Combining Texts

All the ideas for 'fragments/reports', 'Some Remarks on Essentialism' and 'What are Sets and What are they For?'

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15 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Even pointing a finger should only be done for a reason [Epictetus]
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]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
Essentialism says some of a thing's properties are necessary, and could not be absent [Cartwright,R]
9. Objects / D. Essence of Objects / 14. Knowledge of Essences
The difficulty in essentialism is deciding the grounds for rating an attribute as essential [Cartwright,R]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Essentialism is said to be unintelligible, because relative, if necessary truths are all analytic [Cartwright,R]
9. Objects / F. Identity among Objects / 3. Relative Identity
An act of ostension doesn't seem to need a 'sort' of thing, even of a very broad kind [Cartwright,R]