Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'Five Milestones of Empiricism' and 'Investigations in the Foundations of Set Theory I'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
5 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887
|
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891
|
Arithmetical undecidability is always settled at the next stage up [Koellner]
|
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
18178
|
For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
|
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13027
|
Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]
|
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9627
|
Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
|