Combining Texts

All the ideas for 'Justified Belief as Responsible Belief', 'Repetition' and 'Elements of Set Theory'

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14 ideas

2. Reason / A. Nature of Reason / 6. Coherence
Coherentists seek relations among beliefs that are simple, conservative and explanatory [Foley]
3. Truth / A. Truth Problems / 8. Subjective Truth
Subjective truth can only be sustained by repetition [Kierkegaard, by Carlisle]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
We can only define functions if Choice tells us which items are involved [Enderton]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / c. Disjunctivism
Externalists want to understand knowledge, Internalists want to understand justification [Foley]
13. Knowledge Criteria / B. Internal Justification / 2. Pragmatic justification
We aren't directly pragmatic about belief, but pragmatic about the deliberation which precedes it [Foley]
Justification comes from acceptable procedures, given practical constraints [Foley]
23. Ethics / F. Existentialism / 8. Eternal Recurrence
Life is a repetition when what has been now becomes [Kierkegaard]