The theory of constructive types (principles of logic and mathematics). By Leon Chwistek.

35
Dem.-P.221 q — - IJ
j-. 3.pD.q --- r:.'
[3-3.5s32]0 1 -. Prop.
Analogous remarks as those given above apply to the. theory
of apparent variables (numbers - 10 and l 11 of Principia).
Nevertheless this theory cannot be taken textually from Prinm
cipia, the following modifications being necessary:
10 We omit all verbal propositions, using our directions exclusively.
20 We use the expressions given above instead of those of
Principia.
3 We use other definitions.
4~ Numbers. 9 and 12 of Principia are to be omitted.
De/fi initions.
10-01 (r )- () -
c'lJ
10-011 ('F U) =- () -
The Whitehead-Russellia definition: (4 x)f {x} = (x) -f/{}
is useless, because e. g. the expression (xL)f{x, y} has no
meaning at all. We could as a natter of fact use the expression: (Hx)[f {z,y}] {x}, but here z[f{z,y}j{x} would not be
treated as a functional pattern, no other operations than simple substitution being allowed in defined symbols For the same
reason we cannot use the abbreviations 10'02'03 of Principia.
110:1 (x, ) =( ) (Y)
dt
111)9, (x. q- z) (x) i; K)
11-021 (x, z, x) = x) (y) () (x')
11-03 (Ç x, y) = (3 x) (a y)
4f
11.04 (,x. y, z)=-( x, y) (i7z)
df
Analogous abbreviations are to be assumed for fundamental
letters. The following propositions are to be used below:
10-24 g-., 1 {} 3 (r )./'{}.