Combining Texts

All the ideas for 'fragments/reports', 'What are Sets and What are they For?' and 'Beyond internal Foundations to external Virtues'

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21 ideas

2. Reason / A. Nature of Reason / 6. Coherence
8877 We can't attain a coherent system by lopping off any beliefs that won't fit [Sosa]
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]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
8884 The phenomenal concept of an eleven-dot pattern does not include the concept of eleven [Sosa]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
8878 It is acceptable to say a supermarket door 'knows' someone is approaching [Sosa]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8880 In reducing arithmetic to self-evident logic, logicism is in sympathy with rationalism [Sosa]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
8881 Most of our knowledge has insufficient sensory support [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
8882 Perception may involve thin indexical concepts, or thicker perceptual concepts [Sosa]
8883 Do beliefs only become foundationally justified if we fully attend to features of our experience? [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / d. Rational foundations
8885 Some features of a thought are known directly, but others must be inferred [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / e. Pro-foundations
8876 Much propositional knowledge cannot be formulated, as in recognising a face [Sosa]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
8879 Fully comprehensive beliefs may not be knowledge [Sosa]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
1556 By nature people are close to one another, but culture drives them apart [Hippias]