Combining Texts

All the ideas for 'fragments/reports', 'What are Sets and What are they For?' and 'The Problem of Knowledge'

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17 ideas

2. Reason / F. Fallacies / 1. Fallacy
19463 Induction assumes some uniformity in nature, or that in some respects the future is like the past [Ayer]
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]
11. Knowledge Aims / B. Certain Knowledge / 5. Cogito Critique
19461 Knowing I exist reveals nothing at all about my nature [Ayer]
19459 To say 'I am not thinking' must be false, but it might have been true, so it isn't self-contradictory [Ayer]
19460 'I know I exist' has no counterevidence, so it may be meaningless [Ayer]
14. Science / A. Basis of Science / 6. Falsification
19464 We only discard a hypothesis after one failure if it appears likely to keep on failing [Ayer]
14. Science / C. Induction / 2. Aims of Induction
19462 Induction passes from particular facts to other particulars, or to general laws, non-deductively [Ayer]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]