Combining Texts

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

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27 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 / 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]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
The goal is rationality in the selection of things according to nature [Diogenes of Babylon, by Blank]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
Freedom to live according to our own conception of the good is the ultimate value [Nozick, by Kymlicka]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
The good is what is perfect by nature [Diogenes of Babylon, by Blank]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
Justice is a disposition to distribute according to desert [Diogenes of Babylon, by Blank]
23. Ethics / E. Utilitarianism / 2. Ideal of Pleasure
If an experience machine gives you any experience you want, should you hook up for life? [Nozick]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
A minimal state should protect, but a state forcing us to do more is unjustified [Nozick]
24. Political Theory / D. Ideologies / 2. Anarchism
Individual rights are so strong that the state and its officials must be very limited in power [Nozick]
24. Political Theory / D. Ideologies / 6. Liberalism / c. Liberal equality
States can't enforce mutual aid on citizens, or interfere for their own good [Nozick]
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
My Anarchy, State and Utopia neglected our formal social ties and concerns [Nozick on Nozick]
25. Social Practice / A. Freedoms / 4. Free market
If people hold things legitimately, just distribution is simply the result of free exchanges [Nozick, by Kymlicka]
25. Social Practice / C. Rights / 4. Property rights
Property is legitimate by initial acquisition, voluntary transfer, or rectification of injustice [Nozick, by Swift]
Nozick assumes initial holdings include property rights, but we can challenge that [Kymlicka on Nozick]
Can I come to own the sea, by mixing my private tomato juice with it? [Nozick]
How did the private property get started? If violence was involved, we can redistribute it [Kymlicka on Nozick]
If property is only initially acquired by denying the rights of others, Nozick can't get started [Kymlicka on Nozick]
Unowned things may be permanently acquired, if it doesn't worsen the position of other people [Nozick]
Maybe land was originally collectively owned, rather than unowned? [Cohen,GA on Nozick]