Combining Texts

All the ideas for 'fragments/reports', 'An Outline of Philosophy' and 'What are Sets and What are they For?'

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21 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]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
21740 I doubt whether ethics is part of philosophy [Russell]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
21741 'You ought to do p' primarily has emotional content, expressing approval [Russell]
22. Metaethics / B. Value / 2. Values / g. Love
21746 Unlike hate, all desires can be satisfied by love [Russell]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
21747 Goodness is a combination of love and knowledge [Russell]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
21743 In wartime, happiness is hating the enemy, because it gives the war a purpose [Russell]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
21742 Originally virtue was obedience, to gods, government, or custom [Russell]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
21745 Act so as to produce harmonious rather than discordant desires [Russell]
25. Social Practice / D. Justice / 3. Punishment / d. Reform of offenders
21744 Legally curbing people's desires is inferior to improving their desires [Russell]
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]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
22891 We could be aware of time if senses briefly vibrated, extending their experience of movement [Russell, by Bardon]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]