Combining Texts

All the ideas for 'Set Theory', 'A Version of Internalist Foundationalism' and 'Letters to Blijenburgh'

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24 ideas

2. Reason / A. Nature of Reason / 6. Coherence
8893 For any given area, there seem to be a huge number of possible coherent systems of beliefs [Bonjour]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13030 Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
13032 Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
13033 Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13037 Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13038 Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13034 Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
13039 Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13036 Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
13029 Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
13031 Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
13040 Constructibility: V = L (all sets are constructible) [Kunen]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
8888 The concept of knowledge is so confused that it is best avoided [Bonjour]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
8887 It is hard to give the concept of 'self-evident' a clear and defensible characterization [Bonjour]
12. Knowledge Sources / B. Perception / 8. Adverbial Theory
8897 The adverbial account will still be needed when a mind apprehends its sense-data [Bonjour]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
8896 Conscious states have built-in awareness of content, so we know if a conceptual description of it is correct [Bonjour]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
8891 My incoherent beliefs about art should not undermine my very coherent beliefs about physics [Bonjour]
8892 Coherence seems to justify empirical beliefs about externals when there is no external input [Bonjour]
8894 Coherentists must give a reason why coherent justification is likely to lead to the truth [Bonjour]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
8889 Reliabilists disagree over whether some further requirement is needed to produce knowledge [Bonjour]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
8890 If the reliable facts producing a belief are unknown to me, my belief is not rational or responsible [Bonjour]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / f. Higher-order thought
8895 If neither the first-level nor the second-level is itself conscious, there seems to be no consciousness present [Bonjour]
28. God / A. Divine Nature / 3. Divine Perfections
7829 God no more has human perfections than we have animal perfections [Spinoza]
28. God / C. Attitudes to God / 4. God Reflects Humanity
7830 A talking triangle would say God is triangular [Spinoza]