Strokes towards the apocryphal history of mathematical logic Cover Image
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Щрихи към апокрифната история на математическата логика
Strokes towards the apocryphal history of mathematical logic

Author(s): Rosen Ljutskanov
Subject(s): Philosophy
Published by: Фондация за хуманитарни и социални изследвания - София
Keywords: mathematical logic; history; completeness theorem; genealogy; methodology

Summary/Abstract: This article poses the commonly neglected problem of the origins of contemporary mathematical logic. The cause of this neglect is twofold: as far as it is "logic", it is committed to the trans-historical ideology descending from the Eleatic discovery of abstract concepts; as far as it is "mathematical", it suffers from the distorting effects of the ordinary "Euclidean" methodology. But if we adhere to the so-called "maverick tradition", we can overcome this neglect and introduce in mathematical historiography the techniques which were elaborated by Foucault in his "Archaeology of Knowledge". Thus we may recognize at the same time the importance of Principia Mathematica as the fi rst supposed paradigm of the newly constituted discipline of mathematical logic and the reasons for its failure to overcome the requirement for epistemological foundation of mathematical knowledge. Finally, we establish the claim that the true establishment of mathematical logic is effected by Hilbert's proof theory and Gödel's completeness theorem. This means that the history of mathematical logic is much shorter and its relation to philosophy is more essential than is commonly believed.

  • Issue Year: 2007
  • Issue No: 24
  • Page Range: 267-279
  • Page Count: 14
  • Language: Bulgarian