The question whether Kuhn's theory of scientific revolutions could be applied to mathematics caused many interesting problems to arise. The aim of this paper is to discuss whether there are different kinds of scientific revolution, and if so, how many. The basic idea of the paper is to discriminate between the formal and the social aspects of the development of science and to compare them. The paper has four parts. In the first introductory part we discuss some of the questions which arose during the debate of the historians of mathematics. In the second part, we introduce the concept of the epistemic framework of a theory. We propose to discriminate three parts of this framework, from which the one called formal frame will be of considerable importance for our approach, as its development is conservative and gradual. In the third part of the paper we define the concept of epistemic rupture as a discontinuity in the formal frame. The conservative and gradual nature of the changes of the formal frame open the possibility to compare different epistemic ruptures. We try to show that there are four different kinds of epistemic rupture, which we call idealisation, re-presentation, objectivisation and re-formulation. In the last part of the paper we derive from the classification of the epistemic ruptures a classification of scientific revolutions. As only the first three kinds of rupture are revolutionary (the re-formulations are rather cumulative), we obtain three kinds of scientific revolution: idealisation, re-presentation, and objectivisation. We discuss the relation of our classification of scientific revolutions to the views of Kuhn, Lakatos, Crowe, and Dauben.
Keywords scientific revolutions  epistemic ruptures  epistemicframework  incommensurability  paradigm  Kuhn  Lakatos  Crowe  Dauben
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DOI 10.1023/A:1008317930920
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References found in this work BETA

The Structure of Scientific Revolutions.Thomas Samuel Kuhn - 1962 - Chicago: University of Chicago Press.
Falsification and the Methodology of Scientific Research Programmes.Imre Lakatos - 1970 - In Imre Lakatos & Alan Musgrave (eds.), Criticism and the Growth of Knowledge. Cambridge University Press. pp. 91-196.
Revolutions in Mathematics.Donald Gillies (ed.) - 1992 - Oxford University Press.
The Fregean Revolution in Logic.Donald Gillies - 1992 - In Revolutions in Mathematics. Oxford University Press. pp. 265--305.
The Nineteenth-Century Revolution in Mathematical Ontology.Jeremy Gray - 1992 - In Donald Gillies (ed.), Revolutions in Mathematics. Oxford University Press. pp. 226--248.

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Citations of this work BETA

Why It Is Time To Move Beyond Nagelian Reduction.Marie I. Kaiser - 2012 - In D. Dieks, W. J. Gonzalez, S. Hartmann, M. Stöltzner & M. Weber (eds.), Probabilities, Laws, and Structures. The Philosophy of Science in a European Perspective. Heidelberg, GER: Springer. pp. 255-272.
Thematic Reclassifications and Emerging Sciences.Raphaël Sandoz - 2021 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 52 (1):63-85.
Kuhn’s Structure of Scientific Revolutions Between Sociology and Epistemology.Ladislav Kvasz - 2014 - Studies in History and Philosophy of Science Part A 46:78-84.

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