Tractatus Logico-Philosophicus · Chapter
5.515 explained
Wittgenstein argues that the logical connectives '∨', '.', etc., presuppose that the symbols they connect are propositions.
What happens
Wittgenstein argues that the logical connectives '∨', '.', etc., presuppose that the symbols they connect are propositions. If 'p' in 'p ∨ q' is not a complex sign with sense, then 'p ∨ p' and 'p . p' also lack sense, and consequently 'p ∨ q' cannot have sense either.
Themes in this chapter
Logical Atomism
The passage examines how complex propositions are built from elementary propositions, emphasizing the need for symbols to have sense.
Nonsense and Meaning
Wittgenstein discusses conditions under which propositions lose sense, linking to the broader theme of meaningful vs. nonsensical combinations.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, presenting the logical requirement that connectives only apply to propositions.
Key passages
“It must be recognized in our symbols that what is connected by “ ∨ ”, “ . ”, etc. , must be propositions.”
The symbols joined by logical connectives like 'or' and 'and' must themselves be propositions.
Clarifies the fundamental requirement for logical combination.
“If the sign “ p ” in “ p ∨ q ” does not stand for a complex sign, then by itself it cannot have sense; but then also the signs “ p ∨ p ”, “ p . p ”, etc. which have the same sense as “ p ” have no sense.”
If 'p' in 'p or q' is not a complex symbol, it lacks meaning, and so do 'p or p' and 'p and p', which share the same meaning as 'p'.
Shows the dependency of sense on the internal structure of symbols.