Combining Philosophers

All the ideas for Eubulides, Kenneth Kunen and Ralph Cudworth

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24 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 / L. Paradox / 1. Paradox
6007 If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
6006 If you say truly that you are lying, you are lying [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
6008 Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]
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]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / c. Tabula rasa
6230 If the soul were a tabula rasa, with no innate ideas, there could be no moral goodness or justice [Cudworth]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
6228 Senses cannot judge one another, so what judges senses cannot be a sense, but must be superior [Cudworth]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / a. Physicalism critique
6229 Sense is fixed in the material form, and so can't grasp abstract universals [Cudworth]
22. Metaethics / B. Value / 1. Nature of Value / c. Objective value
6227 Keeping promises and contracts is an obligation of natural justice [Cudworth]
23. Ethics / F. Existentialism / 6. Authentic Self
6231 There is a self-determing power in each person, which makes them what they are [Cudworth]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
6225 Obligation to obey all positive laws is older than all laws [Cudworth]
28. God / A. Divine Nature / 4. Divine Contradictions
6224 An omnipotent will cannot make two things equal or alike if they aren't [Cudworth]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
6223 If the will and pleasure of God controls justice, then anything wicked or unjust would become good if God commanded it [Cudworth]
6226 The requirement that God must be obeyed must precede any authority of God's commands [Cudworth]