Science in Axiomatic Perspective
Antonio Florio

Abstract:
The axiomatic method counts two thousand and three hundred years
circa.  Suppes has proposed the category of Euclidean-Archimedean
tradition to refer to the axiomatic theories that have been developed
before the inven- tion/discovery of the non-Euclidean
geometries. Among these theories the first axiomatic system that we
know is Euclid’s Elements, a mathemat- ical tractate consisting of
thirteen books in which three centuries of Greek mathematical
knowledge were given an order and were presented as a unified theory.1
Euclid produced another axiomatic theory, the Optics. This represents
a theory of vision in Euclidean perspective rather than a tractate on
physical optics. It is interesting that Archimedes’s Treatise,
probably the first book on mathematical physics, is an axiomatic
theory.
  The axiomatic method in the Euclidean-Aristotelian tradition was
trans- mitted during the medieval age and scholarship in history of
science has established the use of the axiomatic method in scientific
tractates through all periods from antiquity up to the
sixteenth–seventeenth-century Scientific Revolution. In the context of
the Scientific Revolution an important ax- iomatic theory is Newton’s
Principia.
  The axiomatic method covers a too big period of history and philosophy
of science and we cannot deal with it in this thesis. So we skip the
analysis of the axiomatic method in the Euclean-Archimedean tradition
and begin our analysis in the nineteenth century when the axiomatic
method entered in the modern phase. As Suppes puts it: “The historical
source of the modern viewpoint toward the axiomatic method was the
intense scrutiny of the foundations of geometry in the nineteenth
century. Undoubtedly the most important driving force behind this
effort was the discovery and development of non-Euclidean geometry at
the beginning of the nineteenth century by Bolyai, Lobachevski, and
Gauss.”.