Principia Mathematica

  title={Principia Mathematica},
  author={G. B. M.},
THIS work contains some thousands of propositions, each, with its proof, expressed in a shorthand so concise that if they were all expanded into ordinary language, the room taken up would be ten times as large at least; space, time, and mass are not considered at all, and arithmetic is merely foreshadowed by the introduction of the symbols o, 1, 2, and 2, How then, it may be asked, can the authors pretend to be writing about mathematics? The answer amounts to saying that for every branch of the… 

The dawn of formalized mathematics

When I was a student of mathematics I was told that someone had formalized an entire book on analysis just to put to rest the question whether mathematics could be completely formalized, so that

Book Reviews : Volume II: Geometrical, Threshold, and Probabilistic Representations

In the three volumes of Principia Mathematica, Whitehead and Russell (1925-1927) strove to set the existing practice of higher mathematics on a foundation of logic. That work was hailed for its

A Forgotten Theory of Proofs ?

  • E. Engeler
  • Mathematics
    Log. Methods Comput. Sci.
  • 2019
This essay attempts to revive the idea of an algebra of proofs, place MacLane’s thesis work and its vision in a new framework and try to address his original vision.

What is Neologicism?

According to one well-received view, logicism was replaced by a very different account of the foundations of mathematics, in which mathematics was seen as the study of axioms and their consequences in models consisting of the sets described by Zermelo-Fraenkel set theory (ZF).

Which Arithmetization for Which Logicism? Russell on Relations and Quantities in The Principles of Mathematics

This article aims first at showing that Russell's general doctrine according to which all mathematics is deducible ‘by logical principles from logical principles’ does not require a preliminary

Set-theoretical basis for real numbers

  • Hao Wang
  • Mathematics
    Journal of Symbolic Logic
  • 1950
It is shown that all Tarski's twenty axioms, which are sufficient for the arithmetic of real numbers and are to the effect that real numbers form a complete ordered field, cannot be proved in L without any modification.

The emergence of first-order logic

To most mathematical logicians working in the 1980s, first-order logic is the proper and natural framework for mathematics. Yet it was not always so. In 1923, when a young Norwegian mathematician

Historical Development of Modern Logic

Modern Logic began in 1879, the year in which Gottlob Frege (1848–1925) published his Begriffsschrift. In less than ninety pages this booklet presented a number of discoveries that changed the face


, whose main feature is that they are always subject to unanticipated outcomesin their operation and can receive new information from outside at any time [cf. Hewitt 1991]. WhileGodel's

An Introduction to Symbolic Logic

This project is dedicated to the study of basics of propositional and predicate logic. We will study it based on Russell and Whitehead’s epoch making treatise Principia Mathematica [12]. Logic is a