Axiomatic methods in science
pp. 205-232
in: Marc E. Carvallo (ed), Nature, cognition and system II, Berlin, Springer, 1992Abstract
Philosophical analysis of axiomatic methods goes back at least to Aristotle. In the large literature of many centuries a great variety of issues have been raised by those holding viewpoints that range from that of Proclus to that of Hilbert. Here I try to consider in detail only a highly selected set of ideas, but they are ones I judge important.The first section gives a brief overview of the formalization of theories within first-order logic. The second section develops the axiomatic characterization of scientific theories as set-theoretical predicates. This approach to the foundations of theories is then related to the older history of the axiomatic method in the following section.
