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Abstract Generality, Simplicity, Forgetting, and Discovery

In: Axiomatic Thinking II

Author

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  • Colin McLarty

    (Case Western Reserve University, Department of Philosophy)

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.

Suggested Citation

  • Colin McLarty, 2022. "Abstract Generality, Simplicity, Forgetting, and Discovery," Springer Books, in: Fernando Ferreira & Reinhard Kahle & Giovanni Sommaruga (ed.), Axiomatic Thinking II, chapter 0, pages 145-155, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-77799-9_6
    DOI: 10.1007/978-3-030-77799-9_6
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