The general form of truth-function is: [, , N()].

This is the general form of proposition.

6.001 - 6.002

6.01    The general form of the operation ' () is therefore:

[, N ()]'() (= [, , N()]).

This is the most general form of transition from one proposition to another.

6.02 (2)    And thus we come to numbers: I define

x = ⁰'x  Def.   e
'^v'x = ^v+1'x  Def.

According, then, to these symbolic rules we write the series 
x, 'x, ''x, '''x, . . . . . 
as: ⁰'x, ⁰⁺¹'x, ⁰⁺¹⁺¹'x, ^0+1+1+1'x, . . . . .

Therefore I write in place of "[x, , ' ]" - scrivo: 

"[⁰', ^v'x, ^v+1'x]",

And I define:
0 + 1 = 1  Def.
0 + 1 + 1 = 2  Def.
0 + 1 + 1 + 1 = 3  Def.
and so on.

6.03 (1)    The general form of the cardinal number is:  [0, , +1].