Combining Texts

All the ideas for 'fragments/reports', 'Universals' and 'What are Sets and What are they For?'

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25 ideas

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 [Oliver/Smiley]
14240 The empty set is something, not nothing! [Oliver/Smiley]
14241 We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
14242 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
14243 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
14234 If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
14237 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
14245 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
14246 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
14247 Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
4444 One moderate nominalist view says that properties and relations exist, but they are particulars [Armstrong]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
4445 If properties and relations are particulars, there is still the problem of how to classify and group them [Armstrong]
8. Modes of Existence / D. Universals / 1. Universals
4448 Should we decide which universals exist a priori (through words), or a posteriori (through science)? [Armstrong]
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
4446 It is claimed that some universals are not exemplified by any particular, so must exist separately [Armstrong]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
4440 'Resemblance Nominalism' finds that in practice the construction of resemblance classes is hard [Armstrong]
4439 'Resemblance Nominalism' says properties are resemblances between classes of particulars [Armstrong]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
4431 'Predicate Nominalism' says that a 'universal' property is just a predicate applied to lots of things [Armstrong]
8. Modes of Existence / E. Nominalism / 4. Concept Nominalism
4433 Concept and predicate nominalism miss out some predicates, and may be viciously regressive [Armstrong]
4432 'Concept Nominalism' says a 'universal' property is just a mental concept applied to lots of things [Armstrong]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
4436 'Class Nominalism' may explain properties if we stick to 'natural' sets, and ignore random ones [Armstrong]
4434 'Class Nominalism' says that properties or kinds are merely membership of a set (e.g. of white things) [Armstrong]
4435 'Class Nominalism' cannot explain co-extensive properties, or sets with random members [Armstrong]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
4437 'Mereological Nominalism' sees whiteness as a huge white object consisting of all the white things [Armstrong]
4438 'Mereological Nominalism' may work for whiteness, but it doesn't seem to work for squareness [Armstrong]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]