Combining Texts

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

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22 ideas

1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
9766 Study vagueness first by its logic, then by its truth-conditions, and then its metaphysics [Fine,K]
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 / D. Assumptions for Logic / 2. Excluded Middle
9775 Excluded Middle, and classical logic, may fail for vague predicates [Fine,K]
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
9771 Logic holding between indefinite sentences is the core of all language [Fine,K]
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 / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
9768 Vagueness is semantic, a deficiency of meaning [Fine,K]
7. Existence / D. Theories of Reality / 10. Vagueness / e. Higher-order vagueness
9776 A thing might be vaguely vague, giving us higher-order vagueness [Fine,K]
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
9767 A vague sentence is only true for all ways of making it completely precise [Fine,K]
9770 Logical connectives cease to be truth-functional if vagueness is treated with three values [Fine,K]
9772 Meaning is both actual (determining instances) and potential (possibility of greater precision) [Fine,K]
9773 With the super-truth approach, the classical connectives continue to work [Fine,K]
9774 Borderline cases must be under our control, as capable of greater precision [Fine,K]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
9769 Vagueness can be in predicates, names or quantifiers [Fine,K]
10. Modality / A. Necessity / 8. Transcendental Necessity
490 Everything happens by reason and necessity [Leucippus]