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

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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.

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