Combining Texts

All the ideas for 'Tropes', 'Elements of Set Theory' and 'Contingent Identity'

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

26 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
13204 The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
13206 A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
13200 Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
13199 The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
13203 The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13202 Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13205 We can only define functions if Choice tells us which items are involved [Enderton]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
10467 Individuals consist of 'compresent' tropes [Bacon,John]
10464 A trope is a bit of a property or relation (not an exemplification or a quality) [Bacon,John]
10465 Trope theory is ontologically parsimonious, with possibly only one-category [Bacon,John]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
14064 If a statue is identical with the clay of which it is made, that identity is contingent [Gibbard]
14066 A 'piece' of clay begins when its parts stick together, separately from other clay [Gibbard]
14067 Clay and statue are two objects, which can be named and reasoned about [Gibbard]
14069 We can only investigate the identity once we have designated it as 'statue' or as 'clay' [Gibbard]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
14076 Essentialism is the existence of a definite answer as to whether an entity fulfils a condition [Gibbard]
9. Objects / D. Essence of Objects / 15. Against Essentialism
14077 Essentialism for concreta is false, since they can come apart under two concepts [Gibbard]
9. Objects / E. Objects over Time / 12. Origin as Essential
14070 A particular statue has sortal persistence conditions, so its origin defines it [Gibbard]
9. Objects / F. Identity among Objects / 6. Identity between Objects
14073 Claims on contingent identity seem to violate Leibniz's Law [Gibbard]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
14065 Two identical things must share properties - including creation and destruction times [Gibbard]
14074 Leibniz's Law isn't just about substitutivity, because it must involve properties and relations [Gibbard]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
10466 Maybe possible worlds are just sets of possible tropes [Bacon,John]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
14072 Possible worlds identity needs a sortal [Gibbard]
14078 Only concepts, not individuals, can be the same across possible worlds [Gibbard]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
14079 Kripke's semantics needs lots of intuitions about which properties are essential [Gibbard]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
14071 Naming a thing in the actual world also invokes some persistence criteria [Gibbard]