Combining Texts

All the ideas for 'Set Theory', 'Structure of Scientific Revolutions (2nd ed)' and 'Tarski's Theory of Truth'

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26 ideas

3. Truth / A. Truth Problems / 4. Uses of Truth
10825 The notion of truth is to help us make use of the utterances of others [Field,H]
3. Truth / A. Truth Problems / 9. Rejecting Truth
10820 In the early 1930s many philosophers thought truth was not scientific [Field,H]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
13499 Tarski reduced truth to reference or denotation [Field,H, by Hart,WD]
10818 Tarski really explained truth in terms of denoting, predicating and satisfied functions [Field,H]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
10817 Tarski just reduced truth to some other undefined semantic notions [Field,H]
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]
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
10819 Tarski gives us the account of truth needed to build a group of true sentences in a model [Field,H]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10827 Model theory is unusual in restricting the range of the quantifiers [Field,H]
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]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
10826 'Valence' and 'gene' had to be reduced to show their compatibility with physicalism [Field,H]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
7615 Field says reference is a causal physical relation between mental states and objects [Field,H, by Putnam]