Combining Texts

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

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21 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]
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]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / a. Sovereignty
23418 Liberal state legitimacy is based on a belief in justice, not in some conception of the good life [Kymlicka]
24. Political Theory / B. Nature of a State / 5. Culture
23414 Liberals say state intervention in culture restricts people's autonomy [Kymlicka]
24. Political Theory / D. Ideologies / 6. Liberalism / e. Liberal community
23410 Modern liberals see a community as simply a society which respects freedom and equality [Kymlicka]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
23409 Community can focus on class or citizenship or ethnicity or culture [Kymlicka]
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
23413 Feminism has shown that social roles are far from fixed (as communitarians tend to see them) [Kymlicka]
23419 Communitarianism struggles with excluded marginalised groups [Kymlicka]
23415 Participation aids the quest for the good life, but why should that be a state activity? [Kymlicka]
25. Social Practice / D. Justice / 1. Basis of justice
23411 Communitarians see justice as primarily a community matter, rather than a principle [Kymlicka]
23412 Justice resolves conflicts, but may also provoke them [Kymlicka]
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 / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]