Combining Texts
Ideas for
'Philosophy of Mathematics', 'Critique of Pure Reason' and 'Primitive Thisness and Primitive Identity'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
8 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
|
10201
|
Virtually all of mathematics can be modeled in set theory [Shapiro]
|
6. Mathematics / A. Nature of Mathematics / 2. Geometry
|
8739
|
Geometry studies the Euclidean space that dictates how we perceive things [Kant, by Shapiro]
|
|
8740
|
Geometry would just be an idle game without its connection to our intuition [Kant]
|
|
16899
|
Geometrical truth comes from a general schema abstracted from a particular object [Kant, by Burge]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
|
10213
|
Real numbers are thought of as either Cauchy sequences or Dedekind cuts [Shapiro]
|
|
18243
|
Understanding the real-number structure is knowing usage of the axiomatic language of analysis [Shapiro]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
|
18245
|
Cuts are made by the smallest upper or largest lower number, some of them not rational [Shapiro]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite
|
9632
|
Kant only accepts potential infinity, not actual infinity [Kant, by Brown,JR]
|