Patterns of Change : Linguistic Innovations in the Development of Classical Mathematics
Ladislav Kvasz, K. Andersen, H. J. M. Bos, U. Bottazzini, D. Buchwald, J. Z. Buchwald, K. Chemla, S. S. Demidov, E. A. Fellmann, M. Folkerts, P. Galison, I. Grattan-Guinness, J. Gray, R. Halleux, S. Hildebrandt, Eberhard Knobloch, Helge Kragh, Ch Meinel, J. Peiffer, W. Purkert, D. Rowe, A. I. Sabra, Ch Sasaki, Erhard Scholz, R. H. Stuewer, V. P. Vizgin, H. Wußing
Kvasz’s book is a contribution to the history and philosophy of mat- matics, or, as one might say, the historical approach to the philosophy of mathematics. The ?rst signi?cant work in the history and philosophy of science is perhaps William Whewell’s Philosophy of the Inductive Sciences, founded upon their History.
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9783764388393, 9783764388409, 3764388390, 3764388404
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Preface.- Introduction.- Re-codings as the first pattern of change in mathematics.- Historical description of re-codings.- Philosophical reflections on re-codings.- Relativizations as the second pattern of change in mathematics.- A Historical description of relativizations in synthetic geometry.- Historical description of relativizations in algebra.- Philosophical reflections on relativizations.- Re-formulations as a third pattern of change in mathematics.- Re-formulations and concept-formation.- Re-formulations and problem-solving.- Re-formulations and theory-building.- Mathematics and change.- The question of revolutions in mathematics (Kuhn).- The question of mathematical research programs (Lakatos).- The question of stages of cognitive development (Piaget).- Notes.- Bibliography.