Combining Texts
Ideas for
'Thinking About Mathematics', 'Travels in Four Dimensions' and 'Realism in Mathematics'
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 / 1. Foundations for Mathematics
8764
|
Categories are the best foundation for mathematics [Shapiro]
|
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
8762
|
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
|
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10718
|
A natural number is a property of sets [Maddy, by Oliver]
|
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
8760
|
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
|
8761
|
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
|