Combining Philosophers

All the ideas for Empedocles, Kenneth Kunen and Stanislaw Lesniewski

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35 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]
7. Existence / A. Nature of Existence / 5. Reason for Existence
458 Nothing could come out of nothing, and existence could never completely cease [Empedocles]
7. Existence / B. Change in Existence / 1. Nature of Change
5112 Empedocles says things are at rest, unless love unites them, or hatred splits them [Empedocles, by Aristotle]
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]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
13209 There is no coming-to-be of anything, but only mixing and separating [Empedocles, by Aristotle]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
8249 Class membership is not transitive, unlike being part of a part of the whole [Lesniewski, by George/Van Evra]
9. Objects / E. Objects over Time / 10. Beginning of an Object
457 Substance is not created or destroyed in mortals, but there is only mixing and exchange [Empedocles]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
462 One vision is produced by both eyes [Empedocles]
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
22765 Wisdom and thought are shared by all things [Empedocles]
18. Thought / A. Modes of Thought / 1. Thought
1524 For Empedocles thinking is almost identical to perception [Empedocles, by Theophrastus]
22. Metaethics / B. Value / 2. Values / j. Evil
552 Empedocles said good and evil were the basic principles [Empedocles, by Aristotle]
26. Natural Theory / A. Speculations on Nature / 1. Nature
589 'Nature' is just a word invented by people [Empedocles]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / e. The One
21823 The principle of 'Friendship' in Empedocles is the One, and is bodiless [Empedocles, by Plotinus]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
2680 Empedocles said that there are four material elements, and two further creative elements [Empedocles, by Aristotle]
6002 Empedocles says bone is water, fire and earth in ratio 2:4:2 [Empedocles, by Inwood]
13207 Fire, Water, Air and Earth are elements, being simple as well as homoeomerous [Empedocles, by Aristotle]
459 All change is unity through love or division through hate [Empedocles]
13218 The elements combine in coming-to-be, but how do the elements themselves come-to-be? [Aristotle on Empedocles]
13225 Love and Strife only explain movement if their effects are distinctive [Aristotle on Empedocles]
460 If the one Being ever diminishes it would no longer exist, and what could ever increase it? [Empedocles]
27. Natural Reality / G. Biology / 3. Evolution
5090 Maybe bodies are designed by accident, and the creatures that don't work are destroyed [Empedocles, by Aristotle]
28. God / A. Divine Nature / 2. Divine Nature
466 God is pure mind permeating the universe [Empedocles]
461 God is a pure, solitary, and eternal sphere [Empedocles]
28. God / A. Divine Nature / 4. Divine Contradictions
1719 In Empedocles' theory God is ignorant because, unlike humans, he doesn't know one of the elements (strife) [Aristotle on Empedocles]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
1522 It is wretched not to want to think clearly about the gods [Empedocles]