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Michael Friedman1

  • 1Humboldt-Universität zu Berlin, Exzellenzcluster Bild Wissen Gestaltung. Ein interdisziplinäres Labor, Unter den Linden 6, D-10099, Berlin.

Berichte Zur Wissenschaftsgeschichte
|October 3, 2020
PubMed
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This study explores three historical logics in mathematics, moving beyond identity to include sameness and Gödel

Area of Science:

  • Philosophy of Mathematics
  • History of Mathematics
  • Logic and Set Theory

Context:

  • Examines the evolution of mathematical thought through three distinct logical frameworks.
  • Contrasts the modern conception of science and mechanism with historical mathematical approaches.
  • Investigates the foundational sentence of identity (I=I) as a minimal mathematical condition.

Purpose:

  • To reveal two historical logics of sameness and Gödelian undecidability beyond the dominant logic of identity.
  • To trace the historical emergence of these logics from Babylonian mathematics to Gödel's theorems.
  • To analyze the changing relationship between humanity and mathematics across these logical systems.

Summary:

  • The Babylonian era utilized a 'logic of sameness,' valuing the mathematician's role.
Keywords:
Babylonian MathematicsBabylonische MathematikGnomonGödelKittlerSatz von I=ISerresTuringgnomonthe principle of I=I

Related Experiment Videos

  • The subsequent 'logic of identity' emphasized axiomatic definitions, diminishing the human element.
  • Gödel's incompleteness theorems introduced a third logic, highlighting undecidability and intertwining human and machine roles in mathematics.

    • Impact:

    • Challenges the universality of the logic of identity in mathematics and science.
    • Suggests that Gödel's discoveries introduce inherent instability into both human mathematical reasoning and automated systems.
    • Re-evaluates the position of the human mathematician in light of evolving logical structures and computational capabilities.