Tractatus Logico-Philosophicus · Chapter
4.27 explained
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.
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.
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- Setup
- Escalation
- Breaking point
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- Closing
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Follow the arc while readingThemes in this chapter
- Logical Atomism
The proposition explores the combinatorial structure of atomic facts, a core concept in logical atomism.
Characters to notice
- Mr. Wittgenstein
Author of the proposition, presenting combinatorial logic of atomic facts.
Key passages
“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.
