Combining Texts

All the ideas for 'Realism in Mathematics', 'An Introduction to Political Philosophy (Rev)' and 'Ontology and Mathematical Truth'

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44 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A model is 'fundamental' if it contains only concrete entities [Jubien]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
There couldn't just be one number, such as 17 [Jubien]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
A natural number is a property of sets [Maddy, by Oliver]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
The subject-matter of (pure) mathematics is abstract structure [Jubien]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
If we all intuited mathematical objects, platonism would be agreed [Jubien]
How can pure abstract entities give models to serve as interpretations? [Jubien]
Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
The empty set is the purest abstract object [Jubien]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
Human beings can never really flourish in a long-term state of nature [Wolff,J]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
Collective rationality is individuals doing their best, assuming others all do the same [Wolff,J]
Should love be the first virtue of a society, as it is of the family? [Wolff,J]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
For utilitarians, consent to the state is irrelevant, if it produces more happiness [Wolff,J]
Social contract theory has the attracton of including everyone, and being voluntary [Wolff,J]
Maybe voting in elections is a grant of legitimacy to the winners [Wolff,J]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
We can see the 'general will' as what is in the general interest [Wolff,J]
24. Political Theory / C. Ruling a State / 2. Leaders / c. Despotism
How can dictators advance the interests of the people, if they don't consult them about interests? [Wolff,J]
24. Political Theory / C. Ruling a State / 3. Government / a. Government
'Separation of powers' allows legislative, executive and judicial functions to monitor one another [Wolff,J]
24. Political Theory / D. Ideologies / 1. Ideology
Political choice can be by utility, or maximin, or maximax [Wolff,J]
24. Political Theory / D. Ideologies / 2. Anarchism
A realistic and less utopian anarchism looks increasingly like liberal democracy [Wolff,J]
It is hard for anarchists to deny that we need experts [Wolff,J]
24. Political Theory / D. Ideologies / 4. Social Utilitarianism
Utilitarianism probably implies a free market plus welfare [Wolff,J]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
A system of democracy which includes both freedom and equality is almost impossible [Wolff,J]
Democracy expresses equal respect (which explains why criminals forfeit the vote) [Wolff,J]
Democracy has been seen as consistent with many types of inequality [Wolff,J]
A true democracy could not tolerate slavery, exploitation or colonialism [Wolff,J]
24. Political Theory / D. Ideologies / 5. Democracy / b. Consultation
We should decide whether voting is for self-interests, or for the common good [Wolff,J]
Condorcet proved that sensible voting leads to an emphatically right answer [Wolff,J]
24. Political Theory / D. Ideologies / 5. Democracy / e. Democratic minorities
Occasional defeat is acceptable, but a minority that is continually defeated is a problem [Wolff,J]
25. Social Practice / A. Freedoms / 4. Free market
Market prices indicate shortages and gluts, and where the profits are to be made [Wolff,J]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
Liberty principles can't justify laws against duelling, incest between siblings and euthanasia [Wolff,J]
Either Difference allows unequal liberty, or Liberty makes implementing Difference impossible [Wolff,J]
25. Social Practice / B. Equalities / 1. Grounds of equality
Utilitarians argue for equal distribution because of diminishing utility of repetition [Wolff,J]
Difference Principle: all inequalities should be in favour of the disadvantaged [Wolff,J]
25. Social Practice / B. Equalities / 2. Political equality
Political equality is not much use without social equality [Wolff,J]
25. Social Practice / C. Rights / 1. Basis of Rights
Standard rights: life, free speech, assembly, movement, vote, stand (plus shelter, food, health?) [Wolff,J]
If natural rights are axiomatic, there is then no way we can defend them [Wolff,J]
If rights are natural, rather than inferred, how do we know which rights we have? [Wolff,J]
25. Social Practice / C. Rights / 4. Property rights
Utilitarians might say property ownership encourages the best use of the land [Wolff,J]
25. Social Practice / D. Justice / 1. Basis of justice
Rights and justice are only the last resorts of a society, something to fall back on [Wolff,J]
25. Social Practice / D. Justice / 2. The Law / d. Legal positivism
Following some laws is not a moral matter; trivial traffic rules, for example [Wolff,J]