Combining Texts

All the ideas for 'works', 'Killing and Letting Die' and 'Elements of Set Theory'

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12 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]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / a. Physicalism critique
Do new ideas increase the weight of the brain? [Dance]
20. Action / C. Motives for Action / 5. Action Dilemmas / c. Omissions
It is not true that killing and allowing to die (or acts and omissions) are morally indistinguishable [Foot]
Making a runaway tram kill one person instead of five is diverting a fatal sequence, not initiating one [Foot]
25. Social Practice / C. Rights / 1. Basis of Rights
The right of non-interference (with a 'negative duty'), and the right to goods/services ('positive') [Foot]