Combining Philosophers

All the ideas for Oliver,A/Smiley,T, Micklethwait,J/Wooldridge,A and Eileen John

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19 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
The empty set is something, not nothing! [Oliver/Smiley]
We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
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
The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
Classical liberalism seeks freedom of opinion, of private life, of expression, and of property [Micklethwait/Wooldridge]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
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
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
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
Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
A work can be morally and artistically excellent, despite rejecting moral truth [John,E]
The works we value most are in sympathy with our own moral views [John,E]
We should understand what is morally important in a story, without having to endorse it [John,E]
We value morality in art because that is what we care about - but it is a contingent fact [John,E]
24. Political Theory / D. Ideologies / 8. Socialism
The welfare state aims at freedom from want, and equality of opportunity [Micklethwait/Wooldridge]
24. Political Theory / D. Ideologies / 9. Communism
For communists history is driven by the proletariat [Micklethwait/Wooldridge]
24. Political Theory / D. Ideologies / 11. Capitalism
Fans of economic freedom claim that capitalism is self-correcting [Micklethwait/Wooldridge]
25. Social Practice / C. Rights / 4. Property rights
Roman law entrenched property rights [Micklethwait/Wooldridge]