1 The Birth of Science - MSRI

338 11. The Age-Long Recovery
altogether. 154 In the various areas of physics, conversely, it was the deductive
method that became etiolated, and now even statements that are
provable from simple principles are sometimes regarded as “experimental
laws”; thus, in modern treatments of hydrostatics, the so-called principle
of Archimedes is stated as an experimental law, whereas in Archimedes’
treatise On floating bodies it was deduced as a theorem. 155 A similar slide
can be documented in several other cases (for example, in statics) and may
be suspected in others: for example, “Snell’s law” is generally presented
nowadays as an experimental truth, instead of being deduced from a minimum
principle. 156
The name “mathematics” continued to apply mainly to those areas in
which Greek treatises were still essential. One good reason for this may
be that when mathematics and physics went their separate ways, in the
late seventeenth century, scientists were fluent in the deductive method —
to them an essential feature of mathematics — only in fields where they
could follow the classical model closely. The term “mathematics” was later
extended to new subjects that arose organically from the old ones, but in
the fast-paced development of mathematics in the eighteenth and early
nineteenth centuries, the expansion of content away from the classics was
accompanied by a drift away from the rigor of demonstrations as well.
A second, language-based, factor may have contributed to the fact that
precisely those fields most directly linked to the Greek legacy were seen page 415
as dealing with “abstract” entities, and so labeled as mathematics: in these
fields, the use of Greek-derived technical terms to denote theoretical entities
made it easier to distinguish them from concrete objects. On subjects
where complete Greek texts were not available, the use of terms from everyday
language, such as “force” or “mass”, favored instead a confusion
between theoretical entities and concrete objects to which the theory was
applied. The importance of this effect may not be readily appreciated by
someone who is familiar (as we are) with conventional terminology, but
we must keep in mind that in the late seventeenth century linguistic conventionalism
was not even close to being recovered. 157
154
Considered unworthy of appearing in mathematics textbooks for being too “concrete”, such
constructions were in part shunted to courses in specialized drawing, but not before they were
stripped of their proofs. Thus logical rigor and practical applications, the two main features of
science, are made to stand in exclusion of each other.
155
See page 65.
156
For the conjecture that the law was first obtained as a consequence of a minimum principle,
see page 306.
157
The recovery was a long process, with murky transitional stages that resist neat categorization
and precise dating. A few examples will give an idea of the progression. Linnaeus’ zoological
nomenclature, in the eighteenth century, was an important first stage. In economics, the necessity
to define terms was stressed by Malthus around 1820. Still after that, in Bolzano’s Paradoxien des
Revision: 1.11 Date: 2003/01/06 07:48:20