Combining Texts

All the ideas for 'fragments/reports', 'Elements of Set Theory' and 'The Causal Theory of Names'

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18 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
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
Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
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
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
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
We can only define functions if Choice tells us which items are involved [Enderton]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
We must distinguish what the speaker denotes by a name, from what the name denotes [Evans]
How can an expression be a name, if names can change their denotation? [Evans]
A private intention won't give a name a denotation; the practice needs it to be made public [Evans]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
The Causal Theory of Names is wrong, since the name 'Madagascar' actually changed denotation [Evans]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
Speakers intend to refer to items that are the source of their information [Evans]
The intended referent of a name needs to be the cause of the speaker's information about it [Evans]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
If descriptions are sufficient for reference, then I must accept a false reference if the descriptions fit [Evans]
19. Language / F. Communication / 5. Pragmatics / b. Implicature
We use expressions 'deferentially', to conform to the use of other people [Evans]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
Charity should minimize inexplicable error, rather than maximising true beliefs [Evans]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
A virtue is a combination of intelligence, strength and luck [Ion]