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    Geoffrey Hellman — Carmelics
    Thinkers/Geoffrey Hellman
    GH

    Geoffrey Hellman

    contemporaryAnalytic Philosophy, Philosophy of Mathematics

    b. 1943

    Geoffrey Hellman is an American philosopher of mathematics at the University of Minnesota, best known for developing modal structuralism as an alternative to platonism. His 1989 book Mathematics Without Numbers argues that mathematical claims are best understood as modal assertions about possible structures rather than claims about abstract objects. He has also contributed to the philosophy of quantum mechanics and the foundations of mathematics more broadly.

    Notable Achievements

    1

    Developed modal structuralism in Mathematics Without Numbers (1989)

    2

    Provided a nominalist-friendly reconstruction of classical mathematics using modal logic

    3

    Critiqued Jerrold Katz's platonist argument by elimination

    4

    Contributed to the foundations of real analysis and the philosophy of mathematical practice

    5

    Co-authored work on structuralism and the ontology of mathematics with Stewart Shapiro

    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.

    claim

    Katz's argument by elimination for platonism fails

    Skepticism

    claim

    Katz's argument by elimination for platonism fails

    At a Glance

    Ideas

    2

    Topics

    2

    Era

    contemporary

    Tradition

    Analytic Philosophy, Philosophy of Mathematics

    Topic Influence

    Truth & Knowledge2
    Skepticism1

    Related Thinkers

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    Immanuel Kant
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    Boyd2 shared
    Brian Skyrms2 shared
    Stathis Psillos2 shared
    Bertrand Russell2 shared
    David Hume2 shared
    Aristotle2 shared

    Dive Deeper

    Explore Truth & Knowledge→See Skepticism→