Axiomatic Methods in Science [chapter]

Patrick Suppes
1992 Nature, Cognition and System II  
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 frrst-order logic. The second section develops the axiomatic
more » ... ization 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. 205 M. E. Carvallo (ed.), Nature, Cognition and System II. 205-232. @ 1992 Kluwer Academic Publishers. Printed in the Netherlands. 206 P. SUPPES Example: ordinal rneasurkrnent. As a first example of a theory with standard formalization, we may consider the simple theory of ordinal measurement. To begin with, we use one standard notation for elementary logic. The sentential connectives
doi:10.1007/978-94-011-2779-0_12 fatcat:kmufrzjv4nfzvgoyyxppqdhohu