Tractatus Logico-Philosophicus · Chapter
Formal Series and Internal Relations explained
This chapter introduces the concept of formal series, which are ordered by internal relations rather than external ones.
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.
Free preview opens on this chapter — companions, themes, and character notes appear beside the text.
Narrative arc
Story tension across the book — this chapter sits in Exposition.
- Setup
- Escalation
- Breaking point
- Aftermath
- Closing
This passage marks the story’s dramatic climax because it presents the moment when the protagonist’s obsessive…
Full beat labels and climax notes unlock in the reader.
Follow the arc while readingThemes 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.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, defining formal series and internal relations.
Key passages
“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.
