Combining Texts

All the ideas for 'Set Theory', 'The Principles of Science' and 'Are there propositions?'

expand these ideas     |    start again     |     specify just one area for these texts

25 ideas

3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
13985 A true proposition seems true of one fact, but a false proposition seems true of nothing at all. [Ryle]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
13984 Two maps might correspond to one another, but they are only 'true' of the country they show [Ryle]
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 / A. Overview of Logic / 1. Overview of Logic
13979 Logic studies consequence, compatibility, contradiction, corroboration, necessitation, grounding.... [Ryle]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8628 I hold that algebra and number are developments of logic [Jevons]
7. Existence / D. Theories of Reality / 8. Facts / c. Facts and truths
13988 Many sentences do not state facts, but there are no facts which could not be stated [Ryle]
12. Knowledge Sources / B. Perception / 3. Representation
13983 Representation assumes you know the ideas, and the reality, and the relation between the two [Ryle]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
13980 If you like judgments and reject propositions, what are the relata of incoherence in a judgment? [Ryle]
19. Language / A. Nature of Meaning / 1. Meaning
13978 Husserl and Meinong wanted objective Meanings and Propositions, as subject-matter for Logic [Ryle]
19. Language / A. Nature of Meaning / 3. Meaning as Speaker's Intention
13977 When I utter a sentence, listeners grasp both my meaning and my state of mind [Ryle]
19. Language / D. Propositions / 1. Propositions
13976 'Propositions' name what is thought, because 'thoughts' and 'judgments' are too ambiguous [Ryle]
19. Language / D. Propositions / 4. Mental Propositions
13981 Several people can believe one thing, or make the same mistake, or share one delusion [Ryle]
13987 We may think in French, but we don't know or believe in French [Ryle]
19. Language / D. Propositions / 6. Propositions Critique
13989 There are no propositions; they are just sentences, used for thinking, which link to facts in a certain way [Ryle]
13982 If we accept true propositions, it is hard to reject false ones, and even nonsensical ones [Ryle]