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.
Themes 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.