Abstract
G ödel’s proof of the consistency of his axiom of constructibility relative to that of the usual Zermelo—Fraenkel axioms for set theory touched off a methodological discussion about the acceptability of a theoretical statement, so to speak, within a discipline where such things are by no means common, most people probably reckoning that most twentieth century work is the continuation ad perfectionem of the nineteenth century revolution in rigour. The purpose of this paper is twofold: it is, first, to suggest that what are called the foundational aspects of mathematical research offer workable material for methodological discussion; and second, to see whether a particular account of the evolution of the empirical sciences, due to Imre Lakatos, covers also these parts of mathematics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Bibliography
Clark, P. J.: 1976, ‘Atomism Versus Thermodynamics: A Case Study in the Methodology of Scientific Research Programmes’ in Howson (ed.), 1976.
Gödel, K.: 1964, ‘What is Cantor’s Continuum Problem? in P. Benacerraf and H. Putnam (eds.), Philosophy of Mathematics: Selected Readings, Basil Blackwell, Oxford, pp. 258–273.
Howson, C. (ed.): 1976, Method and Appraisal in the Physical Sciences, Cambridge University Press.
Kolmogorov, A. N.: 1933, Grundbegriffe der Wahrscheinlichkeitsrechnung, English translation by N. Morrison, The Foundations of the Theory of Probability, Chelsea Publishing Company, New York, 1956.
Lakatos, I.: 1963–64, ‘Proof and Refutations’, The British Journal for the Philosophy of Science 14, pp. 1–25, 120–139, 221–245, 296–342.
Lakatos, I.: 1967, ‘A Renaissance of Empiricism in the Recent Philosophy of Mathematics?’, mimeographed.
Worrall, J.: 1976, J.: 1976, ‘Thomas Young and the “Refutation” of Newtonian Optics’, in Howson (ed.), 1976.
Zahar, E. G.: 1973, ‘Why did Einstein’s Programme Supersede Lorentz’s?’, The British Journal for the Philosophy of Science, 24, pp. 95–123 and pp. 223–262.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1979 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Howson, C. (1979). Methodology in Non-Empirical Disciplines. In: Radnitzky, G., Andersson, G. (eds) The Structure and Development of Science. Boston Studies in the Philosophy of Science, vol 59. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9459-1_10
Download citation
DOI: https://doi.org/10.1007/978-94-009-9459-1_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-277-0995-0
Online ISBN: 978-94-009-9459-1
eBook Packages: Springer Book Archive