# Formal Series and Internal Relations explained — Tractatus Logico-Philosophicus

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

## What happens

This chapter introduces the concept of formal series, which are ordered by internal relations rather than external ones. Examples include the series of numbers and a series of propositions about relations, where each proposition is internally related to the next through logical form.

## Themes in this chapter

### Logical Atomism

The discussion of formal series and internal relations reflects the logical atomist view that complex propositions are built from simpler ones through logical relations.

### Limits of Language and Thought

The notion of formal series shows how language can express internal relations that are not contingent but necessary, highlighting the limits of what can be said versus shown.

## Character check-ins

### Mr. Wittgenstein

Author of the Tractatus, defining formal series and internal relations.

## Key lines

> Series which are ordered by internal relations I call formal series.

A series whose order is determined by the intrinsic logical connections between its members is called a formal series.

_Wittgenstein distinguishes formal series from those ordered by external, contingent relations._

> The series of numbers is ordered not by an external, but by an internal relation.

The ordering of numbers arises from their inherent logical properties, not from any arbitrary external arrangement.

_This illustrates the concept of internal relations using the familiar example of numbers._

## Links

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