Correction: (max 500 charact.)
The complaint will not be published.
XXI I
Variables/Russell/Gödel: exist only to enable truth function.
>
Truth functions .
Finite/Infinite/Ramsey: the problem of solving infinite propositions is not so critical. - Gödel: then Russell’s Apercu that propositions about classes can be interpreted as propositions about their elements literally becomes true, provided that n is the number of the (finite) individuals in the world, and provided we neglect the zero class.
>
Proposition , >
Classes/Russell , >
Empty set , >
Individual/Russell .
I 28
Pseudo-variable/Peano/Russell: the symbol (x). φ x denotes a particular proposition and there is no sense of difference between (x). j x and (y). φ y if they occur in the same context. - ((s)> Quine:
alphabetical variant ). - o is x in (x) φ x not an ambiguous part of an expression and such an expression itself remains the bearer of a very specific meaning despite the ambiguity of the x in φ x. Pseudo-variables: exist if the extension does not go over the entire range. A proposition with a state of affairs x is not a function of x. Extension: is the function of which all or some values are asserted.
I 29
Ambiguous assertion and the real variable: any arbitrary value φ x of the function φ x^ can be asserted. - Real Variable: φx. - If x varies, a different proposition results.
I 30
Pseudo-variable: is obtained if we put a universal quantifier before it.
I 73
Pseudo-Variable: several possible values can be meant. Descriptions always contain pseudo-variables. Sentences without pseudo-variables: are observation sentences e.g. This is red.
I 74
Pseudo-Variable/Principia Mathematica
(1) /Russell/(s): E.g. (y).φ(x,y), which is a function of x - here y is a pseudo-variable, x is the real variable. - ((s) E.g. everything smaller than x - instead of y it could also say z here).
1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press.