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John Edensor Littlewood, Littlewood's Miscellany (1986)[ 2] The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913.
v. t. e. In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician Bertrand Russell in 1901. [1] [2] Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions. [3]
Type theory was created to avoid a paradox in a mathematical equation based on naive set theory and formal logic. Russell's paradox (first described in Gottlob Frege's The Foundations of Arithmetic) is that, without proper axioms, it is possible to define the set of all sets that are not members of themselves; this set both contains itself and does not contain itself.
The Principles of Mathematics ( PoM) is a 1903 book by Bertrand Russell, in which the author presented his famous paradox and argued his thesis that mathematics and logic are identical. [ 1] The book presents a view of the foundations of mathematics and Meinongianism and has become a classic reference.
Russell's teapot is an analogy, formulated by the philosopher Bertrand Russell (1872–1970), to illustrate that the philosophic burden of proof lies upon a person making empirically unfalsifiable claims, as opposed to shifting the burden of disproof to others. Russell specifically applied his analogy in the context of religion. [ 1]
Peano–Russell notation. In mathematical logic, Peano–Russell notation was Bertrand Russell 's application of Giuseppe Peano 's logical notation to the logical notions of Frege and was used in the writing of Principia Mathematica in collaboration with Alfred North Whitehead: [ 1] "The notation adopted in the present work is based upon that ...
Introduction to Mathematical Philosophy is a book (1919 first edition) by philosopher Bertrand Russell, in which the author seeks to create an accessible introduction to various topics within the foundations of mathematics. According to the preface, the book is intended for those with only limited knowledge of mathematics and no prior ...
v. t. e. Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power.