Combining Texts

All the ideas for 'Changes in Events and Changes in Things', 'Set Theory' and 'works'

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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]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
22121 The concept of being has only one meaning, whether talking of universals or of God [Duns Scotus, by Dumont]
22122 Being (not sensation or God) is the primary object of the intellect [Duns Scotus, by Dumont]
7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact
15201 That Queen Anne is dead is a 'general fact', not a fact about Queen Anne [Prior,AN]
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
22125 Duns Scotus was a realist about universals [Duns Scotus, by Dumont]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
22127 Scotus said a substantial principle of individuation [haecceitas] was needed for an essence [Duns Scotus, by Dumont]
9. Objects / D. Essence of Objects / 2. Types of Essence
22126 Avicenna and Duns Scotus say essences have independent and prior existence [Duns Scotus, by Dumont]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
22129 Certainty comes from the self-evident, from induction, and from self-awareness [Duns Scotus, by Dumont]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
22130 Scotus defended direct 'intuitive cognition', against the abstractive view [Duns Scotus, by Dumont]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
22128 Augustine's 'illumination' theory of knowledge leads to nothing but scepticism [Duns Scotus, by Dumont]
16. Persons / F. Free Will / 2. Sources of Free Will
22131 The will retains its power for opposites, even when it is acting [Duns Scotus, by Dumont]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
22899 'Thank goodness that's over' is not like 'thank goodness that happened on Friday' [Prior,AN]
28. God / A. Divine Nature / 2. Divine Nature
22123 The concept of God is the unique first efficient cause, final cause, and most eminent being [Duns Scotus, by Dumont]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
22124 We can't infer the infinity of God from creation ex nihilo [Duns Scotus, by Dumont]