164 Dear
no attention to the fact that all these arts are nothing but scaffolding for
achieving science, and not science itself.^48The “scientifi c arts,” according to Buffon, were those bodies of tech-
nique that were good for calculating and classifying but that did not pro-
vide insight into the proper concerns of natural philosophy—namely,
causes and the natures of things.
The continued existence during the middle part of the century of,
especially, French complaints regarding mathematics and its philosophi-
cal shortcomings appears to have subsided by century’s end, as Heilbron
argues in his contribution to this volume. What had overcome the tra-
ditional complaints, and their associated conceptualizations, was a revi-
sion of what should count as natural philosophy, and this was driven by
the Newtonian philosophical ideology already discussed. The stereotype
of merely descriptive mathematics versus causal or explanatory natural
philosophy had become much less clear- cut, in part because of the role
of (loosely) mathematical instruments in the work of experimental phi-
losophy.^49 The experimental cabinets of public as well as college lectur-
ers in natural philosophy in the eighteenth century—Desaguliers, Dufay,
Nollet, and the rest—were fi lled with gadgets that did things, rather than
explained things in themselves; and they sometimes did things that could
even be measured.^50
This is the sense in which Christian Licoppe has argued that Benjamin
Franklin’s work on electricity can be seen as fundamentally mathematical
and Newtonian even though that work was to a great extent qualitative
and apparently unmathematized.^51 The ambiguous category of “physico-
mathematics” became ever more identifi ed with operationalism, that is,
learning how to make experimental setups perform in predictable and
controllable ways. Such a natural philosophy did not require explicit as-
sociation with mathematical formulations in order to import the kind of
causal nescience that had long been perfectly respectable for traditional
mixed mathematical sciences.THE AFTERLIFE OF MIXED MATHEMATICS AND THE RESHAPING OF
NATURAL PHILOSOPHY
This chapter has purposely focused upon the term itself “mixed mathemat-
ics,” on the understanding that such labels are not applied meaninglessly,
even when they may be applied thoughtlessly. The use of the term in the
seventeenth and eighteenth centuries bespeaks the sense that it served