Combining Texts

All the ideas for '', 'Ontological Relativity' and 'Set Theory'

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22 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]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11211 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11210 Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
11212 The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
21642 If quantification is all substitutional, there is no ontology [Quine]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
1633 Absolute ontological questions are meaningless, because the answers are circular definitions [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / d. Commitment of theories
18964 Ontology is relative to both a background theory and a translation manual [Quine]
9. Objects / F. Identity among Objects / 1. Concept of Identity
18965 We know what things are by distinguishing them, so identity is part of ontology [Quine]
13. Knowledge Criteria / E. Relativism / 5. Language Relativism
1634 Two things are relative - the background theory, and translating the object theory into the background theory [Quine]
19. Language / B. Reference / 1. Reference theories
8470 Reference is inscrutable, because we cannot choose between theories of numbers [Quine, by Orenstein]
19. Language / F. Communication / 3. Denial
11214 We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
19. Language / F. Communication / 6. Interpreting Language / b. Indeterminate translation
18963 Indeterminacy translating 'rabbit' depends on translating individuation terms [Quine]