A Solid House of Cards

  • Ole Ravn
  • Ole Skovsmose
Part of the History of Mathematics Education book series (HME)


This chapter investigates the logicist programme that became influential in the first part of the 20th century. Logicism pursues the idea of reducing mathematics to the secure foundation that has been established in logic. It suggests how mathematical concepts can be defined in terms of logical concepts, and how mathematical theorems can be derived from logical proposition.

The chapter considers Frege’s critique of important philosophic conceptions of mathematics, before it presents his elaboration of the logicist programme as provided in his Begriffsschrift. Then follows a presentation of Russell and Whitehead’s continued detailed elaboration in Principia Mathematica. This elaboration was initiated by Russell’s discovery of a paradox that apparently destroyed the solidity of the logical foundation of mathematics in the format suggested by Frege. Russell communicated his discovery of the paradox to Frege, who got deeply chocked. While Frege gave up solving the paradox and paralysed in his logical endeavours, Russell moved on and tried to locate a solution that could save the logicist programme. In his own time, Frege was an unknown German mathematician with a taste for logic. His work remained unknown to the wider public until Russell discovered and developed his ideas. Later, it became evident that Frege was the most important person in the development of modern logic.


Begriffsschrift Logicism Mathematica Mathematics as logic Paradox Principia 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ole Ravn
    • 1
  • Ole Skovsmose
    • 1
    • 2
  1. 1.Department of Learning and PhilosophyAalborg UniversityAalborgDenmark
  2. 2.Department of Mathematics EducationState University of São Paulo, (Universidade Estadual Paulista, Unesp)São PauloBrazil

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