# 5.515 explained — Tractatus Logico-Philosophicus

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

## 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.

## Character check-ins

### Mr. Wittgenstein

Author of the Tractatus, presenting the logical requirement that connectives only apply to propositions.

## Key lines

> 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._

## Links

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