Tractatus Logico-Philosophicus · Chapter
5.451 explained
Wittgenstein argues that if logic has primitive ideas, they must be independent and introduced in all contexts at once, not piecemeal.
What happens
Wittgenstein argues that if logic has primitive ideas, they must be independent and introduced in all contexts at once, not piecemeal. He uses the example of denial to show that introducing a primitive sign for one class of cases and then another would create ambiguity about its meaning. He invokes Frege's remarks on definitions to support this point.
Themes in this chapter
Logic and Tautology
Discusses the independence and uniform introduction of primitive logical ideas, such as denial, which are foundational to logical structure.
Characters to notice
- Frege
Referenced for his work 'Grundgesetze der Arithmetik' on the introduction of signs by definitions, applied analogously to primitive signs.
Key passages
“If logic has primitive ideas these must be independent of one another. If a primitive idea is introduced it must be introduced in all contexts in which it occurs at all.”
Logical primitives must be self-standing and applied uniformly across every context where they appear.
Wittgenstein insists on the holistic introduction of primitive signs to avoid ambiguity.
“We may not first introduce it for one class of cases and then for another, for it would then remain doubtful whether its meaning in the two cases was the same, and there would be no reason to use the same way of symbolizing in the two cases.”
Introducing a primitive sign separately for different cases would cast doubt on whether it has the same meaning, undermining the rationale for using the same symbol.
Highlights the need for consistent symbolic usage in logic.