Abstract Generality, Simplicity, Forgetting, and Discovery

Colin McLarty ()
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Colin McLarty: Case Western Reserve University, Department of Philosophy

Chapter Chapter 6 in Axiomatic Thinking II, 2022, pp 145-155 from Springer

Abstract: Abstract The paper contrasts two ways of generalizing and gives examples: probably most people think of examples like generalizing Cartesian coordinate geometry to differential manifolds. One kind of structure is replaced by another more complicated but more flexible kind. Call this articulating generalization as it articulates some general assumptions behind an earlier concept. On the other hand, by unifying generalization, I mean simply dropping some assumptions from an earlier concept or theorem. Hilbert, Noether, and Grothendieck were all known for highly non-trivial unifying generalizations.

Date: 2022
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DOI: 10.1007/978-3-030-77799-9_6

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