Logic

The Principles of Mathematics

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Bertrand Russell

1903

Russell's first major philosophical work argues that all of mathematics can be derived from purely logical principles — the thesis known as logicism. He undertakes a systematic examination of the foundations of arithmetic, geometry, and analysis, identifying the fundamental logical concepts and relations on which they rest. The book also contains his discovery of what became known as Russell's Paradox — the paradox of the set of all sets that do not contain themselves — which forced a major revision of set theory and led directly to the monumental Principia Mathematica (co-authored with Alfred North Whitehead).