back to areas     |     expand all areas     |     Click on an area to expand it    |      Idea totals are in red.

Expansion for Mathematics

1021 1. Philosophy
610 2. Reason
612 3. Truth
779 4. Formal Logic
1225 5. Theory of Logic

1172 6. Mathematics
A. Nature of Mathematics
30 1. Mathematics
31 2. Geometry
26 3. Nature of Numbers a. Numbers
25 b. Types of number
19 c. Priority of numbers
6 d. Natural numbers
30 e. Ordinal numbers
8 f. Cardinal numbers
29 g. Real numbers
5 h. Reals from Cauchy
11 i. Reals from cuts
2 j. Complex numbers
1 k. Imaginary numbers
7 l. Zero
7 m. One
2 n. Pi
19 4. Using Numbers a. Units
4 b. Quantity
29 c. Counting procedure
12 d. Counting via concepts
8 e. Counting by correlation
10 f. Arithmetic
11 g. Applying mathematics
26 5. The Infinite a. The Infinite
3 b. Mark of the infinite
5 c. Potential infinite
11 d. Actual infinite
1 e. Countable infinity
5 f. Uncountable infinities
15 g. Continuum Hypothesis
8 h. Ordinal infinity
10 i. Cardinal infinity
6 j. Infinite divisibility
9 k. Infinitesimals
6 l. Limits
B. Foundations for Mathematics
15 1. Foundations for Mathematics
7 2. Proof in Mathematics
21 3. Axioms for Geometry
20 4. Axioms for Number a. Axioms for numbers
2 b. Baby arithmetic
2 c. Robinson arithmetic
25 d. Peano arithmetic
9 e. Peano arithmetic 2nd-order
10 f. Mathematical induction
20 g. Incompleteness of Arithmetic
3 5. Definitions of Number a. Defining numbers
10 b. Greek arithmetic
45 c. Fregean numbers
19 d. Hume's Principle
13 e. Caesar problem
3 f. Zermelo numbers
4 g. Von Neumann numbers
36 6. Mathematics as Set Theory a. Mathematics is set theory
13 b. Mathematics is not set theory
33 7. Mathematical Structuralism a. Structuralism
11 b. Varieties of structuralism
13 c. Nominalist structuralism
12 d. Platonist structuralism
23 e. Structuralism critique
C. Sources of Mathematics
33 1. Mathematical Platonism a. For mathematical platonism
21 b. Against mathematical platonism
11 2. Intuition of Mathematics
5 3. Mathematical Nominalism
36 4. Mathematical Empiricism a. Mathematical empiricism
17 b. Indispensability of mathematics
19 c. Against mathematical empiricism
14 5. Numbers as Adjectival
33 6. Logicism a. Early logicism
21 b. Type theory
15 c. Neo-logicism
38 d. Logicism critique
23 7. Formalism
5 8. Finitism
11 9. Fictional Mathematics
16 10. Constructivism a. Constructivism
18 b. Intuitionism
8 c. Conceptualism
19 d. Predicativism
3 e. Psychologism

1015 7. Existence
853 8. Modes of Existence
1515 9. Objects
786 10. Modality
473 11. Knowledge Aims
687 12. Knowledge Sources
621 13. Knowledge Criteria
671 14. Science
526 15. Nature of Minds
478 16. Persons
488 17. Mind and Body
760 18. Thought
819 19. Language
281 20. Action
240 21. Aesthetics
897 22. Metaethics
940 23. Ethics
850 24. Political Theory
656 25. Social Practice
977 26. Natural Theory
704 27. Natural Reality
425 28. God
291 29. Religion