Combining Texts

All the ideas for 'Set Theory', 'Notebooks' and 'On Providence'

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29 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Seek wisdom rather than truth; it is easier [Joubert]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
We must think with our entire body and soul [Joubert]
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
The love of certainty holds us back in metaphysics [Joubert]
2. Reason / A. Nature of Reason / 9. Limits of Reason
The truths of reason instruct, but they do not illuminate [Joubert]
3. Truth / A. Truth Problems / 1. Truth
Truth consists of having the same idea about something that God has [Joubert]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
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
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
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
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
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
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
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
Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
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
Constructibility: V = L (all sets are constructible) [Kunen]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
To know is to see inside oneself [Joubert]
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
The imagination has made more discoveries than the eye [Joubert]
18. Thought / A. Modes of Thought / 1. Thought
A thought is as real as a cannon ball [Joubert]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
Where does the bird's idea of a nest come from? [Joubert]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
To be always happy is to lack knowledge of one half of nature [Seneca]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
He gives his body up to pleasure, but not his soul [Joubert]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
What will you think of pleasures when you no longer enjoy them? [Joubert]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
Virtue is hard if we are scorned; we need support [Joubert]
23. Ethics / C. Virtue Theory / 4. External Goods / a. External goods
Nothing bad can happen to a good man [Seneca]
25. Social Practice / E. Policies / 5. Education / a. Aims of education
In raising a child we must think of his old age [Joubert]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
The ocean changes in volume in proportion to the attraction of the moon [Seneca]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
We can't exactly conceive virtue without the idea of God [Joubert]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
We cannot speak against Christianity without anger, or speak for it without love [Joubert]