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    Carmelics

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    David Hilbert — Carmelics
    Thinkers/David Hilbert
    David Hilbert

    David Hilbert

    modernFormalism, Mathematical Logic, Philosophy of Mathematics

    1862 – 1943

    David Hilbert (1862–1943) was a German mathematician widely regarded as one of the most influential mathematicians of the 19th and 20th centuries. He made foundational contributions to algebra, functional analysis, mathematical physics, and the philosophy of mathematics, most notably through his formalist program seeking to ground all of mathematics in a complete and consistent axiomatic system. His 1900 list of 23 unsolved problems shaped the trajectory of 20th-century mathematics.

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    Notable Achievements

    1

    Proposed Hilbert's Program: the formalist project to axiomatize all of mathematics and prove its consistency via finitary methods

    2

    Published 23 open problems in 1900 that defined the research agenda for 20th-century mathematics

    3

    Developed Hilbert spaces, foundational to functional analysis and quantum mechanics

    4

    Contributed to the axiomatization of Euclidean geometry in Grundlagen der Geometrie (1899)

    5

    Made independent contributions to the field equations of general relativity alongside Einstein

    Positions & Arguments(7)

    Skepticism

    claim

    Reichenbach was not able to recognize the Weyl method as other than an equivalent account of empirical determination of the metric

    Truth & Knowledge

    claim

    Reichenbach was not able to recognize the Weyl method as other than an equivalent account of empirical determination of the metric

    claim

    Metric geometry is neither true nor false.

    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

    The semantics of a formal system rich enough to contain elementary mathematics cannot be fully defined in terms of mathematical functions within that same system.

    claim

    The universal function u_1(i,x) = g_i(x) for unary primitive recursive functions cannot itself be primitive recursive

    Modality & Possibility

    claim

    Metric geometry is neither true nor false.

    claim

    The universal function u_1(i,x) = g_i(x) for unary primitive recursive functions cannot itself be primitive recursive

    claim

    Mensuration in relativity need not depend on clocks and rigid bodies.

    Natural Theology

    claim

    Divine creative intervention is not causally necessary for the nonconservative appearance of new matter in steady-state cosmology.

    Causation

    claim

    Divine creative intervention is not causally necessary for the nonconservative appearance of new matter in steady-state cosmology.

    claim

    Mensuration in relativity need not depend on clocks and rigid bodies.

    Philosophy of Language

    claim

    The semantics of a formal system rich enough to contain elementary mathematics cannot be fully defined in terms of mathematical functions within that same system.

    At a Glance

    Ideas

    7

    Topics

    6

    Era

    modern

    Tradition

    Formalism, Mathematical Logic, Philosophy of Mathematics

    Topic Influence

    Truth & Knowledge5
    Modality & Possibility3
    Causation2
    Natural Theology1
    Philosophy of Language1
    Skepticism1

    Related Thinkers

    Immanuel Kant6 sharedAristotle6 sharedPlato6 sharedRené Descartes6 sharedThomas Aquinas6 sharedDavid Lewis5 sharedBertrand Russell5 shared

    Dive Deeper

    Explore Truth & Knowledge→See Modality & Possibility→
    David Hume5 shared