Combining Philosophers
Ideas for Robert Hanna, Isaac Newton and Karl Weierstrass
expand these ideas
|
start again
|
choose
another area for these philosophers
display all the ideas for this combination of philosophers
8 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
|
18079
|
Newton developed a kinematic approach to geometry [Newton, by Kitcher]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
|
13152
|
We can talk of 'innumerable number', about the infinite points on a line [Newton]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
|
13151
|
Not all infinites are equal [Newton]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
|
18086
|
Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
|
18082
|
Quantities and ratios which continually converge will eventually become equal [Newton]
|
|
18092
|
Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock]
|
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
|
17783
|
A number is not a multitude, but a unified ratio between quantities [Newton]
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
|
11063
|
Logicism struggles because there is no decent theory of analyticity [Hanna]
|