Combining Texts
Ideas for
'Axiomatic Theories of Truth', 'Outline of a System of Utilitarianism' and 'Russell's Metaphysical Logic'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
10 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
16321
|
The compactness theorem can prove nonstandard models of PA [Halbach]
|
16343
|
The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach]
|
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
16312
|
To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach]
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
21723
|
The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B]
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
21721
|
Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B]
|
21703
|
Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B]
|
21714
|
The ramified theory subdivides each type, according to the range of the variables [Linsky,B]
|
16308
|
Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach]
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
21713
|
Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B]
|
21715
|
For those who abandon logicism, standard set theory is a rival option [Linsky,B]
|