Combining Texts

All the ideas for 'Set Theory', 'Of Organum or Ars Magna of Thinking' and 'The Nature of Mental States'

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22 ideas

1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
5021 An idea is analysed perfectly when it is shown a priori that it is possible [Leibniz]
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]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / d. Rational foundations
5020 Our thoughts are either dependent, or self-evident. All thoughts seem to end in the self-evident [Leibniz]
17. Mind and Body / B. Behaviourism / 2. Potential Behaviour
2590 Dispositions need mental terms to define them [Putnam]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
2591 Total paralysis would mean that there were mental states but no behaviour at all [Putnam]
17. Mind and Body / C. Functionalism / 1. Functionalism
2588 Is pain a functional state of a complete organism? [Putnam]
2589 Functionalism is compatible with dualism, as pure mind could perform the functions [Putnam]
2592 Functional states correlate with AND explain pain behaviour [Putnam]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
2587 Temperature is mean molecular kinetic energy, but they are two different concepts [Putnam]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
6376 Neuroscience does not support multiple realisability, and tends to support identity [Polger on Putnam]
2330 If humans and molluscs both feel pain, it can't be a single biological state [Putnam, by Kim]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
5019 Supreme human happiness is the greatest possible increase of his perfection [Leibniz]