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Language peer sets for Principia Mathematica:
United Kingdom↑
United Kingdom/1908↑
Designed 1908 ↑
languages ↑
↑
↑
Genus Symbolic ↑
Excluded from Sammet ↑
Symbolic↑
Logical↑
Expression-oriented ↑
Symbolic/1908↑
Logical/1908↑
Expression-oriented/1908↑
Symbolic/United Kingdom↑
Logical/United Kingdom↑
Expression-oriented/United Kingdom↑
Excluded from Sammet ↑
Excluded from Sammet/1908↑
Excluded from Sammet/uk ↑

Principia Mathematica(ID:6961/pri008)

R & W symbolic treatment of maths 

alternate simple view
Country: United Kingdom
Designed 1908
Genus: Symbolic
Sammet category: Excluded from Sammet

Russell and Whitehead's mathematical formalistic language expressed with great clarity. Based largely on the Peano synax, with extensions, with logical system based on Frege. Provides the intellectual formalism for types.

Ramified Type Theory - "whatever involves all of a collection must not be one of a collection"

The orders of types were eliminated by Ramsay.
Related languages
Boole → Principia Mathematica   Extension of
Cantor set theory → Principia Mathematica   Incorporated some features of
Frege → Principia Mathematica   Strong Reaction to
Peano → Principia Mathematica   Extension of
Principia Mathematica → Lincos   Extension of
Principia Mathematica → New Foundations   Incorporated some features of
Principia Mathematica → Simplified Type Theory   Simplification of
References:
  • Russel, Bertrand (1908) Russel, Bertrand "Mathematical Logic as based on a Theory of Types" in American Journal of Mathematics, 30 pp222-262, 1908
  • Whitehead, A. (1910) Whitehead, A. N., and Russell, B. Principia Mathematica. Cambridge, 1910, 1912, 1913.
  • Fairouz Kamareddine, Twan Laan and Rob Nederpelt (2000) Fairouz Kamareddine, Twan Laan and Rob Nederpelt "A History of Types in Logic and Mathematics" Abstract
          in [Proceedings] (2000) Workshop on History of Logics, Types and Rewriting Heriot-Watt University, Edinburgh Tuesday 5 December 2000
  • Grattan-Guiness, I. (2000) Grattan-Guiness, I. "Mathematics and symbolic logics: an uneasy relationship of the 20th century" Abstract
          in [Proceedings] (2000) Workshop on History of Logics, Types and Rewriting Heriot-Watt University, Edinburgh Tuesday 5 December 2000
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