Combining Texts

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

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31 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14240 The empty set is something, not nothing! [Oliver/Smiley]
14239 The empty set is usually derived from Separation, but it also seems to need Infinity [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]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10405 In the iterative conception of sets, they form a natural hierarchy [Swoyer]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
10407 Logical Form explains differing logical behaviour of similar sentences [Swoyer]
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]
7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
10421 Supervenience is nowadays seen as between properties, rather than linguistic [Swoyer]
7. Existence / D. Theories of Reality / 4. Anti-realism
10410 Anti-realists can't explain different methods to measure distance [Swoyer]
8. Modes of Existence / B. Properties / 1. Nature of Properties
10416 Can properties have parts? [Swoyer]
10399 If a property such as self-identity can only be in one thing, it can't be a universal [Swoyer]
8. Modes of Existence / B. Properties / 5. Natural Properties
10417 There are only first-order properties ('red'), and none of higher-order ('coloured') [Swoyer]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10413 The best-known candidate for an identity condition for properties is necessary coextensiveness [Swoyer]
8. Modes of Existence / D. Universals / 1. Universals
10402 Various attempts are made to evade universals being wholly present in different places [Swoyer]
8. Modes of Existence / E. Nominalism / 4. Concept Nominalism
10400 Conceptualism says words like 'honesty' refer to concepts, not to properties [Swoyer]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
10403 If properties are abstract objects, then their being abstract exemplifies being abstract [Swoyer]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
10406 One might hope to reduce possible worlds to properties [Swoyer]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
10404 Extreme empiricists can hardly explain anything [Swoyer]
18. Thought / C. Content / 8. Intension
10408 Intensions are functions which map possible worlds to sets of things denoted by an expression [Swoyer]
18. Thought / D. Concepts / 4. Structure of Concepts / e. Concepts from exemplars
10409 Research suggests that concepts rely on typical examples [Swoyer]
19. Language / C. Assigning Meanings / 3. Predicates
10401 The F and G of logic cover a huge range of natural language combinations [Swoyer]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
10420 Maybe a proposition is just a property with all its places filled [Swoyer]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
10412 If laws are mere regularities, they give no grounds for future prediction [Swoyer]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
10411 Two properties can have one power, and one property can have two powers [Swoyer]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]