Combining Philosophers

Ideas for Hippocrates, Oliver,A/Smiley,T and Alain Badiou

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7 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST

12337

There is 'transivity' iff membership ∈ also means inclusion ⊆ [Badiou]

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set

14239

The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]

14240

The empty set is something, not nothing! [Oliver/Smiley]

14241

We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]

14242

Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]

4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets

14243

The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

12321

The axiom of choice must accept an indeterminate, indefinable, unconstructible set [Badiou]