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All the ideas for 'Armstrong on combinatorial possibility', 'Axiomatic Theories of Truth (2005 ver)' and 'Set Theory'

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26 ideas

1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
15545 Armstrong's analysis seeks truthmakers rather than definitions [Lewis]
3. Truth / A. Truth Problems / 2. Defining Truth
15647 Truth definitions don't produce a good theory, because they go beyond your current language [Halbach]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
15546 Predications aren't true because of what exists, but of how it exists [Lewis]
3. Truth / B. Truthmakers / 5. What Makes Truths / d. Being makes truths
15548 Say 'truth is supervenient on being', but construe 'being' broadly [Lewis]
3. Truth / B. Truthmakers / 9. Making Past Truths
14399 Presentism says only the present exists, so there is nothing for tensed truths to supervene on [Lewis]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
15649 In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
15650 Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach]
15648 Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach]
15655 Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach]
15654 If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
15656 Deflationists say truth merely serves to express infinite conjunctions [Halbach]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
15657 To prove the consistency of set theory, we must go beyond set theory [Halbach]
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 / C. Ontology of Logic / 1. Ontology of Logic
15652 We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach]
5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
15651 Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach]
7. Existence / D. Theories of Reality / 9. States of Affairs
15543 How do things combine to make states of affairs? Constituents can repeat, and fail to combine [Lewis]