Combining Texts

All the ideas for 'Set Theory', 'Treatise 4: The Moral Sense' and 'Two Dogmas of Empiricism'

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46 ideas

1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Any statement can be held true if we make enough adjustment to the rest of the system [Quine]
2. Reason / A. Nature of Reason / 1. On Reason
Reason is our power of finding out true propositions [Hutcheson]
2. Reason / D. Definition / 1. Definitions
Definition rests on synonymy, rather than explaining it [Quine]
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]
5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
Quine's arguments fail because he naively conflates names with descriptions [Fine,K on Quine]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Quine blurs the difference between knowledge of arithmetic and of physics [Jenkins on Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
Quine is hopeless circular, deriving ontology from what is literal, and 'literal' from good ontology [Yablo on Quine]
9. Objects / A. Existence of Objects / 1. Physical Objects
If physical objects are a myth, they are useful for making sense of experience [Quine]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Aristotelian essence of the object has become the modern essence of meaning [Quine]
10. Modality / A. Necessity / 6. Logical Necessity
Contrary to some claims, Quine does not deny logical necessity [Quine, by McFetridge]
10. Modality / A. Necessity / 11. Denial of Necessity
Quine's attack on the analytic-synthetic distinction undermined necessary truths [Quine, by Shoemaker]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
Metaphysical analyticity (and linguistic necessity) are hopeless, but epistemic analyticity is a priori [Boghossian on Quine]
Quine challenges the claim that analytic truths are knowable a priori [Quine, by Kitcher]
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
Quine's objections to a priori knowledge only work in the domain of science [Horwich on Quine]
Science is empirical, simple and conservative; any belief can hence be abandoned; so no a priori [Quine, by Horwich]
Logic, arithmetic and geometry are revisable and a posteriori; quantum logic could be right [Horwich on Quine]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
Empiricism makes a basic distinction between truths based or not based on facts [Quine]
Our outer beliefs must match experience, and our inner ones must be simple [Quine]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
The second dogma is linking every statement to some determinate observations [Quine, by Yablo]
14. Science / B. Scientific Theories / 6. Theory Holism
Statements about the external world face the tribunal of sense experience as a corporate body [Quine]
19. Language / A. Nature of Meaning / 1. Meaning
It is troublesome nonsense to split statements into a linguistic and a factual component [Quine]
19. Language / A. Nature of Meaning / 8. Synonymy
'Renate' and 'cordate' have identical extensions, but are not synonymous [Quine, by Miller,A]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
Once meaning and reference are separated, meaning ceases to seem important [Quine]
19. Language / E. Analyticity / 1. Analytic Propositions
Analytic statements are either logical truths (all reinterpretations) or they depend on synonymy [Quine]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
Did someone ever actually define 'bachelor' as 'unmarried man'? [Quine]
Quine's attack on analyticity undermined linguistic views of necessity, and analytic views of the a priori [Quine, by Boghossian]
Quine attacks the Fregean idea that we can define analyticity through synonyous substitution [Quine, by Thomasson]
The last two parts of 'Two Dogmas' are much the best [Miller,A on Quine]
Erasing the analytic/synthetic distinction got rid of meanings, and saved philosophy of language [Davidson on Quine]
The analytic needs excessively small units of meaning and empirical confirmation [Quine, by Jenkins]
If we try to define analyticity by synonymy, that leads back to analyticity [Quine]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
Can't the moral sense make mistakes, as the other senses do? [Hutcheson]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
Happiness is a pleasant sensation, or continued state of such sensations [Hutcheson]
23. Ethics / D. Deontological Ethics / 1. Deontology
You can't form moral rules without an end, which needs feelings and a moral sense [Hutcheson]
28. God / A. Divine Nature / 6. Divine Morality / a. Divine morality
We are asked to follow God's ends because he is our benefactor, but why must we do that? [Hutcheson]
Why may God not have a superior moral sense very similar to ours? [Hutcheson]