Combining Texts

All the ideas for 'Set Theory', 'Structure of Scientific Revolutions (2nd ed)' and 'The Morality of Happiness'

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25 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]
14. Science / A. Basis of Science / 6. Falsification
18076 Most theories are continually falsified [Kuhn, by Kitcher]
22191 Kuhn's scientists don't aim to falsifying their paradigm, because that is what they rely on [Kuhn, by Gorham]
14. Science / B. Scientific Theories / 4. Paradigm
22183 Switching scientific paradigms is a conversion experience [Kuhn]
14. Science / B. Scientific Theories / 5. Commensurability
6162 Kuhn has a description theory of reference, so the reference of 'electron' changes with the descriptions [Rowlands on Kuhn]
22184 Incommensurability assumes concepts get their meaning from within the theory [Kuhn, by Okasha]
7619 Galileo's notions can't be 'incommensurable' if we can fully describe them [Putnam on Kuhn]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
3546 'Phronesis' should translate as 'practical intelligence', not as prudence [Annas]
22. Metaethics / C. The Good / 3. Pleasure / d. Sources of pleasure
3547 Epicureans achieve pleasure through character development [Annas]
23. Ethics / A. Egoism / 3. Cyrenaic School
3543 Cyrenaics pursue pleasure, but don't equate it with happiness [Annas]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
3541 Ancient ethics uses attractive notions, not imperatives [Annas]
23. Ethics / D. Deontological Ethics / 1. Deontology
3550 Principles cover life as a whole, where rules just cover actions [Annas]
23. Ethics / D. Deontological Ethics / 2. Duty
3551 Virtue theory tries to explain our duties in terms of our character [Annas]
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
3552 If excessively good actions are admirable but not required, then duty isn't basic [Annas]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
3542 We should do good when necessary, not maximise it [Annas]