152 Dear
cal writers, displacing the previous terms but not itself representing any
conceptual reformation.^9
Around the middle of the sixteenth century, philosophical arguments
had been put forward that challenged the traditional Aristotelian assump-
tion that the mathematical disciplines, whether “pure” or “subordinate,”
were truly sciences. Among others, the humanist churchman Alessandro
Piccolomini and the Jesuit theologian and philosopher Benito Pereira
were prominent proponents of the position that mathematical demon-
strations could not be scientifi c in Aristotle’s sense because they failed to
specify the causes responsible for the truth of their conclusions—causal
necessary demonstration being the strict Aristotelian defi nition of a sci-
ence.^10 Unsurprisingly, this claim proved unpopular among mathemati-
cians, including some of Pereira’s fellow Jesuits. Clavius defended what
he clearly saw as attacks on the intellectual standing of mathematics in
policy documents concerning the establishment of the curriculum of the
new Jesuit colleges, writing in the 1580s of the importance of dissuading
philosophy teachers from downplaying the status of the mathematical
disciplines by denying that they were truly sciences at all. Clavius’s pro-
testations aside, later Jesuit mathematicians also provided counterargu-
ments to undermine the claims of mathematical nonscientifi city, those
of Giuseppe Biancani from 1615 being particularly well known and read
throughout the rest of the seventeenth century. Among other points, Bi-
ancani noted that in the case of mixed mathematics, Aristotle had been
at pains to explain, through his idea of subordinate sciences, how they
too counted as true sciences; he thereby used Aristotle’s authority as part
of his defense. Biancani also argued that mathematical arguments, both
in mixed and in pure mathematics, did in fact employ causes of the usual
Aristotelian kinds (formal, fi nal, material, and effi cient) in proving their
conclusions. After all, what kinds of demonstrations were as necessary
and conclusive as those of mathematics? Certainly not those of natural
philosophy.^11
Seen in this light, attempts during the second half of the sixteenth
century to extend the reach of the mathematical sciences into realms
previously reserved for natural philosophy (physica, or physics in its Ar-
istotelian sense) appear as a kind of cultural muscle- fl exing on the part
of mathematicians. Most notably, the so- called Archimedean revival in
Italy in that period involved exploitation of the works of Archimedes and
Pappus as ancient exemplars of a new, theoretically grounded mechan-
ics that had ambitions to develop an understanding of moving bodies as
well as of statical situations. The fi gures of Tartaglia, Commandino, Baldi,
Benedetti, Guidobaldo dal Monte, and fi nally Galileo not only regarded