Combining Texts

All the ideas for 'What are Sets and What are they For?', 'Philosophy of Mind (Encylopedia III)' and 'The General Theory of Employment'

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13 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
The empty set is something, not nothing! [Oliver/Smiley]
We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
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
The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
16. Persons / F. Free Will / 2. Sources of Free Will
Freedom is produced by the activity of the mind, and is not intrinsically given [Hegel]
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
Geist is distinct from nature, not as a substance, but because of its normativity [Hegel, by Pinkard]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
Laissez-faire individualism doesn't work, especially in troublesome times [Keynes]