# 4.27 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein discusses the combinatorial possibilities of atomic facts, stating that for n atomic facts there are K_n = ∑_{ν=0}^{n} (n choose ν) possibilities, meaning all combinations of atomic facts can either exist or not exist.

## Themes in this chapter

### Logical Atomism

The proposition explores the combinatorial structure of atomic facts, a core concept in logical atomism.

## Character check-ins

### Mr. Wittgenstein

Author of the proposition, presenting combinatorial logic of atomic facts.

## Key lines

> With regard to the existence of n atomic facts there are K n = ∑ ν = 0 n ( n ν ) possibilities. It is possible for all combinations of atomic facts to exist, and the others not to exist.

For n atomic facts, the number of possible combinations of their existence is given by the sum of binomial coefficients from ν=0 to n, meaning any subset of atomic facts can exist while the rest do not.

_Clarifies the combinatorial principle underlying atomic facts._

## Links

- HTML: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters/4-27
- Book: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se
- All chapters: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters