Combining Texts
Ideas for
'The Evolution of Logic', 'Frege philosophy of mathematics' and 'Hobbes'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
15 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
9896
|
A prime number is one which is measured by a unit alone [Dummett]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
18255
|
Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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]
|
13492
|
Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [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 / 4. Using Numbers / a. Units
9895
|
A number is a multitude composed of units [Dummett]
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
9852
|
We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
|
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 / 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]
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
9876
|
Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
|
13471
|
Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD]
|