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Number/statement/property/Mates: every statement in which a number occurs, represents a property of the corresponding number Denkform - e.g. no person under 18 receives permission- property of the number 18, that it is a number k with the property, that no person obtains a permit under k years - therefore complete induction can be applied to such statements.
Numbers/Frege/Mates: Definition cardinal number: of a set a: set of all sets which are numerically equivalent to a - Definition one/1: the set of all sets a, satisfying the condition (x) (Ey) (y e a <> y = x). - Definition Two/2: set of all sets which satisfy the condition (x)(y)(x not equal y u (z)(z e a <> (z = x v z = y))). ((s) Excluding right?) -
Definition sum: the sum p + q of two integers p and q is the set of all sets g which satisfying the condition (a)(Eb)(a e p u b e q u a U b = g u a D b = L) - Definition set of all positive numbers: the average ((s) Common) of all sets a which satisfying the condition
1 e a u (n)(n e a > n + 1 e a). ((S) successor) - thus Frege shows that arithmetic can be lead back entirely on logic, and thus that it is part of the logic.
Elementare Logik Göttingen 1969