Combining Texts

All the ideas for 'fragments/reports', 'Set Theory' and 'Launching Points to the Realm of the Mind'

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33 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
18450 Philosophy has its own mode of death, by separating soul from body [Porphyry]
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]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
18451 The presence of the incorporeal is only known by certain kinds of disposition [Porphyry]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
18459 Diversity arises from the power of unity [Porphyry]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
18452 Memory is not conserved images, but reproduction of previous thought [Porphyry]
15. Nature of Minds / A. Nature of Mind / 1. Mind / c. Features of mind
18453 Intelligence is aware of itself, so the intelligence is both the thinker and the thought [Porphyry]
15. Nature of Minds / A. Nature of Mind / 1. Mind / d. Location of mind
18462 The soul is everywhere and nowhere in the body, and must be its cause [Porphyry]
16. Persons / C. Self-Awareness / 2. Knowing the Self
18463 Successful introspection reveals the substrate along with the object of thought [Porphyry]
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
18458 The soul is bound to matter by the force of its own disposition [Porphyry]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
18464 Justice is each person fulfilling his function [Porphyry]
22. Metaethics / B. Value / 2. Values / g. Love
18448 We should avoid the pleasures of love, or at least, should not enact our dreams [Porphyry]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
5996 Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
18444 Civil virtues make us behave benevolently, and thereby unite citizens [Porphyry]
18445 Civil virtues control the passions, and make us conform to our nature [Porphyry]
18446 Purificatory virtues detach the soul completely from the passions [Porphyry]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
18447 There are practical, purificatory, contemplative, and exemplary virtues [Porphyry]
26. Natural Theory / A. Speculations on Nature / 1. Nature
18456 Unified real existence is neither great nor small, though greatness and smallness participate in it [Porphyry]
27. Natural Reality / D. Time / 1. Nature of Time / c. Idealist time
18454 Time is the circular movement of the soul [Porphyry]
27. Natural Reality / D. Time / 1. Nature of Time / e. Eventless time
18455 Some think time is seen at rest, as well as in movement [Porphyry]
28. God / A. Divine Nature / 2. Divine Nature
18460 God is nowhere, and hence everywhere [Porphyry]
28. God / C. Attitudes to God / 2. Pantheism
18461 Everything existing proceeds from divinity, and is within divinity [Porphyry]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
18449 Nature binds or detaches body to soul, but soul itself joins and detaches soul from body [Porphyry]
18457 Individual souls are all connected, though distinct, and without dividing universal Soul [Porphyry]