1 The Birth of Science - MSRI

6
The Hellenistic Scientific Method
6.1 Origins of Scientific Demonstration
One essential characteristic of scientific theories, as we have defined them page 190
and as we have encountered them in the Hellenistic works considered,
is the use of demonstrations, that is, deductions of certain statements from
others, following a chain of logical steps that makes these deductions, in
principle, irrefutable: someone who accepts the premises cannot reject the
conclusions, except by finding an error in the deduction.
The English word “demonstrate” is a calque, through Latin, of the Greek
verb , which initially meant “show, display, expound” (and
was interchangeable with the unprefixed ). The original meaning
of the corresponding noun, apodeixis (), was “a showing, display,
exposition” of an object or subject: Herodotus, for example, presents his
work as an apodeixis (exposition) of his findings. 1 The evolution from this
wider meaning, still present in the English “demonstration”, 1a to the scientific
meaning that interests us went hand-in-hand with the establishment
and consolidation of what is called the hypothetico-deductive method. This
evolution went through at least two intermediate stages, which we can
exemplify through the use of apodeixis in Plato and Aristotle.
1 Herodotus, Historiae, I, 1.
1a This English word — also a calque, through Latin, of apodeixis — means showings of various
kinds, and it has even spawned the clipped version “demo”, which applies to some of these senses.
In the scientific meaning that is the subject of this chapter, it has been losing ground: it is now more
common to hear “proof” than “demonstration”. We will generally write “demonstration” to stress
the semantic origins of the term.
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