@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 28 Mar 2024}, author = {Mates,Benson}, subject = {Numbers}, note = {I 212 Number/statement/property/Mates: every statement in which a number occurs, represents a property of the corresponding number. 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. I 288 Numbers/Frege/Mates: Def cardinal number: of a set a: set of all sets which are numerically equivalent to a. Def One/1: the set of all sets a, satisfying the condition (x) (Ey) (y e a <> y = x). Def 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))). Def 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) Def 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). Mates: Thus Frege shows that arithmetic can be lead back entirely on logic, and thus that it is part of the logic. >Numbers/Frege, >Successor, >Sets, >Set theory.}, note = { Mate I B. Mates Elementare Logik Göttingen 1969 Mate II B. Mates Skeptical Essays Chicago 1981 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=286652} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=286652} }