is a long and complex story, which Joseph Needham, 1962,229-334 discussed at some length. The more important point is that —as with my comparison between Greek and Chinese 'mathematics' —we are dealing with different perceptions of the relevant subject-matter.If we say the phenomena in question are in a sense the same ('change'),that is only because they are multidimensional. We are dealing withdifferent styles of inquiry, where they are to be defined by the aims andmethods of the investigators and the intellectual maps they had of theinvestiganda.

These points can be elaborated but also qualified by considering twosubject areas that look to be among the most promising for a directcomparison between Greece and China, namely, the study of the heav-ens and that of sounds. We have, on the face of it, common interests incalendar regulation, especially well developed in China where each newdynasty generally needed to establish its own calendar, less well devel-oped, but certainly not ignored, in Greece. There are common interests,too, in determining the periodicities of the movements of the planets,sun and moon, and in the case of the sun and moon in cycles of eclipses.In both Greece and China the heavens were scrutinized not just forthemselves, but for the signs they may give for the future for individualsand for states. Where is the problem, one might then be prompted toask, in assessing both Greek and Chinese 'astronomy' and 'astrology' inthe same terms?

Where what we call astrology is concerned, many of the same featuresdo indeed recur, though I would point to one important difference,namely the explicit controversiality of celestial divination in Greece. Forevery thinker who argued that it was possible, there was another who




denied that.'3 But then remember that the Greeks also disputed theviability of astronomy. The Epicureans rejected much of it as merespeculation and the sceptics withheld judgement, of course, on all mat-ters to do with hidden reality.

But it is even more important for my purposes here to point to thedifferent conduct of the study of the heavens itself. The recording ofobservational data could serve very different purposes in Greece andChina. The Chinese undertook a massive observational programmewithin the Astronomical Bureau, from Han times onwards, designed,among other things, to establish eclipse cycles: the focus was on theability to predict such. But as is well known, they did not normallyexplore geometrical models for the sun, moon and planets, the topicwhich, from Eudoxus on, was the primary goal of one tradition (at least)in Greek inquiry.

Those Greek models provided explanations, of planetary movementsand eclipses: they enabled the phenomena to be deduced, though in-itially, before the models were given detailed, quantitative parameters,they were not much use for the purposes of prediction. Eventually, whenPtolemy brought to bear far more extensive data than had been availableto anyone before Hipparchus — much of it derived from Babyloniansources — the models were predictive as well as explanatory. But inorigin the main aim was to show how apparent irregularities could bereduced to regularities. Like many others, I do not credit the story thatclaims that it was Plato who set that task to the astronomers,16 but thedevelopment of Greek astronomical model-building itself provides evi-dence enough that it was a primary preoccupation. On the one hand, itserved to explain the phenomena: on the other, the ideologists claimedthat it showed the order in the universe. But while, as I said, the Chinese

15 Ptolemy certainly thought astrology was based on tried and tested experience andmounts arguments to defend it in the Tetrabiblos The principal arguments on eitherside, both pro and contra, are set out at some length in Cicero's On Divination.

16 At OH Aristotle's On the lienvens (in Cad) 488.18ff Simplicius purports to be citingSosigenes who may in turn be drawing on Eudemus' history of astronomy. Accord-ing to the story, Plato set contemporary astronomers the task of accounting for theapparent irregular motions of the planets in terms of combinations of uniform andorderly motions At in Cael 49231ff Simplicius further specifies that the motionsshould be circular Brought to you by | University of Haifa


20 G.E.R. Lloyd

focus was on prediction, rather than on explanation, teleology was neveron their agenda.

The situation in harmonics is similar in that again there are commonconcerns, as between Greece and China, for example to give numericalvalues to the main concords, or rather to make the most of the fact thatthose concords can be expressed in terms of ratios between simplenumbers — and then further to make the most of the symbolic associa-tions that concords suggested. Both the Huainanzi and the Shiji explorethe ratios in the pentatonic scale and those of the twelve pitch-pipes thatgive the twelve notes of what we would call the twelve-tone scale.17 Insome respects the Chinese eventually went far beyond anything we findin Greece: they get to the notion of equal temperament, defined byintervals of the twelfth root of two, but that was not until the sixteenthcentury. In one second-century BCE account of how the twelve-tonescale is generated, in Huainanzi 3 (21B), the twelve notes are got byalternate ascending fifths and descending fourths. The Chinese hereproceeded very much in the same way as Aristoxenus did, when heinsisted that musical scales should be constructed on the basis of inter-vals identifiable directly by perception — fifths and fourths indeed.

But in Greece the Aristoxenians were confronted by an opposingmethodology, arithmetical rather than geometrical in orientation, wheremusical relations are construed as essentially ratios between numbersand the task of the harmonic theorist becomes one of deducing variouspropositions in the mathematics of ratios, for example that neither thetone nor the semitone can, strictly, be halved. That methodological/epis-temological debate reaches its highest point in Ptolemy's Harmonics, withits examination of previous theories, some based on reason, some onperception, leading to Ptolemy's own sophisticated via media (whichAndrew Barker, 2000 has recently analysed). Ptolemy insisted that theconcords correspond, indeed, to simple ratios, but that those mathemati-cal ratios must be brought to empirical test, for example on the kanön.Ptolemy is clear that some of the positions adopted by opposing meth-odologies are incompatible with one another. Some theorists asserted,while others denied, that an octave equals six tones, a fifth three and a

17 Lloyd, 2002, Chapter 3 briefly sets out the main divergent Chinese and Greekharmonic analyses. The main passage from Huainanzi 3 has been translated in Major,1993. Brought to you by | University of Haifa



half, and a fourth two and a half tones exactly. That is why there are priorquestions, to do with methodology, that need to be settled before em-barking on the detailed analysis of musical phenomena.

But in classical Chinese writings there is no sense of an either/or, thatan epistemological or methodological decision has to be taken, forexample as between line segments treating sounds as a continuum, andpurely arithmetical ratios. They stuck to the latter but had no compunc-tion in introducing, explicitly or implicitly, some rounding adjustmentsto make the analysis work when the ratios became too complex. That isvery much what Greek astronomers, Ptolemy himself included, allowthemselves in their application of astronomical parameters, and cer-tainly what Greek musicians did in their actual music-making. Yet suchfudges, if we care to call them that, were always a liability or an embar-rassment for the underlying rational epistemology.

Let me turn now to the implications of the analyses I have proposed, andthe first lesson I would draw is simply to underline the importance ofthe diversity of ancient investigations. There was nothing inevitableabout the way in which the studies of the heavens, or of change, or ofharmonics, or even of mathematics, had to develop, and one can add thatthe same is true in the study of the body, of disease, or of animals andplants.18 It is not that those studies had to take the Greek, or the Chinese,or, come to that the Babylonian or the Egyptian, route — as if, once suchinquiries began, the subject-matter itself dictated that it should be inves-tigated in a particular way. Rather, we can and should ask why theinvestigations that were undertaken took the form they did in differentancient societies.

One argument that Nathan Sivin and I have proposed is that theconcern for foundations, the preoccupation with epistemology, thesearch for certainty, and the development of axiomatic-deductive dem-onstration, in Greece, can be correlated with the competitiveness ofGreek intellectual life, where rival Masters of Truth sought knock-downarguments to defeat all comers. It is not as if there were no rivalries inChina, to be sure: but one of the main contexts of communicativeexchange there differed, in that the goal of many important intellectuals,both before the unification of the Empire and after it, was to advise rulers,

18 I have discussed these issues in Lloyd, 1996, Chapter 9, and 2002, Chapter 8.Brought to you by | University of HaifaAuthenticated | 142.58.101.27


22 G.E.R. Lloyd

and that necessitated a certain discretion (cf Lloyd and Sivin, 2002). Therewas not much point in suggesting (in the way some Greeks do) thateveryone else had got it wrong, to the individual who had been ulti-mately responsible for the previous conduct of inquiries. Moreover, afterthat unification, especially, state involvement in 'scientific' investiga-tions — from astronomy through to medicine — was considerable andthat meant the investigators working to an agenda determined by,certainly it had to be acceptable to, the authorities. There was much moreof a sense of working within an agreed framework than there ever wasin Greece.

Those conjectures are controversial. But I would insist that to improveon them one has to think comparatively. It is only the comparativehistory of ancient science that provides the means of testing whichfeatures of which types of inquiry can be correlated with what otheraspects of the intellectual, cultural and political situation in which theinvestigators worked.

That is a far-reaching project, for sure: history of science as so con-strued is appreciably more demanding than it is generally thought to be.Moreover the heterogeneity of early investigations serves to bring outthe importance of the problems in the philosophy of science that we ashistorians have to come to terms with. Let me end with some commentson the problems I mentioned at the beginning.

Is this history of science in the first place? There has been much heatedcontroversy over this in recent years, some of it, in my view, rather sterilebecause merely definitional. Of course, as I said, the institutions withinwhich scientific research is nowadays carried out would be unrecogniz-able to anyone living before the nineteenth century, and that makes, forsure, a profound difference. But we cannot define science in terms oftoday's knowledge, today's results — for who can say how much oftoday's science will remain by tomorrow's lights? Rather we have todefine it more loosely in terms of aims, namely those of understanding,explaining, predicting, the phenomena of the world around us, allowing,as I have done, that different views can be and have been taken aboutwhat such understanding, explaining, predicting will consist in. Thereare, naturally, massive differences in the ways in which such aims areimplemented in the ancient, and in the modern, world. But the ambition,at least, links the most modern with even some very ancient investiga-tors.

But then my second main problem concerned the basis on whichcomparisons can be made. The more I stress the actual diversity ofinquiries undertaken in antiquity, the more that seems to point to



Νειυ Issues in the History of Ancient Science 23

relativist conclusions, even maybe to their incommensurability. Yet themore one insists (as I have also done) on the points of contact betweenthose inquiries, the more it may appear that we shall be driven back toa nai've realism. Yet neither option will do. Naive realism, in any case,falls with the fall of the correspondence theory of truth. There is no realityout there to which direct access is possible in a totally theory-neutralvocabulary. Yet if the correspondence theory of truth (in that form) isimpossible, a coherence or consistency one is not enough, since we areall familiar with plenty of sets of statements that are internally consistentbut false. Nor do I think that that view can be shored up by claiming thatit is what is accepted by some group, maybe even by a group of expertssuch as scientists or philosophers, that is to count as true, for it cannotbe enough that it should be just by that token that it should count as true.

These are large issues, indeed, and I can do no more than sketch howmy answers would go here. But the dilemma with regard to truth tendsto be overdrawn, and incommensurability overstated. On the first scoreI side with those, such as Bernard Williams, 2002, most recently, whowould resist the demand for a single theory of truth, applicable acrossthe board. The protocols that are appropriate to verify a claim varyenormously from one context to another and verification in science isalways provisional, never definitive. We just have to use our best judge-ment, even if we have no algorithm to tell us when we have got it right.

Then as to incommensurability, that has been used to make valuablepoints about the ways in which not just single concepts but clusters ofthem are implicated in the evaluation of a world-view. But what incom-mensurability tends to downplay is that while all language is theory-laden, there are important differences in the degrees of theory-ladenness.The associations of the terms helios and selene, ri and yue, 'sun' and'moon', vary a great deal: yet the primary referents are not in seriousdoubt. Eclipses were a topic of interest in many ancient societies, eventhough the understanding of what an eclipse is, and of its causes, varies.That does not mean that there was just one legitimate interest in aninvestigation of eclipses, for example to predict, or alternatively toexplain, them. There is no single set of phenomena that constitutes theunique target of scientific inquiry. The phenomena are, as I said, alwaysmulti-dimensional and the possible aims, or styles, of inquiry are di-verse. We cannot just lay it down that in considering change, the focusof interest should have been on processes rather than substances, or viceversa. We cannot say that what astronomy needed was geometrical,rather than arithmetical, models, or that advances or new knowledge inmathematics depended on Euclidean axiomatisation, rather than Liu



24 G.E.R. Lloyd

Hui's focus on extrapolation. Yet in each case those differences do notrule out, they presuppose comparison.

This is not to say that just any definition of the subject-matter, just anystyle of inquiry, goes, in a spirit of Feyerabend's Against Method, 1975.Judgement about the success of an inquiry not only can, but mustinevitably, be made — for I am committed, as I said, to there being notheory-neutral language in which pure description can be couched. Butif judgements are unavoidable, on what basis can they be made? Thereare two parts to the answer. First we can invoke the ancients' own criteriaof success (for neither in Greece nor in China was there any lack ofcriticism of contemporary or past inquiries on the grounds of theirinadequacies). And then the second mode of evaluation that is open tous is indeed to exercise our judgement on their success, hazardous thoughthis often is.

We can illustrate this once again with the example of eclipses. Weknow, for instance, that Chinese astronomers were more concerned notto miss an eclipse than with predicting one that did not occur (for whichvarious rationalizations were sometimes given, including the idea thatthe eclipse did not occur because the Emperor was exceptionally virtu-ous). But we also know, because we can work it out, that some eclipserecords were forged. Some eclipses that happened were passed over insilence: but some too were stated to have occurred that never did—againfor largely ideological reasons: they were a mark of the Emperor's mis-behaviour or that his mandate was coming to an end.19

We are not limited to an ancient perspective, even though on manyissues it is wise to keep pretty close to one especially in the early stagesof our investigation. We can and must identify mistakes, from somerelatively easy cases in such a domain as mathematics to the far moredifficult ones in a field like medicine — not that we do so from anyvantage-point of Olympian infallibility.

I recognize that we have to get on with detailed analyses of concreteproblems, whatever culture or period it is we study. Many participantsin this colloquium, concentrating on Greece in the Hellenistic period,exemplify the point, and Philippa Lang's comparisons between Greekand indigenous Egyptian medical practice in Hellenistic Egypt are anexcellent example of the type of study I think we need. But we also need

19 I draw on the work of Huang Yi-Long, 2001, here.Brought to you by | University of HaifaAuthenticated | 142.58.101.27



to raise our sights from time to time, to examine other cultures and notjust other periods, to investigate how the subjects were defined there —for we cannot take 'astronomy' for granted, let alone 'physics', nor even'mathematics'. We need to examine radically different traditions indifferent cultures, to study what the aims and methods of differentinvestigators were, their styles of inquiry, as I put it, for it is only whenwe do so that we can move from the description of what happened todecently testable hypotheses about why — why the developments tookthe form they did, why were those styles of inquiry the ones cultivated— difficult though such questions are always going to be to answer. Ofcourse we do not need to travel outside Greece to find variety — myexample of the heterogeneity of Greek mathematike is a reminder of this,and there is heterogeneity, though to a lesser extent, also in China. Butif we are to come to terms with Greek and Chinese work as a whole,including coming to terms with why the heterogeneities took the par-ticular forms they did, then it seems to me that we need to be compara-tivists — ideally ecumenical ones — even though I appreciate that thatis likely to prove unpopular with specialists, for the obvious reason thatit is so much harder work.

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Νετυ Issues in the History of Ancient Science 27

Glossary of Chinese Terms

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