Combining Philosophers

All the ideas for Engelbretsen,G/Sayward,C, Pierre-Joseph Proudhon and Kenneth Kunen

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21 ideas

4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
13913 The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward]
13914 Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
13915 Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward]
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
13916 Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward]
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 / 4. Pure Logic
13850 In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
13849 Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
13851 Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
13852 Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward]
8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation
18465 An 'equivalence' relation is one which is reflexive, symmetric and transitive [Kunen]
25. Social Practice / C. Rights / 4. Property rights
20523 Property is theft! [Proudhon]