Tractatus Logico-Philosophicus states simply that
6 The general form of the truth function is: $[\bar p, \bar\xi, N(\bar \xi)]$. This is the general form of the sentence.
Wikipedia and other sources say
- $\bar p$ stands for an atomic proposition;
- $\bar \xi$ stands for a set of propositions;
- $N(\xi)$ stands for the set of all negations of propositions in $\bar \xi$.
However, this couldn't possibly be correct, because
6.03 The general form of the integer is: $[0, \xi, \xi+1]$.
And not a single negation is here. Not only that, $0$ is not an atomic proposition. Not only that, as far as I see, $[0, \xi, \xi+1]$ is not a function of type
$$[0, \xi, \xi+1]: \mathrm{Something} \to \{\top, \bot\}$$
So, what is the logical system of Tractatus Logico-Philosophicus?
For the general form of an integer, the notation introduced at 5.2522 is used:
5.2521 If an operation is applied repeatedly to its own results, I speak of successive applications of it. (‘O’O’O’a’ is the result of three successive applications of the operation ‘O’ξ’ to ‘a’.) In a similar sense I speak of successive applications of more than one operation to a number of propositions.
5.2522 Accordingly I use the sign ‘[a, x, O’x]’ for the general term of the series of forms a, O’a, O’O’a, . . . .This bracketed expression is a variable: the first term of the bracketed expression is the beginning of the series of forms, the second is the form of a term x arbitrarily selected from the series, and the third is the form of the term that immediately follows x in the series.
It should be remarked that Wittgenstein's Tractatus Logico-Philosophicus is not entirely clear of equivocal formulations which have subsequently lead to debates. For example, see the papers, P.T. Geach's “Wittgenstein's Operator N” and R. J. Fogelin's “Wittgenstein's Operator N”.