1 The Birth of Science - MSRI

158 6. The Hellenistic Scientific Method
things can be understood without definition” — of presupposing, that is,
the existence of some definitionless entities — was still taken into consideration
in his time.
How were the first Greek purely scientific terms, and therefore the first page 203
theoretical entities of science, created? It is not hard to realize that the essential
tools were provided by the postulates of the various theories and
the hypothetico-deductive method. Take the first postulate of the Elements,
for example. In Euclid’s text it reads, literally,
Let it be demanded that a straight line be drawn [i.e., drawable] from
every sign to every sign. 37
This statement contains words from ordinary Greek, signifying concrete
objects: “straight lines” are originally traces drawn or carved (the Greek
word indicates this explicitly), the “signs” are equally concrete in
nature, and the whole can be read as a sentence of ordinary language, with
a clear meaning relating to the concrete activity of a draftsman. Naturally
the draftsman can draw, for instance, a green or a red line, thicker or thinner,
and make signs of different types. But now suppose that we take this
sentence, together with the other four that Euclid wrote, as postulates in
his theory based on the hypothetico-deductive method. Because none of
the postulates mentions color, clearly no proposition deducible from them
can say anything about color. The “lines” of the theory are thus automatically
colorless. The same can be said of their thickness or the shape of
the “signs”. In other words, the use of the hypothetico-deductive method
automatically restricts the semantic extension of the terms used in the postulate,
generating new entities that are “theoretical” in the sense that the
only statements one can make about them are those deducible from the
postulates of the theory.
Another example: in the Optics, again of Euclid, the initial assumptions
of the theory contain an essential term, opsis, which in Section 3.1 we translated
as “visual ray”. The meanings of the word in Greek are manifold:
view, aspect, image, spectacle; or yet, in an active sense, sight, look, organs
of sight; it can even mean the “evil eye”. 38 In natural philosophy page 204
there were various doctrines of sight based on the idea that an opsis was
something actually emitted from the eye. In the Euclidean theory all of
that no longer matters; all these possible meanings of the term, since they
do not play a role in the theory’s assumptions, are automatically eliminated
from the theory itself. The visual rays of Euclidean optics are completely
characterized as entities that associate (according to precise rules)
37 ¨ ¨
38 Plutarch, Quaestionum convivialium libri vi, 681A.
Revision: 1.7 Date: 2002/09/14 23:17:37