Combining Texts

All the ideas for 'Set Theory', 'Introduction to 'Language Truth and Logic'' and 'Euthydemus'

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24 ideas

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]
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
304 Beautiful things must be different from beauty itself, but beauty itself must be present in each of them [Plato]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
16120 Knowing how to achieve immortality is pointless without the knowledge how to use immortality [Plato]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
5163 Basic propositions refer to a single experience, are incorrigible, and conclusively verifiable [Ayer]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
303 Say how many teeth the other has, then count them. If you are right, we will trust your other claims [Plato]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
5167 The argument from analogy fails, so the best account of other minds is behaviouristic [Ayer]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
5164 A statement is meaningful if observation statements can be deduced from it [Ayer]
5165 Directly verifiable statements must entail at least one new observation statement [Ayer]
5166 The principle of verification is not an empirical hypothesis, but a definition [Ayer]
19. Language / D. Propositions / 1. Propositions
5162 Sentences only express propositions if they are meaningful; otherwise they are 'statements' [Ayer]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
302 What knowledge is required to live well? [Plato]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / i. Prescriptivism
5168 Moral approval and disapproval concerns classes of actions, rather than particular actions [Ayer]
22. Metaethics / C. The Good / 1. Goodness / e. Good as knowledge
301 Only knowledge of some sort is good [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
305 Something which lies midway between two evils is better than either of them [Plato]