Advertisement

Limitations of the Axiomatic Method in Ancient Greek Mathematical Sciences

  • Patrick Suppes
Part of the Synthese Library book series (SYLI, volume 145)

Abstract

My thesis in this paper is that the admiration many of us have for the rigor and relentlessness of the axiomatic method in Greek geometry has given us a misleading view of the role of this method in the broader framework of ancient Greek mathematical sciences. By stressing the limitations of the axiomatic method or, more explicitly, by stressing the limitations of the role played by the axiomatic method in Greek mathematical science, I do not mean in any way to denigrate what is conceptually one of the most important and far-reaching aspects of Greek mathematical thinking. I do want to emphasize the point that the use of mathematics in the mathematical sciences and the use in foundational sciences, like astronomy, compare rather closely with the contemporary situation. It has been remarked by many people that modern physics is by and large scarcely a rigorous mathematical subject and, above all, certainly not one that proceeds primarily by extensive use of formal axiomatic methods. It is also often commented upon that the mathematical rigor of contemporary mathematical physics, in relation to the standards of rigor in pure mathematics today, is much lower than was characteristic of the 19th-century. However, my point about the axiomatic method applies also to 19th-century physics.

Keywords

Mathematical Rigor Axiomatic Method Unequal Weight Conjoint Measurement mUltiplicative Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dijksterhuis, E.J.: 1956, Archimedes, Humanities Press, New York.Google Scholar
  2. H. E Burton, trans 1945 ‘Euclid Optics’Journal of the Optical Society of America 35 357–372CrossRefGoogle Scholar
  3. Heath, T.L. (ed.): 1897, The Works of Archimedes with the Method of Archimedes, Dover, New York.Google Scholar
  4. Krantz, D.H., Luce, R.D., Suppes, P., and Tversky, A.: 1971, Foundations of Measurement, Vol. 1, Academic Press, New York.Google Scholar
  5. Mach, E.: 1942, The Science of Mechanics (5th English ed.; T.J. McCormack, trans.), Open Court, La Salle,Google Scholar
  6. Schmidt, O.: 1975, ‘A system of axioms for the Archimedean theory of equilibrium and centre of gravity’, Centaurus 19, 2–35.CrossRefGoogle Scholar
  7. Stein, W.: 1930, ‘Der Begriff des Schwerpunktes bei Archimedes’, Quellen und Studien zur Geschichte der Mathematik, Physik und Astronomie 1, 221–224.Google Scholar
  8. Suppes, P.: 1951, ‘A set of independent axioms for extensive quantities,’ Portugaliae Mathematica 10, 163–172.Google Scholar
  9. Toomer, G.J. (ed.): 1976, Diocles on Burning Mirrors, Springer-Verlag,Google Scholar
  10. Berlin, von Neumann, J.: 1955, Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, N.J., (Originally published in 1932.)Google Scholar

Copyright information

© D. Reidel Publishing Company 1980

Authors and Affiliations

  • Patrick Suppes
    • 1
  1. 1.Stanford UniversityUSA

Personalised recommendations