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...ciple was stated as a theorem of propositional logic by [[Bertrand Russell|Russell]] and [[Alfred North Whitehead|Whitehead]] in ''[[Principia Mathematica]]' ...

...orbed" by the term <math>P</math> in the [[consequent]].<ref>Whitehead and Russell, ''[[Principia Mathematica]]'', p. 14.</ref> The rule can be stated: ...ciple was stated as a theorem of propositional logic by [[Bertrand Russell|Russell]] and [[Alfred North Whitehead|Whitehead]] in ''[[Principia Mathematica]]' ...

...of existential assumptions, and so make it a free logic. Taking [[Bertrand Russell]]'s predicate logic in his ''[[Principia Mathematica]]'' as standard, one r ...from [[Hintikka]] allows for a contradiction by a correlate in logic to [[Russell's paradox]]. He introduces the predicate <math>(\lambda x)(\phi x \land \ne ...

{{Short description|Book by Bertrand Russell}} {{Distinguish|text=[[Principia Mathematica]]—a book of Russell and Whitehead published in 1910–1913}} ...

The band name was inspired by [[Bertrand Russell]]'s never published article titled "Is There a God?", commissioned by Illus |Bertrand Russell}} ...

...rand Russell]] discovered a conflict in it in 1902 which became known as [[Russell's paradox]]. As a result, it became generally known that you can not safely ...which allowed only a restricted use of class terms. Among mathematicians, Russell's type theory was superseded by an alternative axiomatization of set theory ...

...Alfred North Whitehead|last2=Russell|first2=Bertrand|author-link2=Bertrand Russell|url=http://archive.org/details/principiamathema01anwh|title=Principia Mathe Introducing progressions, Russell invoked the axiom of connection: ...

...aterialist dialectic could be seen in the mathematical logic of [[Bertrand Russell]]; however, this was criticized by [[Deborin]] and the Deborinists as panlo ...

...was described with axioms in 1898 by [[Giovanni Vailati]].<ref>[[Bertrand Russell]] (1903) [[The Principles of Mathematics]], [https://archive.org/details/pr ...

...isometry that preserves [[orientation (vector space)|orientation]].<ref>B. Russell (1903) [[Principles of Mathematics]] p 418. See also pp 406, 436</ref> ...

...s a list of the notation used in [[Alfred North Whitehead]] and [[Bertrand Russell]]'s ''[[Principia Mathematica]]'' (1910–1913). * Whitehead, Alfred North, and Bertrand Russell. ''Principia Mathematica'', 3 vols, Cambridge University Press, 1910, 1912, ...

...is the same as that which holds between ''b'' and ''d''.|author=[[Bertrand Russell]]|source=''[[The Principles of Mathematics]]'', page 432}} ...

[[Bertrand Russell|Russell]]'s axiom system:<ref name="Pro I"/> Russell–Bernays axiom system: ...

...ence of regular polygons to a circle.<ref>{{Cite book |last=Russell |first=Bertrand |url=https://books.google.com/books?id=Ey94E3sOMA0C&pg=PA202 |title=History ...

...of identity]]: 'Whatever is, is.'<ref name="Russell 1912:72,1997 edition">Russell 1912:72,1997 edition.</ref> For all a: a = a. ...1912:72, 1997 edition.</ref>): 'Nothing can both be and not be.'<ref name="Russell 1912:72,1997 edition" /> ...

...robably be summed up best by {{harvard citations |nb |first=Bertrand |last=Russell |year=1903 |p=9}} – "to fulfil two objects, first, to show that all mathema ...is intense: see the introduction by [[Willard Quine]] preceding {{harvnb |Russell |1908a}} ''Mathematical logic as based on the theory of types'' in {{harvnb ...

...-ratio is merely a double ratio of previously defined distances.{{sfnp|ps=|Russell|1898|p=32}} In particular, he showed that non-Euclidean geometries can be b * {{citation |last1=Russell |first1=Bertrand |author1-link=Bertrand Russell |year=1898 |title=An Essay on the Foundations of Geometry }} re-issued 1956 ...

...ege's treatment of quantification went largely unremarked until [[Bertrand Russell]]'s 1903 ''Principles of Mathematics''. ...ematica]]'' of [[Alfred North Whitehead|Whitehead]] and [[Bertrand Russell|Russell]], [[Willard Van Orman Quine|Quine]], and [[Alonzo Church]]. In 1935, [[Gen ...

[[Bertrand Russell]] expressed his sense of mathematical beauty in these words: ...out appeal to any part of our weaker nature without the gorgeous trappings Russell.|access-date=2008-08-22}}</ref> ...

...edia of Philosophy | date=4 October 2005 | access-date=2011-10-16 | author=Russell, Paul}}</ref> In his ''[[Dialogues Concerning Natural Religion]]'', the cha ===Bertrand Russell=== ...