Bertrand Russell

Bertrand Russell was a British philosopher, logician and mathematician whose work with Alfred North Whitehead produced Principia Mathematica, published in three volumes between 1910 and 1913, an ambitious attempt to derive the whole of mathematics from a small set of logical axioms and rules of inference, a project known as logicism. In his 1903 book The Principles of Mathematics, Russell had already set out logicism as his central thesis, and in the course of this work he discovered what is now called Russell's paradox, showing that Gottlob Frege's own logical system for founding arithmetic was internally inconsistent, a discovery that forced a fundamental rethinking of the logical foundations of mathematics. To address the paradox, Russell developed the theory of types, a hierarchy restricting how sets and properties could refer to themselves, together with the axiom of reducibility, both incorporated into Principia Mathematica's formal system. Russell's 1905 essay On Denoting, analyzing how definite descriptions such as the present King of France function logically even when they refer to nothing that exists, became one of the most influential papers in twentieth-century philosophy of language. Russell was elected a Fellow of the Royal Society in 1908 in recognition of this body of logical and mathematical work.