Combining Texts
Ideas for
'works', 'Must We Believe in Set Theory?' 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
7 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
|
13487
|
In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
|
10491
|
Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
|
10483
|
Mathematics and science do not require very high orders of infinity [Boolos]
|
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]
|
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
|
10490
|
Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
|