Tractatus Logico-Philosophicus · Chapter
5.2522 explained
Wittgenstein introduces a notation for the general term of a formal series, using the expression '[a, x, O'x]' to represent the series a, O'a, O'O'a, ...
What happens
Wittgenstein introduces a notation for the general term of a formal series, using the expression '[a, x, O'x]' to represent the series a, O'a, O'O'a, ... He explains that this bracketed expression is a variable, where the first term is the beginning of the series, the second is the form of an arbitrary term x, and the third is the form of the term immediately following x.
Characters to notice
- Mr. Wittgenstein
Introduces notation for the general term of a formal series.
Key passages
“The general term of the formal series a , O ′ a , O ′ O ′ a , … I write thus: “ [ a , x , O ′ x ] ”.”
I write the general term of the formal series a, O'a, O'O'a, ... as '[a, x, O'x]'.
Wittgenstein defines a notation for expressing the general form of a series generated by repeated application of an operation.
“This expression in brackets is a variable. The first term of the expression is the beginning of the formal series, the second the form of an arbitrary term x of the series, and the third the form of that term of the series which immediately follows x.”
The bracketed expression is a variable: the first term is the starting point of the series, the second is the pattern of any term x, and the third is the pattern of the term that comes right after x.
Wittgenstein explains the components of his notation for the formal series.