Tractatus Logico-Philosophicus · Chapter
5.31 explained
Wittgenstein explains that the schemata from 4.31 remain significant even when the propositional variables are not elementary propositions, and that the propositional sign in 4.442 expresses a truth-function of elementary propositions regar
What happens
Wittgenstein explains that the schemata from 4.31 remain significant even when the propositional variables are not elementary propositions, and that the propositional sign in 4.442 expresses a truth-function of elementary propositions regardless of the complexity of its components.
Themes in this chapter
Logical Atomism
The passage emphasizes that all propositions, even complex ones, are ultimately truth-functions of elementary propositions, a core tenet of logical atomism.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, presenting the logical structure of propositions.
Key passages
“The schemata No. 4.31 are also significant, if “ p ”, “ q ”, “ r ”, etc. are not elementary propositions.”
The truth-table schemata from 4.31 still apply even when the variables stand for complex propositions rather than simple ones.
Wittgenstein extends the applicability of truth-functional analysis beyond elementary propositions.
“And it is easy to see that the propositional sign in No. 4.442 expresses one truth-function of elementary propositions even when “ p ” and “ q ” are truth-functions of elementary propositions.”
The notation in 4.442 still represents a truth-function of basic propositions, even if its components are themselves truth-functions.
This reinforces the idea that all propositions reduce to truth-functions of elementary propositions.