Combining Texts

All the ideas for 'fragments/reports', 'Truthmakers and Converse Barcan Formula' and 'Set Theory'

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25 ideas

3. Truth / B. Truthmakers / 5. What Makes Truths / b. Objects make truths
15134 The truthmaker principle requires some specific named thing to make the difference [Williamson]
3. Truth / B. Truthmakers / 7. Making Modal Truths
15141 Truthmaker is incompatible with modal semantics of varying domains [Williamson]
15140 The converse Barcan formula will not allow contingent truths to have truthmakers [Williamson]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
15131 If metaphysical possibility is not a contingent matter, then S5 seems to suit it best [Williamson]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
15135 If the domain of propositional quantification is constant, the Barcan formulas hold [Williamson]
15139 Converse Barcan: could something fail to meet a condition, if everything meets that condition? [Williamson]
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 / G. Quantification / 1. Quantification
18492 Not all quantification is either objectual or substitutional [Williamson]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
15136 Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances [Williamson]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
15138 Not all quantification is objectual or substitutional [Williamson]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
15137 If 'fact' is a noun, can we name the fact that dogs bark 'Mary'? [Williamson]
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
15142 Our ability to count objects across possibilities favours the Barcan formulas [Williamson]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
15133 A thing can't be the only necessary existent, because its singleton set would be as well [Williamson]