Natural Knowledge in the Classical World 47already established. The lay of the scientifi c land, the established inter-
connectedness of certain kinds of problem sets and the tools for attack-
ing them, all this meant that there was more than enough work to be
done as it was. Moreover, his training and his reading, his very encultura-
tion as a scientist, immersed him in these problem sets as sets, a pack-
age with known questions and promising avenues of approach already
sketched in, just waiting for further exploration. These sets were rich and
varied: a heady combination of mathematical tools, cosmologies, theolo-
gies, and a set of well- defi ned goals, all of which Ptolemy would build on
and develop.
But not all sciences are mathematized or mathematizable, and there
was work to be done in those fi elds as well. If Ptolemy could plead for the
high status of his own subjects on the basis of mathematical certainty,
that did not mean that work could or should not proceed apace in fi elds
where mathematics was not applicable. Nor did it mean that the investi-
gators in those fi elds could not bring sophisticated logical and analytical
tools to bear on their subjects, tools that could, when used well, provide
nonmathematical kinds of knowledge.
TREES, FOR EXAMPLE
So what about nonmathematized sciences? If we jump back in time again
to Aristotle, we fi nd that he did a vast amount of work in biology, work
that was carried on and further developed by his successor in the Lyceum,
Theophrastus of Eresus.^22 In addition to classifi catory work, one of the ar-
eas of fundamental innovation in Aristotle was his analysis of growth and
development. How, the old question goes, do acorns become oaks?
Aristotle did not spend a lot of time on plants in his oeuvre, but he
did do a lot of work on animals (about a quarter of his extant work is
zoological). Where he did discuss plant development specifi cally, it does
not differ fundamentally from his discussion of animal development. He
began by looking at the qualities of the mature organism and saw these as
actually existing in the adult. Here, “actual” is a technical term meaning
that the particular qualities both can be present and are present at the par-
ticular time of analysis. In the case of a deciduous tree at higher latitudes,
for example, green leaves are actually present only part of the year, but
they are potentially present in winter. This winter potential is not a way
of saying they could grow in winter, but that in winter the green leaves
are not actually present, even though under different circumstances (at a
different time of year) they can be. The qualifi cation of potential covers