Mirqāt The Ascent of Logic

Intermediate · a field of logic

The Modern Revolution

Frege, Russell, Hilbert: symbolic logic and the logicist dream of deriving mathematics itself from logic.

The problem
Could the whole of mathematics be reduced to pure logic, on a perfectly explicit symbolic foundation?
The turning point
Frege’s Begriffsschrift: quantifiers and bound variables give, for the first time, a fully formal language of predicates.
An open question
After Russell’s paradox and Gödel, what remains of the logicist dream, and what replaced it?

The Canon

  • Frege Begriffsschrift 1879
  • Whitehead & Russell Principia Mathematica 1910–13
  • Hilbert Grundlagen der Geometrie 1899

To study it

  • Dummett Frege: Philosophy of Language
  • Grattan-Guinness The Search for Mathematical Roots
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