@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}
}