On Logic and the Theory of Science by Jean Cavailles

Author:Jean Cavailles [Cavailles, Jean]
Language: eng
Format: epub
ISBN: 9781913029418
Publisher: MIT Press
Published: 2021-03-30T05:00:00+00:00

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1 [See ‘Mathematical Thought’ on thematisation (which there, however, Cavaillès opposes to ‘idealisation or adjunction’): he describes it as the procedure ‘whereby the gestures carried out on a model or a field of individuals can, in turn, be considered as individuals upon which the mathematician can work, considering them as a new field. The topology of topological transformations, for example (and there are many other examples). This procedure allows mathematical reflections to be superimposed upon one another, and it also has the interest of showing us that there is an unbroken link between the concrete activity of the mathematician from the first moments of his development—placing two symmetrical objects side-by-side, swapping them around—and the most abstract operations; for each time this linkage is found in the fact that the system of objects under consideration is a system of operations which, themselves, are operations upon other operations which, ultimately, are founded upon concrete objects’—trans.]

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