Combining Texts

All the ideas for 'Necessary Existents', 'Sophistical Refutations' and 'Set Theory'

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19 ideas

2. Reason / A. Nature of Reason / 1. On Reason
2676 Didactic argument starts from the principles of the subject, not from the opinions of the learner [Aristotle]
2. Reason / A. Nature of Reason / 4. Aims of Reason
2675 Reasoning is a way of making statements which makes them lead on to other statements [Aristotle]
2. Reason / C. Styles of Reason / 1. Dialectic
2677 Dialectic aims to start from generally accepted opinions, and lead to a contradiction [Aristotle]
2. Reason / C. Styles of Reason / 3. Eristic
2674 Competitive argument aims at refutation, fallacy, paradox, solecism or repetition [Aristotle]
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]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
16967 'Are Coriscus and Callias at home?' sounds like a single question, but it isn't [Aristotle]
9. Objects / D. Essence of Objects / 10. Essence as Species
16149 Generic terms like 'man' are not substances, but qualities, relations, modes or some such thing [Aristotle]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
11840 Only if two things are identical do they have the same attributes [Aristotle]
19. Language / D. Propositions / 3. Concrete Propositions
19216 Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]