Combining Texts

All the ideas for 'Against Coherence', 'Elements of Set Theory' and 'Occasions of Identity'

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18 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]
13206 A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
13204 The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [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]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
13437 A CAR and its major PART can become identical, yet seem to have different properties [Gallois]
9. Objects / E. Objects over Time / 1. Objects over Time
16233 Gallois hoped to clarify identity through time, but seems to make talk of it impossible [Hawley on Gallois]
9. Objects / F. Identity among Objects / 3. Relative Identity
14755 Gallois is committed to identity with respect to times, and denial of simple identity [Gallois, by Sider]
9. Objects / F. Identity among Objects / 6. Identity between Objects
16231 Occasional Identity: two objects can be identical at one time, and different at others [Gallois, by Hawley]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
21515 Incoherence may be more important for enquiry than coherence [Olsson]
21514 Coherence is the capacity to answer objections [Olsson]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
21496 Mere agreement of testimonies is not enough to make truth very likely [Olsson]
21499 Coherence is only needed if the information sources are not fully reliable [Olsson]
21502 A purely coherent theory cannot be true of the world without some contact with the world [Olsson]
21512 Extending a system makes it less probable, so extending coherence can't make it more probable [Olsson]