1 The Birth of Science - MSRI

150 6. The Hellenistic Scientific Method
The next few sections will be devoted to these aspects of the Hellenistic
scientific method.
6.2 Postulates or Hypotheses
One important aspect of scientific method was that it marked explicitly
and unambiguously the premises that were to be accepted within a given
theory. These premises were called (postulates, which is to say
demands), or (assumptions), or yet ¥ (“hypotheses”).
This last term merits a digression. Its original meaning, “foundation,
base”, never disappeared in Greek: Aristotle uses the expression ¥
for the foundations of government, and Theophrastus says
that the trunk is the © of the tree. 12 In either case there is nothing
“hypothetical” in the sense familiar to us. In philosophy the term was
used for the logical foundation of a chain of deductions, and in scientific
theories for more or less what we call principles. 13 When Archimedes, in
describing the heliocentrism of Aristarchus of Samos, writes that the latter
© (published the text of some “hypotheses”),
13a he means that the immobility of the sun and the rotation and revo- page 194
lution of the earth were the ground assumptions of the Aristarchan theory
(though oddly, many commentators have taken the word in the modern
meaning of “hypotheses”).
What criterion was used in choosing the initial assumptions (postulates
or “hypotheses”) of a theory? The first that may come to mind, namely
picking the simplest and most easily checked statements, has been put
forth by many authors, ancient and modern, but it does not agree at all
with the facts.
First of all, the statements that seem simplest may turn out to be useless
for deriving interesting consequences. In astronomy, for instance, an
assumption that the earth is fixed may look like an obvious choice, but
does not offer a particularly useful basis for the description of planetary
motion. In geometry one might think that the simplest entities are points,
but the attempts of the Pythagorean school to build up geometry on statements
dealing with points alone ended with failure (as we saw in Section
2.1) and with the acknowledgement that one may not even recover the
properties of the straight line by starting from statements about points
12 Theophrastus, Historia plantarum, IV, xiii, 4.
13 For example, Sextus Empiricus calls an © each of the postulates of geometry (Adversus
mathematicos, III, 1 ff.). We will return later to the question of the somewhat different meaning of
“principles” in modern physics.
13a Archimedes, Arenarius, 135, 8–9 (ed. Mugler, vol. II).
Revision: 1.7 Date: 2002/09/14 23:17:37