Combining Texts

All the ideas for 'Set Theory and Its Philosophy', 'Ecce Homo' and 'Elements of Mathematical Logic'

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23 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
4424 A warlike philosopher challenges problems to single combat [Nietzsche]
4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
8942 Lukasiewicz's L3 logic has three truth-values, T, F and I (for 'indeterminate') [Lukasiewicz, by Fisher]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10702 Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
10713 Usually the only reason given for accepting the empty set is convenience [Potter]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13044 Infinity: There is at least one limit level [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10708 Nowadays we derive our conception of collections from the dependence between them [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13546 The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
10707 Mereology elides the distinction between the cards in a pack and the suits [Potter]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10704 We can formalize second-order formation rules, but not inference rules [Potter]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
10703 Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
10712 If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17882 It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
13043 A relation is a set consisting entirely of ordered pairs [Potter]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
13042 If dependence is well-founded, with no infinite backward chains, this implies substances [Potter]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
13041 Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
22. Metaethics / B. Value / 2. Values / i. Self-interest
2886 The distinction between egoistic and non-egoistic acts is absurd [Nietzsche]
22. Metaethics / C. The Good / 1. Goodness / i. Moral luck
4426 A bad result distorts one's judgement about the virtue of what one has done [Nietzsche]
23. Ethics / C. Virtue Theory / 3. Virtues / f. Compassion
4425 The overcoming of pity I count among the noble virtues [Nietzsche]
23. Ethics / F. Existentialism / 6. Authentic Self
20132 To become what you are you must have no self-awareness [Nietzsche]
23. Ethics / F. Existentialism / 8. Eternal Recurrence
20144 Eternal recurrence is the highest attainable affirmation [Nietzsche]
25. Social Practice / E. Policies / 5. Education / c. Teaching
2889 One repays a teacher badly if one remains only a pupil [Nietzsche]
28. God / C. Attitudes to God / 5. Atheism
2887 I am not an atheist because of reasoning or evidence, but because of instinct [Nietzsche]