Combining Texts
Ideas for
'Thinking About Mathematics', 'Frege philosophy of mathematics' and 'Reference and Generality (3rd ed)'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
6 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 / 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]
|
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9829
|
The identity of a number may be fixed by something outside structure - by counting [Dummett]
|
9828
|
Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
|