Combining Texts

Ideas for 'Metaphysics', 'What are Sets and What are they For?' and '24: Book of Jeremiah'

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7 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL

562	Axioms are the underlying principles of everything, and who but the philosopher can assess their truth? [Aristotle]

573	The axioms of mathematics are part of philosophy [Aristotle]

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]