166 Dear
when one looks over the centuries from the sixteenth to the twentieth is
the unsettled character of notions of “causes” and “essences” themselves.
For those physicists in the later nineteenth and twentieth centuries who
steered well clear of German idealism, for example, the concept of “things
in themselves” as their ultimate quarry (whether actually capturable or
not) need not have made any sense at all; for them, a positivistic focus
on instruments and measurement was, and could not but be, enough.
The dispute between Bohr and Einstein may be taken as exemplary of a
version of this issue.^56 And one person’s deep causes might be another’s
instrumental conveniences. The philosophical distinctions that had char-
acterized the early- modern demarcation between mathematics and phys-
ics—even for Newton—had never been absolute, but were always open to
renegotiation and disagreement. So, similarly, it has never been entirely
clear exactly what the concept of “natural philosophy” means.
Thus (to return to the fading of the category “mixed mathematics”
in the nineteenth century), the German physics community, unlike its
British rival, spoke throughout that period not of “mixed mathematics”
as a crucial adjunct of physics, but of “applied mathematics” (angewandte
Mathematik), evidently to refer to much the same array of techniques
and concepts.^57 German applied mathematics made use of mathematical
models and conceptualizations to attain its ends, just as did the mixed
mathematics of Cambridge- trained physicists, but it tended to be regarded
more as a set of tools to be used in physics rather than a research area
with its own boundaries and coherence.^58 One of the arguments for the
continuing preeminence of mixed mathematics in Cambridge even by
the end of the century was that, being intimately associated with me-
chanics, it appealed to the foundational conceptual elements of physical
understanding.^59
One fi nal observation about this curious history: to the extent that
early- modern natural philosophy had been in part characterized, and
codifi ed academically, in the terms of its distinction from practical knowl-
edge, it had needed be kept clear of more than just mathematics. But in
the seventeenth century, instrumental practicality had begun to fi nd its
way into newer, rather heretical reconceptualizations of what natural phi-
losophy ought to be—Francis Bacon being the most obvious spokesman.
By the later seventeenth century, the idea that natural philosophy had
some special relationship to practical know- how had become widely ac-
cepted in the circles represented by the scientifi c societies and academies
of the period. Meanwhile, another new category of natural knowledge had
appeared by midcentury: “experimental philosophy.” Experimentalism
taken as a set of knowledge- generating tools was an important aspect of