Tractatus Logico-Philosophicus · Chapter
5.252 explained
Wittgenstein discusses the necessity of a formal series for the progression from term to term, critiquing Russell and Whitehead for implicitly using such progress in their hierarchy while failing to formally admit it.
What happens
Wittgenstein discusses the necessity of a formal series for the progression from term to term, critiquing Russell and Whitehead for implicitly using such progress in their hierarchy while failing to formally admit it.
Themes in this chapter
Logical Atomism
The discussion of formal series and progression between types relates to the logical structure of propositions and the composition of facts.
Characters to notice
- Bertrand Russell
Referenced alongside Whitehead for their hierarchy and implicit use of formal series progression.
Key passages
“Only in this way is the progress from term to term in a formal series possible (from type to type in the hierarchy of Russell and Whitehead). (Russell and Whitehead have not admitted the possibility of this progress but have made use of it all the same.)”
The only way to move from one term to the next in a formal series—or from one type to another in Russell and Whitehead's hierarchy—is through a specific logical operation, which they implicitly rely on but never formally acknowledge.
Wittgenstein criticizes Russell and Whitehead for using a logical progression they fail to explicitly justify.