# 5.252 explained — Tractatus Logico-Philosophicus

> Chapter companion for Tractatus Logico-Philosophicus by Ludwig Wittgenstein.

## 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.

## Character check-ins

### Bertrand Russell

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

## Key lines

> 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._

## Links

- HTML: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters/5-252
- Book: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se
- All chapters: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters