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
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14242
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Maybe we can treat the empty set symbol as just meaning an empty term
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14239
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The empty set is usually derived from Separation, but it also seems to need Infinity
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14240
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The empty set is something, not nothing!
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14241
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We don't need the empty set to express non-existence, as there are other ways to do that
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
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14243
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The unit set may be needed to express intersections that leave a single member
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5. Theory of Logic / G. Quantification / 6. Plural Quantification
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14234
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If you only refer to objects one at a time, you need sets in order to refer to a plurality
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14237
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We can use plural language to refer to the set theory domain, to avoid calling it a 'set'
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
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14245
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Logical truths are true no matter what exists - but predicate calculus insists that something exists
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
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14246
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If mathematics purely concerned mathematical objects, there would be no applied mathematics
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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14247
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Sets might either represent the numbers, or be the numbers, or replace the numbers
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