Tractatus Logico-Philosophicus · Chapter
5.5301 explained
Wittgenstein argues that identity is not a relation between objects, using the proposition '(x): fx ⊃ x = a' to show that it expresses only that a uniquely satisfies the function f, not that objects have a relation to a.
What happens
Wittgenstein argues that identity is not a relation between objects, using the proposition '(x): fx ⊃ x = a' to show that it expresses only that a uniquely satisfies the function f, not that objects have a relation to a. He notes that expressing such a relation would itself require the identity sign.
Free preview opens on this chapter — companions, themes, and character notes appear beside the text.
Narrative arc
Story tension across the book — this chapter sits in Falling action.
- Setup
- Escalation
- Breaking point
- Aftermath
- Closing
This passage marks the story’s dramatic climax because it presents the moment when the protagonist’s obsessive…
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Follow the arc while readingThemes in this chapter
- Logical Atomism
The analysis of propositions into their logical components, here examining the role of identity in logical notation.
- Limits of Language and Thought
The discussion reveals the limits of expressing identity as a relation within the framework of logical language.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, presenting the argument that identity is not a relation between objects.
Key passages
“That identity is not a relation between objects is obvious.”
It is clear that identity does not function as a relation holding between distinct objects.
Wittgenstein asserts the non-relational nature of identity.
“What this proposition says is simply that only a satisfies the function f , and not that only such things satisfy the function f which have a certain relation to a .”
The proposition '(x): fx ⊃ x = a' means that a is the sole satisfier of f, not that only things bearing a specific relation to a satisfy f.
Clarifying the logical meaning of the identity-involving proposition.
