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.

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.

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.