Ideas from 'What Numbers Are' by Nicholas P. White [1974], by Theme Structure
[found in 'Philosophy of Mathematics: anthology' (ed/tr Jacquette,Dale) [Blackwell 2002,0-631-21870-x]].
green numbers give full details |
back to texts
|
unexpand these ideas
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17813
|
Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers
|
|
|
|
Full Idea:
The Löwenheim-Skolem theorem tells us that any theory with a true interpretation has a model in the natural numbers.
|
|
|
|
From:
Nicholas P. White (What Numbers Are [1974], V)
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17812
|
Finite cardinalities don't need numbers as objects; numerical quantifiers will do
|
|
|
|
Full Idea:
Statements involving finite cardinalities can be made without treating numbers as objects at all, simply by using quantification and identity to define numerically definite quantifiers in the manner of Frege.
|
|
|
|
From:
Nicholas P. White (What Numbers Are [1974], IV)
|
|
|
|
A reaction:
[He adds Quine 1960:268 as a reference]
|