Bertrand Russell

Frege

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

Russell is Wittgenstein's mentor and early supporter, though their relationship becomes strained due to philosophical disagreements.

Tractatus Logico-Philosophicus

Influential figure whose logical atomism and theory of descriptions are engaged with critically.

3.318

Mentioned alongside Frege as sharing the view of propositions as functions of expressions.

3.325

His logical symbolism is mentioned alongside Frege's as a step toward correct logical syntax.

3.331

Subject of Wittgenstein's critique regarding the Theory of Types.

3.333

His paradox is referenced as the problem that is resolved by the distinction between inner and outer functions.

4.0031

Merited for showing the distinction between apparent and real logical form of propositions.

4.1272

Mentioned alongside Frege as having the same error regarding formal concepts.

4.12721

Criticized for introducing both the concept of function and special functions as primitive ideas, and similarly for number.

4.1273

Mentioned alongside Frege as having overlooked the formal concept, leading to a vicious circle in their expression of general propositions.

4.241

Referenced for his use of the definition form 'a = b Def.'

4.442

Mentioned alongside Frege as using the assertion sign to mark propositions they hold as true.

5.02

Referenced for his notation '+c' as an example of indexing.

5.132

Mentioned alongside Frege as employing laws of inference.

5.252

Referenced alongside Whitehead for their hierarchy and implicit use of formal series progression.

5.4

Mentioned alongside Frege as holding the view that logical constants exist.

5.42

Mentioned in context of logical primitive signs

5.452

Co-author of Principia Mathematica, criticized for introducing words without justification.

5.4731

Referenced for his extensive discussion of self-evidence in logic.

5.513

Referenced for his notation

5.521

Along with Frege, introduced generality in connection with logical product or sum, criticized by Wittgenstein.

5.525

Mentioned as the target of Wittgenstein's criticism regarding the rendering of '(∃x).fx' as 'fx is possible.'

5.5302

Russell's definition of identity is critiqued by Wittgenstein.

5.532

His notation for existence statements is critiqued and reformulated by Wittgenstein.

5.535

His Axiom of Infinity is discussed as a source of pseudo-propositions.

5.5351

Mentioned for his use of 'p ⊃ p' in Principles of Mathematics

5.541

Mentioned as a modern epistemologist who conceives psychological propositions relationally.

5.5422

His theory of judgment is criticized for not showing that judging nonsense is impossible.

5.553

Russell is mentioned as having asserted that there are simple relations between different numbers of individuals, a view Wittgenstein challenges.

6.123

Mentioned as the proponent of the view that each logical type requires its own law of contradiction, which Wittgenstein rejects.

6.1232

Referenced for his 'axiom of reducibility,' which Wittgenstein argues is not a logical proposition.

Endnotes

Russell is referenced in the endnotes as the author of a clarifying note about the form of laws.