Russell and Whitehead's Principia Mathematica

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Russell and Whitehead's Principia Mathematica

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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 (developed further in Russell's paradox).

Bertrand Arthur William Russell

Bertrand Arthur William Russell, 3rd Earl Russell of Kingston Russell, Viscount Amberley of Amberley and of Ardsalla (May 18, 1872 - February 2, 1970) was one of the most influential mathematicians, philosophers and logicians working (mostly) in the 20th century, an important political liberal, activist and a popularizer of philosophy. Millions looked up to Russell as a sort of prophet of the creative and rational life; at the same time, his stance on many topics was extremely controversial. He was born in 1872, at the height of Britain's economic and political ascendancy, and died, of influenza, in 1970 when Britain's empire had all but vanished and her power had been drained in two victorious but debilitating world wars. At his death, however, his voice still carried moral authority, for he was one of the world's most influential critics of nuclear weapons and the American war in Vietnam.

Alfred North Whitehead

Alfred North Whitehead (1861 - 1947) was a British philosopher and mathematician who worked in logic, mathematics, philosophy of science and metaphysics. His best known work in mathematics is the Principia Mathematica which he wrote with Bertrand Russell. In philosophy, Whitehead is perhaps most well known for developing process philosophy, which was then developed into process theology by many liberal theologian/philosophers, such as Charles Hartshorne. Process theology has since been accepted as a valid way of understanding God by some liberal Christian and Jewish scholars and laypeople.

Math Not Physics

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 theorem in 1931.

RUSSELL and WHITEHEAD

Reference

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