Combining Texts
Ideas for
'Metaphysics', 'Letters to Russell' and 'The Evolution of Logic'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
17 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
|
560
|
Mathematical precision is only possible in immaterial things [Aristotle]
|
|
9076
|
Mathematics studies the domain of perceptible entities, but its subject-matter is not perceptible [Aristotle]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
|
10958
|
Perhaps numbers are substances? [Aristotle]
|
|
13273
|
Pluralities divide into discontinous countables; magnitudes divide into continuous things [Aristotle]
|
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]
|
|
13491
|
The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD]
|
|
13463
|
There are at least as many infinite cardinals as transfinite ordinals (because they will map) [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
|
18253
|
I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege]
|
|
13446
|
19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
|
12074
|
The one in number just is the particular [Aristotle]
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
|
17844
|
The unit is stipulated to be indivisible [Aristotle]
|
|
17845
|
If only rectilinear figures existed, then unity would be the triangle [Aristotle]
|
|
17859
|
Units came about when the unequals were equalised [Aristotle]
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
|
17861
|
Two men do not make one thing, as well as themselves [Aristotle]
|
|
646
|
When we count, are we adding, or naming numbers? [Aristotle]
|
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]
|