My assignment today, as I understand it, is to say something about the Second International Congress of the History of Science, the only previous one held in the United Kingdom; to mention some of the great historians of science which these islands have produced; and to direct our thoughts for a few moments to the historiography of science, technology and medicine, namely the guiding ideas in the light of which one should attempt to write it. So much has already been said in thanks to the city and the university in which we are now assembled that I could hardly add to it, except to express my personal sense of elation at coming on this occasion to the ‘Athens of the North’ where so many distinguished men have lived in the past, from mediaeval times onwards.

The relations between different areas of knowledge have been a subject of interest to philosophers as well as to scientists and mathematicians from antiquity. While recent work in this direction has been largely concerned with the question whether one branch of knowledge (such as arithmetic) can be reduced to another (such as logic), the questions which exercised the Greek philosophers on these matters have a different starting point. Taking for granted that there are a number of distinct areas of knowledge, they proceeded to consider a variety of relations which they observed to hold among the sciences as they knew them; the question of the priority of one science to another is a recurrent theme. In fact, three sorts of orderings were noticed, and the associated conceptions of priority are interesting. Only one of them is the concern of the present paper, though, and I shall briefly describe the remaining two only for purposes of contrast.

The view that religious orthodoxy stifled geological progress has had many distinguished exponents, one of the earliest being Georges Cuvier. To Cuvier, however, efforts to combine Genesis with geology ended before the middle of the eighteenth century, and opened the way not for progress but for wild speculation. We may admire the genius of Leibniz and Buffon, he declared, but this should not lead us to confuse system-building with geology as ‘une science positive’. While Cuvier's younger contemporary, Charles Lyell, agreed that ‘extravagant systems’ had retarded progress, he insisted that ‘scriptural authority’ had had a similar effect until late in the eighteenth century.

Manuscript Add. 3965, section 13, folios 541r–542r and 545r–546r is in the Portsmouth Collection of manuscripts and housed in the University Library, Cambridge. These drafts contain a careful account, in Newton's hand, of his views on place, time, and God. They are part of a large number of drafts relating to the three official editions of the Principia published in Newton's lifetime.

Recently there has been considerable revaluation of the development of natural sciences in the early nineteenth century, dealing among other things with the works and ideas of Charles Lyell. The task of interpreting Lyell in balanced terms is extremely complex because his activities covered many fields of research, and because his views have been unwarrantably distorted in order to make him the precursor of various modern scientific positions. Martin Rudwick in particular has contributed several papers relating to Lyell's Principles of geology, and has repeatedly stressed the need for a comprehensive evaluation of Lyell's scientific proposals, and of his position in the culture of his time. In the present paper I hope to contribute to the reassessment of Lyell's work by concentrating on his discussion of transformism, which constituted the central theme of the second volume of the Principles of geology: the very length of Lyell's detailed and critical analysis of Lamarck's theories reveals the importance he attributed to the question of transformism in the contemporary natural sciences.

In a paper which examined the ‘simultaneous emergence of evolutionary theories in biology and sociology in the nineteenth century’, J. C. Greene said of Comte that ‘it was not from biology that his inspiration [the inspiration of his evolutionary view] was drawn; his writings and letters in the formative period sing the praises of Bichat and Gall but not of Lamarck. His intellectual debt in social theory lay in a different direction—to Condorcet's Sketch of an historical picture of the progress of the human mind, to the historical writings of Hume and Robertson, and to the ideas of Saint-Simon’. This statement from a paper published almost twenty years ago as an exploratory reconnaissance of virgin territory is representative of the kind of confused judgements which still surround a discussion of the inter-relations between social, biological and medical thought in the century 1750 to 1850. It makes some valid points which a critical examination should not be allowed to overwhelm, the most significant being that Comte is unequivocally identified with the Enlightenment tradition represented here by Condorcet, Robertson and Hume. But since it is a very condensed statement about a complex set of relationships, it invites interpretations which the author did not necessarily intend.

How are social and institutional circumstances linked to the knowledge that scientists produce? To answer this question it is necessary to take risks: speculative but testable theories must be proposed. It will be my aim to explain and then apply one such theory. This will enable me to propose an hypothesis about the connexion between social processes and the style and content of mathematical knowledge.

Science is an occupation as well as an intellectual endeavour. This fact is extremely well known, but its consequences have been little explored by historians of science. Sociologists such as Merton, Hagstrom, and Storer have argued that occupational rewards motivate a scientist to publish and thereby further the intellectual ends of the scientific community. Yet, as I have shown in a recent paper, such rewards can also lead to work which is hasty, superficial, and blindly uncritical of the dominant paradigm. Thus the relationship between career motivation and genuine intellectual achievement must be regarded as problematic at best.

Although there are numerous and significant differences between the theories of scientific growth and change proposed by Kuhn, Lakatos, and Laudan, they all hold that specific scientific theories should be viewed as constitutive of more comprehensive theories. Kuhn calls those more general theories ‘paradigms’, Lakatos labels them ‘research programmes’ and Laudan refers to them as ‘research traditions’. They all argue that scientists are much more willing to give up the specific theory within a given research programme rather than the programme itself, and that individual theories should be viewed as attempts to increase the overall explanatory power of the more general theories, since the ultimate concern of the scientist is with the success of the general rather than the specific theory. When a basic theory or research programme is confronted with severe criticism, proponents attempt to protect the hard core or central elements of their programme through the invention of auxiliary hypotheses. Good auxiliary hypotheses adequately answer the objections for which they are designed, and suggest new avenues of research. In 1928, Arthur Holmes provided proponents of continental drift theory with an auxiliary hypothesis which afforded them a badly needed account of the forces responsible for continental drift. Although Holmes' proposal was not ultimately correct, it was the first plausible alternative offered by an exponent of the continental drift research programme.

The reception of Euclid's Optica in the West has received scant attention, in contrast with the interest evoked by the Latin tradition of the Elements. A study of the extremely complex manuscript tradition of the Optica reveals that the translations of this work too were soon in the hands of many teachers, eager to learn what the great Geometer taught concerning vison and visual perspective. Three translations—two from the Arabic (Liber de radiis visualibus and Liber de aspectibus) and one from the Greek (Liber de visu)—were available to scholars before the close of the twelfth century. Furthermore, the Greco-Latin Liber de visu, by far the most widely known and carefully studied of the translations, appeared in at least three different versions before 1200. One of these versions is of particular interest as providing evidence of the diffusion of texts among the scholarly community in the latter part of the twelfth century. The version in question has survived in two manuscripts, Bodleian Library, Corpus Christi College 283, folios 163r–165v, and Seville, Bibl. Columbina 7.6.2, folios 43(44)v–54(55)r. Although the various translations and many other versions of Liber de visu are anonymous, the authors of this text are explicitly given in the colophon, which reads: Nota quod sexaginta et tria toreumata continentur in is to libra. Aimare, gralias age quia hoc opus sic glosulasti sub magistro Johanne de Beaumont. Explicit feliciter liber de visu. Whether Aimar was merely the scribe or perhaps the student of John of Beaumont, it is undoubtedly the latter that is to be primarily credited with the contents of the treatise. Unfortunately, neither The complete peerage nor the Dictionary of national biography list a John of Beaumont from the twelfth century, although the Beaumont family, with some reputation for learning, was prominent at that time in Normandy and England, particularly in the regions near Oxford. Whether John was a member of that illustrious line remains merely a matter for speculation. In any case, the treatise remains of interest to Euclidian scholars and historians of optics as a good witness to the twelfth century concern, not only with Euclid's visual theory, but particularly with his attempts to employ geometry in solving the problems of visual perspective.