1 The Birth of Science - MSRI

6.1 Origins of Scientific Demonstration 149
arose, at least to some extent, from consideration of the rhetoricians’ enthymemes.
8
For some deductive schemes we can recognize an origin in fifth-century
rhetoric and sophistics: the scheme called “consequentia mirabilis” in the
Middle Ages (a variant of the proof by contradiction, consisting in proving
A by proving that non-A implies A) was used by Protagoras and Gorgias. 9
The link between apodeixis and rhetoric was still discernible during the
imperial age, when rhetoric was used only in law. Quintilian writes, illustrating
the usefulness of the study of geometry in the training of orators:
Geometry proves consequences from premises and unestablished
things from established ones; do we [orators] not do the same when
we make a speech? Doesn’t the solution of the proposed questions
rely almost entirely on syllogisms? . . . So also [the orator] will use, if
necessary, syllogisms and of course enthymemes, which are rhetorical
syllogisms. Finally, of all lines of proof the most powerful are
those called [linear demonstrations]; and what
could be more desirable in an oration than good lines of proof? 10
. . . so that an orator cannot ever be ignorant of geometry. 11
Syllogistic demonstrations were an important element in the scientific
method, but one that gave it life only in combination with other elements,
which, through the creation of scientific theories, profoundly altered the
very role of demonstrations. page 193
A Hellenistic scientific theory is something very different from a set of
syllogisms. To begin with, the statements of the theory make up a single
network, being all provable from a small number of premises. They also
involve theoretical terms, that is, terms specific to the theory, in contrast
with the syllogisms considered by Aristotle. To build a scientific theory,
then, is is not enough to be able to deduce one statement from another;
one must choose appropriately the premises and terms of discourse. Also
essential was the use of elements other than verbal argumentation, drawn
from observation and from technical activities; one important example is
the role played by constructions in geometric demonstrations.
8 It seems that Aristotle was the first to use the title The art of rhetoric. Earlier works on the subject
had probably been called The art of discourse ( ), a terminological foreshadowing also
of later works on “logic” (from logos). Mathematics too had certainly been food for thought for the
founders of logic. But it should be noted that Egyptians and Babylonians, who for centuries had
cultivated mathematics, but not democracy or rhetoric, never did reach the demonstration stage.
9 For Protagoras see Sextus Empiricus, Adversus dogmaticos, I, 389–390. The history of “consequentia
mirabilis” is discussed in [Bellissima, Pagli].
10 Quintilian, Institutio oratoria, I, 10, 37–38.
11 Quintilian, Institutio oratoria, I, 10, 49.
Revision: 1.7 Date: 2002/09/14 23:17:37