1 The Birth of Science - MSRI

11.8 The Rift Between Mathematics and Physics 337
established. The Greek term phenomenon, too, had taken on its modern
meaning: no longer a phainomenon — what is perceived, via the interaction
of subject and object — but an objective fact, thought to be describable
without any reference to the method by which it is observed. The awareness
that different theories can save the same phainomena is abandoned
for the conviction that phenomena unambiguously and definitively lead page 413
to “true principles”. Although the technical structure of modern physics
is built on results of ancient mathematics, its epistemology is profoundly
affected by Aristotelian thinking and the theological tradition.
We have seen how the relativity of motion was introduced in Hellenistic
science as an application of the much more general idea that different but
equivalent explanations, based on different premises, can be offered for
the same phainomena. Thus is it not surprising that with Newton we lose
again the awareness that all motion is relative (which had been recovered
by Galileo, at least in part, after seventeen centuries), and return to a an
essentially Aristotelian conception of space.
The theoretical views put forth by Newton and Cotes spread together
with Newtonian mechanics, leading to a split of exact science into two
streams, mathematics and physics (in the modern sense). Both inherited
from ancient mathematics the quantitative method and many technical
results, and from ancient physics (which is to say, natural philosophy) the
goal of producing absolutely true statements. The two streams diverged in
the nature of their subject matter and the criterion of truth applied to their
statements. Mathematical entities, though applicable to the description of
concrete objects, were regarded as abstract, while physical entities were
felt to be as concrete as the the objects to which they applied. Whereas the
assumptions of mathematics (called postulates) were seen as immediately
obvious truths, those of physics (called principles or laws) were seen as true
if and only if they were “proved by phenomena”, to use Cotes’ words.
Other statements could be deduced from the initial ones; but whereas in
mathematics the deductive method was essential and constituted the only
way through which truths not immediately evident could be established,
physics statements, though deducible from principles often enough, were
also considered to be directly verifiable, and this lessened interest for the
deductive method in physics, where it became optional.
The scope of what was considered mathematics or physics may seem to
some extent arbitrary. For example, statics and optics ended up in physics,
whereas geometry remained an essential part of mathematics. Work meth- page 414
ods, which in Antiquity had been the same in all three, changed according
to the new classification. In geometry, the ties to drawing wore off, and
now Euclid’s “problems” (constructions) are left out of the curriculum
Revision: 1.11 Date: 2003/01/06 07:48:20