### Ideas of Oliver,A/Smiley,T, by Theme

#### [British, fl. 2006, Both at the University of Cambridge.]

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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