1 The Birth of Science - MSRI

6.6 Postulates and the Meaning of “Mathematics” and “Physics” 163
It is not by accident that the already quoted theoretical reflection of page 209
Philo of Byzantium on the experimental method 49 appears in a work on
the construction of catapults and mentions the experiments needed to determine
the optimal design features of the weapon. Likewise the science of
pneumatics, in which the experimental aspect is more evident, is closely
linked to the construction of objects such as pumps or water supply systems.
50 An analogous link can be glimpsed between acoustics and the design
of theaters and musical instruments.
6.6 Postulates and the Meaning of “Mathematics” and
“Physics”
The criterion we have identified for the choice of postulates, namely the
ability to “save the phainomena”, is certainly essential, but it does not lead
to a unique choice of postulates. Consider again the example of motion:
as Euclid observes, 51 the same phainomena can be saved by different sets
of postulates saying which objects are really stationary and which are in
motion, inasmuch as the same visual impressions are deducible from both
sets. This eventually led to the idea of a free choice of a reference system
with respect to which motion is to be measured, but it predates the
notion of a reference system. Because they were stated using verbs from
ordinary language, postulates about states of motion necessarily had to
involve “absolute” motion at first, so what we regard as a free choice of
reference systems was then seen as an equivalence of mutually contradictory
postulates. The epistemological importance of this example was
therefore much greater than it might appear today.
Sextus Empiricus writes that one must suspend judgement about the
question of what objects are truly stationary. 52 Here as elsewhere, he is
probably echoing a thought that goes back at least to Herophilus, as seems page 210
to be implied by the following passage of Galen:
Again, he [Herophilus] will express doubt in another manner by
justly making the following distinction . . . : “That which sees produces
sense-perception of that which is seen, either because what
sees is stationary, and so is what is seen, or because what sees is in
motion and the seen object stationary, or because both are in motion,
or because what sees is stationary and the object is in motion.” Then,
49 See page 97.
50 See Section 4.6.
51 Euclid, Optics, Prop. 51. Compare page 153 above.
52 Sextus Empiricus, Pyrrhoneae hypotyposes, I, xiv, 107.
Revision: 1.7 Date: 2002/09/14 23:17:37