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 can be reduced to another , 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. (shrink)

: Marin Mersenne was central to the new mathematical approach to nature in Paris in the 1630s and 1640s. Intellectually, he was one of the most enthusiastic practitioners of that program, and published a number of influential books in those important decades. But Mersenne started his career in a rather different way. In the early 1620s, Mersenne was known in Paris primarily as a writer on religious topics, and a staunch defender of Aristotle against attacks by those who would replace (...) him by a new philosophy. In this essay, I would like to examine Mersenne's changing attitude toward Galileo. In the early 1620s, Mersenne lists Galileo among the innovators in natural philosophy whose views should be rejected. However, by the early 1630s, less than a decade later, Mersenne has become one of Galileo's most ardent supporters. How, then, did Mersenne learn to love Galileo? (shrink)