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    Richard Dedekind — Carmelics
    Thinkers/Richard Dedekind
    Richard Dedekind

    Richard Dedekind

    modernPhilosophy of Mathematics

    1831 – 1916

    Richard Dedekind was a 19th-century German mathematician known for his foundational contributions to abstract algebra, algebraic number theory, and the rigorous definition of real numbers. His construction of real numbers via 'Dedekind cuts' provided a rigorous foundation for analysis, and his work on ideals transformed modern algebra.

    WWikipediaSEPStanford Encyclopedia

    Notable Achievements

    1

    Developed Dedekind cuts to rigorously define real numbers

    2

    Formulated the Dedekind-Peano axioms for natural numbers

    3

    Introduced the theory of ideals in algebraic number theory

    4

    Authored 'Was sind und was sollen die Zahlen?' on the foundations of arithmetic

    5

    Advanced the logicist and structuralist approach to mathematics

    Positions & Arguments

    (2)

    Truth & Knowledge

    claim

    For any real number x, the terms of a conditionally convergent series can be rearranged so that x is the sum of the rearranged series.

    Modality & Possibility

    claim

    Ordinary objects include both actually concrete objects and possible objects that are not in fact concrete but could have been.

    At a Glance

    Ideas

    2

    Topics

    2

    Era

    modern

    Tradition

    Philosophy of Mathematics

    Topic Influence

    Truth & Knowledge1
    Modality & Possibility1

    Related Thinkers

    David Lewis2 sharedImmanuel Kant2 sharedAristotle2 sharedBrian Skyrms2 sharedBertrand Russell2 sharedDavid Hume2 sharedPlato2 sharedStathis Psillos2 shared

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