# Bertrand Russell — Tractatus Logico-Philosophicus character guide > Bertrand Russell in Tractatus Logico-Philosophicus by Ludwig Wittgenstein. **Role:** minor **Also known as:** Russell **First appearance:** 0004-tractatus-logico-philosophicus ## Who they are Influential philosopher and logician referenced in the work. ## Relationships ### [Frege](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/characters/frege) _professional_ Russell and Frege are colleagues and correspondents in the development of logic and the foundations of mathematics, with mutual respect but also critical engagement. ### [Mr. Wittgenstein](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/characters/mr_wittgenstein) _professional_ Russell is Wittgenstein's mentor and early supporter, though their relationship becomes strained due to philosophical disagreements. ## In the story ### [Tractatus Logico-Philosophicus](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/tractatus-logico-philosophicus) Influential figure whose logical atomism and theory of descriptions are engaged with critically. ### [3.318](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/3-318) Mentioned alongside Frege as sharing the view of propositions as functions of expressions. ### [3.325](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/3-325) His logical symbolism is mentioned alongside Frege's as a step toward correct logical syntax. ### [3.331](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/3-331) Subject of Wittgenstein's critique regarding the Theory of Types. ### [3.333](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/3-333) His paradox is referenced as the problem that is resolved by the distinction between inner and outer functions. ### [4.0031](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/4-0031) Merited for showing the distinction between apparent and real logical form of propositions. ### [4.1272](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/4-1272) Mentioned alongside Frege as having the same error regarding formal concepts. ### [4.12721](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/4-12721) Criticized for introducing both the concept of function and special functions as primitive ideas, and similarly for number. ### [4.1273](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/4-1273) Mentioned alongside Frege as having overlooked the formal concept, leading to a vicious circle in their expression of general propositions. ### [4.241](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/4-241) Referenced for his use of the definition form 'a = b Def.' ### [4.442](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/4-442) Mentioned alongside Frege as using the assertion sign to mark propositions they hold as true. ### [5.02](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-02) Referenced for his notation '+c' as an example of indexing. ### [5.132](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-132) Mentioned alongside Frege as employing laws of inference. ### [5.252](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-252) Referenced alongside Whitehead for their hierarchy and implicit use of formal series progression. ### [5.4](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-4) Mentioned alongside Frege as holding the view that logical constants exist. ### [5.42](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-42) Mentioned in context of logical primitive signs ### [5.452](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-452) Co-author of Principia Mathematica, criticized for introducing words without justification. ### [5.4731](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-4731) Referenced for his extensive discussion of self-evidence in logic. ### [5.513](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-513) Referenced for his notation ### [5.521](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-521) Along with Frege, introduced generality in connection with logical product or sum, criticized by Wittgenstein. ### [5.525](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-525) Mentioned as the target of Wittgenstein's criticism regarding the rendering of '(∃x).fx' as 'fx is possible.' ### [5.5302](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-5302) Russell's definition of identity is critiqued by Wittgenstein. ### [5.532](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-532) His notation for existence statements is critiqued and reformulated by Wittgenstein. ### [5.535](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-535) His Axiom of Infinity is discussed as a source of pseudo-propositions. ### [5.5351](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-5351) Mentioned for his use of 'p ⊃ p' in Principles of Mathematics ### [5.541](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-541) Mentioned as a modern epistemologist who conceives psychological propositions relationally. ### [5.5422](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-5422) His theory of judgment is criticized for not showing that judging nonsense is impossible. ### [5.553](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/5-553) Russell is mentioned as having asserted that there are simple relations between different numbers of individuals, a view Wittgenstein challenges. ### [6.123](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/6-123) Mentioned as the proponent of the view that each logical type requires its own law of contradiction, which Wittgenstein rejects. ### [6.1232](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/6-1232) Referenced for his 'axiom of reducibility,' which Wittgenstein argues is not a logical proposition. ### [Endnotes](https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/chapters/endnotes) Russell is referenced in the endnotes as the author of a clarifying note about the form of laws. ## Links - HTML: https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/characters/bertrand_russell - Book: https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se - All characters: https://www.betterreads.dev/discover/tractatus_logico_philosophicus_se/characters