Combining Texts

All the ideas for 'fragments/reports', 'Set Theory' and 'Four Dimensionalism'

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42 ideas

1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
Metaphysical enquiry can survive if its conclusions are tentative [Sider]
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]
7. Existence / B. Change in Existence / 2. Processes
Four-dimensionalism sees things and processes as belonging in the same category [Sider]
8. Modes of Existence / B. Properties / 6. Categorical Properties
Proper ontology should only use categorical (actual) properties, not hypothetical ones [Sider]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
If sortal terms fix the kind and the persistence conditions, we need to know what kinds there are [Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
If Tib is all of Tibbles bar her tail, when Tibbles loses her tail, two different things become one [Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Artists 'create' statues because they are essentially statues, and so lack identity with the lump of clay [Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
The stage view of objects is best for dealing with coincident entities [Sider]
9. Objects / C. Structure of Objects / 5. Composition of an Object
'Composition as identity' says that an object just is the objects which compose it [Sider]
9. Objects / D. Essence of Objects / 12. Essential Parts
Mereological essentialism says an object's parts are necessary for its existence [Sider]
9. Objects / E. Objects over Time / 3. Three-Dimensionalism
Three-dimensionalists assert 'enduring', being wholly present at each moment, and deny 'temporal parts' [Sider]
Some might say that its inconsistency with time travel is a reason to favour three-dimensionalism [Sider]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
Four-dimensionalists assert 'temporal parts', 'perduring', and being spread out over time [Sider]
4D says intrinsic change is difference between successive parts [Sider]
4D says each spatiotemporal object must have a temporal part at every moment at which it exists [Sider]
9. Objects / E. Objects over Time / 5. Temporal Parts
Temporal parts exist, but are not prior building blocks for objects [Sider]
Temporal parts are instantaneous [Sider]
How can an instantaneous stage believe anything, if beliefs take time? [Sider]
Four-dimensionalism says temporal parts are caused (through laws of motion) by previous temporal parts [Sider]
9. Objects / E. Objects over Time / 9. Ship of Theseus
The ship undergoes 'asymmetric' fission, where one candidate is seen as stronger [Sider]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
If you say Leibniz's Law doesn't apply to 'timebound' properties, you are no longer discussing identity [Sider]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Counterparts rest on similarity, so there are many such relations in different contexts [Sider]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
Maybe motion is a dynamical quantity intrinsic to a thing at a particular time [Sider]
27. Natural Reality / C. Space / 6. Space-Time
Space is 3D and lacks a direction; time seems connected to causation [Sider]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
Between presentism and eternalism is the 'growing block' view - the past is real, the future is not [Sider]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
For Presentists there must always be a temporal vantage point for any description [Sider]
Presentists must deny truths about multiple times [Sider]
27. Natural Reality / D. Time / 2. Passage of Time / c. Tenses and time
Talk using tenses can be eliminated, by reducing it to indexical connections for an utterance [Sider]
27. Natural Reality / D. Time / 2. Passage of Time / f. Tenseless (B) series
The B-theory is adequate, except that it omits to say which time is present [Sider]
The B-series involves eternalism, and the reduction of tense [Sider]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]