Combining Texts

All the ideas for 'fragments/reports', 'Set Theory' and 'Davidson on himself'

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27 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
Truth and objectivity depend on a community of speakers to interpret what they mean [Davidson]
There are no ultimate standards of rationality, since we only assess others by our own standard [Davidson]
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]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
If someone squashed a horse to make a dog, something new would now exist [Mnesarchus]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
There are no such things as minds, but people have mental properties [Davidson]
17. Mind and Body / D. Property Dualism / 1. Reductionism critique
If the mind is an anomaly, this makes reduction of the mental to the physical impossible [Davidson]
17. Mind and Body / D. Property Dualism / 2. Anomalous Monism
Obviously all mental events are causally related to physical events [Davidson]
There are no strict psychophysical laws connecting mental and physical events [Davidson]
Mental entities do not add to the physical furniture of the world [Davidson]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
The correct conclusion is ontological monism combined with conceptual dualism [Davidson]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Absence of all rationality would be absence of thought [Davidson]
18. Thought / C. Content / 6. Broad Content
Our meanings are partly fixed by events of which we may be ignorant [Davidson]
19. Language / D. Propositions / 6. Propositions Critique
Propositions explain nothing without an explanation of how sentences manage to name them [Davidson]
19. Language / F. Communication / 4. Private Language
Thought is only fully developed if we communicate with others [Davidson]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
There is simply no alternative to the 'principle of charity' in interpreting what others do [Davidson]
25. Social Practice / E. Policies / 5. Education / c. Teaching
Without a teacher, the concept of 'getting things right or wrong' is meaningless [Davidson]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
Cause and effect relations between events must follow strict laws [Davidson]