Combining Texts

All the ideas for 'Individuals without Sortals', 'talk' and 'Set Theory'

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27 ideas

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]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
17518 Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers]
17516 If counting needs a sortal, what of things which fall under two sortals? [Ayers]
7. Existence / B. Change in Existence / 4. Events / a. Nature of events
17520 Events do not have natural boundaries, and we have to set them [Ayers]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
17519 To express borderline cases of objects, you need the concept of an 'object' [Ayers]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
17510 Speakers need the very general category of a thing, if they are to think about it [Ayers]
17522 We use sortals to classify physical objects by the nature and origin of their unity [Ayers]
17515 Seeing caterpillar and moth as the same needs continuity, not identity of sortal concepts [Ayers]
17511 Recognising continuity is separate from sortals, and must precede their use [Ayers]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
17517 Could the same matter have more than one form or principle of unity? [Ayers]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
17513 If there are two objects, then 'that marble, man-shaped object' is ambiguous [Ayers]
9. Objects / D. Essence of Objects / 5. Essence as Kind
17523 Sortals basically apply to individuals [Ayers]
9. Objects / E. Objects over Time / 5. Temporal Parts
17521 You can't have the concept of a 'stage' if you lack the concept of an object [Ayers]
17514 Temporal 'parts' cannot be separated or rearranged [Ayers]
9. Objects / F. Identity among Objects / 1. Concept of Identity
17509 Some say a 'covering concept' completes identity; others place the concept in the reference [Ayers]
9. Objects / F. Identity among Objects / 3. Relative Identity
17512 If diachronic identities need covering concepts, why not synchronic identities too? [Ayers]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
4688 We imagine small and large objects scaled to the same size, suggesting a fixed capacity for imagination [Lavers]