1 The Birth of Science - MSRI

148 6. The Hellenistic Scientific Method
In Plato the word is used in the sense of a rational argument capable of
convincing someone else. In the Hippias minor, for example, Hippias proposes
to demonstrate that Homer portrays Achilles in a better light than page 191
Ulysses 2 and in the Republic various demonstrations are given of the possibility
of realizing the proposed state model. Plato seldom uses the term in
connection with geometry. 3 We have already remarked that Plato’s work
contains very interesting demonstrations (in the later, technical sense of
the word), 4 but the method used in such cases is not distinguished by a
specific term from convincing arguments of another nature.
In Aristotle’s works on logic, apodeixis is associated with the feature of
absolute irrefutability considered today to be necessary in a mathematical
demonstration. This new type of demonstration is identified by Aristotle
as the object of the Prior analytics, a work in which he describes and analyzes
syllogisms. 5 He defines a demonstration as a true syllogism (that is,
a syllogism whose premises are true). 6
A survey of the evolution of apodeixis from general argumentation to
what we can call Aristotelian “syllogistic demonstration” would require a
reexamination of a good part of the history of Greek philosophy, with particular
attention to the Eleatic school. But it would not be a story limited to
philosophy in the narrow sense that this word usually has now, because
the evolution owes much to the development of deliberative and judicial
rhetoric — the art of arguing convincingly in assemblies and courts —
which evolved especially in the Greek democracies of the fifth century.
There was an important link between the existence of certain forms of
democracy and the development of the argumentation skills that led to the
hypothetico-deductive method. The relationship between public speaking
and demonstrations is clearest in the Aristotelian Rhetoric, where the author
stresses that the so-called enthymemes are none other than syllogisms,
and identifies twenty-eight distinct types of rhetorical lines of argument. 7
Aristotle presents rhetoric, in large measure, as an application of the instruments
he elaborated in his works on logic, but the historical order was page 192
clearly the reverse. A century before his day there were already treatises
on rhetoric (now lost), so we can imagine that the theory of syllogisms
2 Plato, Hippias minor, 369c.
3 One exception is in the Theaetetus (162e–163a), where a contrast is drawn between methods that
do not provide “true demonstrations” and the method used by Theodorus and other geometers.
4 See page 31 and note 21 thereon.
5 Analytica priora, I, 1, 24a, 11–15.
6 Analytica posteriora, I, 2, 71b, 18–25.
7 Ars rhetorica, 1355a, 1397a ff.
Revision: 1.7 Date: 2002/09/14 23:17:37