1 The Birth of Science - MSRI

160 6. The Hellenistic Scientific Method
not the same as the modern formalist reduction of the “meaning” of terms
to the logical rules that must be followed in their use in discourse (à la
Hilbert with his tables, chairs and beer mugs). Instead, it is a consequence
of the choice of assuming as postulates certain statements formulated in
ordinary language and regarding them as unambiguous. Of course, the
postulates, once the theory was developed, also took on a new face (following
the semantic pruning) as statements in the theory, but they also
kept their original naïve meaning, thus playing the role of a bridge between
concrete reality and what we would now call the theoretical model.
It may be asked whether and to what extent Greek scientists were aware
of the procedure we have described. There are many indications that they
were. An awareness of the model nature of scientific theories is unavoidable
in cases where alternative models were used simultaneously; we have
discussed one such case (Archimedean hydrostatics) and will see others in
the next sections. Likewise, an awareness about the mode of formation of
new scientific terms is attested by surviving references to Stoic semantics,
a framework in which the meaning of words boils down to whatever is
intended by their user (see Section 7.5 for further discussion). Regarding
the implicit definition of entities by means of postulates, the procedure
appears to be conscious whenever a fundamental entity of the theory is
introduced without definition, as in the case of the notion of visual rays
in Euclid’s Optics or that of barycenter in the Archimedean treatise On the
equilibrium of plane figures or that of the length of a class of curves in the
work On the sphere and cylinder by the same author.
6.5 Episteme and Techne
Humans interact with the external world by observing it and acting on page 206
it. These two fundamental modes provide the heuristic bases of ancient
science: phainomena or perceptions on the one hand, and technical activities
on the other. Geometry, in particular, kept a close link with the techniques
of drawing; we have seen that, in the Elements, three of the postulates
(dealing with the possible uses of ruler and compass) and many of
the propositions are feasibility statements: in effect, problems, whose solution
ends not with the formula “as was to be shown” but with “as was to
be done”. 39 In the demonstration of problems and theorems alike, many
logical steps are not verbal, but consist in drawing lines or carrying out
other, more complex, operations whose feasibility had been demonstrated
earlier.
39 See note 30 on page 34.
Revision: 1.7 Date: 2002/09/14 23:17:37