Tractatus Logico-Philosophicus · Chapter
5.501 explained
Wittgenstein explains the notation for bracketed expressions of propositions, introducing the variable 'ξ' with a line over it to represent all its values.
What happens
Wittgenstein explains the notation for bracketed expressions of propositions, introducing the variable 'ξ' with a line over it to represent all its values. He distinguishes three methods for determining the values of the variable: direct enumeration, giving a function whose values are the propositions, and giving a formal law for constructing them.
Themes in this chapter
Logical Atomism
The discussion of variables and propositional expressions reflects the atomistic approach to breaking down propositions into their constituent parts.
Limits of Language and Thought
The formal methods for describing propositions highlight the boundaries of what can be expressed through logical notation.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, explaining the notation for propositional expressions.
Key passages
“An expression in brackets whose terms are propositions I indicate—if the order of the terms in the bracket is indifferent—by a sign of the form “ ( ξ ‾ ) ”.”
When the order of propositions in a bracketed list does not matter, I represent the whole list with the notation '(ξ‾)'.
Introduces a shorthand for unordered sets of propositions.
“We may distinguish 3 kinds of description: 1. Direct enumeration. 2. Giving a function f x , whose values for all values of x are the propositions to be described. 3. Giving a formal law, according to which those propositions are constructed.”
There are three ways to specify which propositions a variable stands for: listing them directly, using a function that yields them, or providing a rule for generating them.
Classifies the methods for determining the values of a propositional variable.