Combining Texts
Ideas for
'Thinking About Mathematics', 'What is an Idea?' and 'Metaphysics'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
8 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 / b. Greek arithmetic
17843
|
The idea of 'one' is the foundation of number [Aristotle]
|
17850
|
Each many is just ones, and is measured by the one [Aristotle]
|
17851
|
Number is plurality measured by unity [Aristotle]
|
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
9793
|
Mathematics studies abstracted relations, commensurability and proportion [Aristotle]
|
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]
|