Encyclopedia > Principia Mathematica

  Article Content

Principia Mathematica

For Isaac Newton's 1687 book containing basic laws of physics, see Philosophiae Naturalis Principia Mathematica.


The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Bertrand Russell and Alfred North Whitehead and published in 1910-1913. It is an attempt to derive all mathematical truths from a well-defined set of axioms and inference rules in symbolic logic. The main inspiration and motivation for the Principia was Frege's earlier work on logic, which had led to some contradictions discovered by Russell. These were avoided in the Principia by building an elaborate system of types: a set has a higher type than its elements and one can not speak of the "set of all sets" and similar constructs which lead to paradoxes (see Russell's paradox).

The Principia only covered set theory, cardinal numbers, ordinal numbers and real numbers; deeper theorems from real analysis were not included, but by the end of the third volume it was clear that all known mathematics could in principle be developed in the adopted formalism.

The questions remained whether a contradiction could be derived from the Principia's axioms, and whether there exists a mathematical statement which could neither be proven nor disproven in the system. These questions were settled, in a rather disappointing way, by Gödel's incompleteness theorems in 1931.

Reference:

  • B. Russell, A. N. Whitehead: Principia Mathematica, Cambridge, University Press, 1910-1913



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Ocean Beach, New York

... out with 21.7% under the age of 18, 5.1% from 18 to 24, 32.6% from 25 to 44, 31.2% from 45 to 64, and 9.4% who are 65 years of age or older. The median age is 42 ...

 
 
 
This page was created in 60.2 ms