Combining Texts
Ideas for
'The Evolution of Logic', 'Lectures on the Philosophy of (World) History' and 'Our Knowledge of Mathematical Objects'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
11 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
|
13492
|
Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD]
|
|
13459
|
The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD]
|
|
13463
|
There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD]
|
|
13491
|
The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
|
13446
|
19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
|
13509
|
We can establish truths about infinite numbers by means of induction [Hart,WD]
|
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
|
13474
|
Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD]
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
|
9224
|
Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K]
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
|
13471
|
Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD]
|
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
|
9222
|
The objects and truths of mathematics are imperative procedures for their construction [Fine,K]
|
|
9223
|
My Proceduralism has one simple rule, and four complex rules [Fine,K]
|