6.00

Home
Su
1.
2.
3.
4.
5.

 

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

This is the general form of proposition.

6.001 - 6.002

6.01    The general form of the operation  OMEGA ' ( eta-bar ) is therefore:

[ xi-bar , N ( xi-bar )]'( eta-bar ) (= [ eta-bar ,  xi-bar , N( xi-bar )]).

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

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

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

"[ OMEGA 0',  OMEGA v'x,  OMEGA 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,  xi ,  xi +1].

6.1 - 6.5