1 The Birth of Science - MSRI

6.3 Saving the Phainomena 151
alone. 14 The road chosen by Euclid consists in not starting from absolutely
“elementary” theoretical entities, such as points appear to be, but directly
from statements on lines and circles.
In the second place, were the postulates or “hypotheses” of Hellenistic
theories verifiable statements?
In almost every case, verifiability is excluded by the universal character
of the statement in question: how can one check that something holds “for
every pair of points” or “for every straight-line segment”? We can only
check (approximately) particular statements implied by the postulates.
And generality is not the only problem. Consider, for example, the postulate
on which the Archimedean treatment of hydrostatics is based (see
page 65). This statement cannot be verified even in particular cases. How page 195
can one check, in non-equilibrium conditions (for instance, immediately
after opening a dam), the action that a particular small portion of liquid,
immersed in the whole, exerts on a neighboring portion? It is clear that
Archimedes is making an assumption that is not directly verifiable, and
that its interest for him lies in the possibility of deducing from it many
verifiable statements about what happens in equilibrium conditions.
In sum, it is clear that the initial assumptions of Hellenistic scientific
theories were neither obvious nor verifiable. What, then, could have been
the criterion with which they were chosen? The next sections are devoted
to this problem.
6.3 Saving the Phainomena
In his Outlines of Pyrrhonism, the Skeptic Sextus Empiricus writes:
We [Skeptics] do not contest that which compels us to involuntary
assent [©] to a sensorial impression, which is to say the
phainomena. 15
He is reporting here the Stoic conception of phainomena or “appearances”
(). According to the Stoics, a phainomenon does not involve just
a (passive) sensorial impression; also essential is the assent (©)
of the subject, at once active and involuntary. 16 Strato of Lampsacus, too,
14 An interesting work dealing with this problem has survived: the pseudo-Aristotelian De lineis
insecabilibus, dating probably form the late fourth century B.C. It argues for the impossibility of
constructing geometric magnitudes (and lines, in particular) by putting points together.
15 Sextus Empiricus, Pyrrhoneae hypotyposes, I, x, 19.
16 The Stoics considered also voluntary assent, but we will be interested primarily in the involuntary
kind, a typical example of which is provided by the recognition of a known person, which
happens through a comparison between visual impression and memory. The Stoics discussed at
length the possibility of identifying an erroneously given assent; see [Gould] (pp. 56–62), [Frede]
Revision: 1.7 Date: 2002/09/14 23:17:37