Ideas from 'What are Sets and What are they For?' by Oliver,A/Smiley,T [2006], by Theme Structure

[found in 'Metaphysics (Philosophical Perspectives 20)' (ed/tr Hawthorne,John) [Blackwell 2006,978-1-4051-6792-5]].

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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

14240

The empty set is something, not nothing!

14241

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

14242

Maybe we can treat the empty set symbol as just meaning an empty term

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

5. Theory of Logic / G. Quantification / 6. Plural Quantification

14234

If you only refer to objects one at a time, you need sets in order to refer to a plurality

14237

We can use plural language to refer to the set theory domain, to avoid calling it a 'set'

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth

14245

Logical truths are true no matter what exists - but predicate calculus insists that something exists

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics

14246

If mathematics purely concerned mathematical objects, there would be no applied mathematics

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

14247

Sets might either represent the numbers, or be the numbers, or replace the numbers