Correction: (max 500 charact.)
The complaint will not be published.
VII (f) 116
Validity/Quine: even validity and extension of predicates can be eliminated in favor of truth value tables - validity in the quantifier theory can be eliminated by proof theory.
---
VII (i) 161
Validity/Quine: sentences that are valid for a universe, are also valid for a small universe - except for an empty universe. - Therefore, laws for large universes also should consider possible smaller universes. - Test, whether theorems are also valid for empty universes: put all universal quantifiers as true and all existential quantifiers as false.
---
X 77
Validity/valid/Quine: There are two definitions of validity,
a) (so far) as a property of schemes that refer to insertion.
b) uses the set theory: therefore two auxiliary terms:
1. Auxiliary term "set-theoretic analogue": a logical scheme, open sentence of set theory: instead of predications "Fx", "Fy", "Gx" etc., so we write
"X ε a" y ε α "x ε β" etc. the values of the variable "α", "β" etc. are amounts.
Two-digit predicate letters. For "Hxy" we use ordered pairs
ε γ".
Existential quantification: E.g. (Ex)(Fx.Gx): Set-theoretic analogue: the open sentence "Ex(x ε α. x ε β)".
N.B.: This sentence talks about quantities and allows quantification about them. E.g. "(α)".
Schematic letters "F" etc. on the other hand, only predicates represent and are not variables that take values.
>Schematic letters , >Quantification .
Set-theoretic analogue/s.a.: while the scheme is only the logical form of sentences, the set-theoretic analogue is actually a sentence of this form.
2. Auxiliary term for the new definition of validity: model.
>Models .