Combining Philosophers

All the ideas for Marcus Aurelius, Richard Dedekind and Adam Swift

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58 ideas

1. Philosophy / A. Wisdom / 2. Wise People
A philosopher should have principles ready for understanding, like a surgeon with instruments [Aurelius]
2. Reason / D. Definition / 9. Recursive Definition
Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
An infinite set maps into its own proper subset [Dedekind, by Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
Numbers are free creations of the human mind, to understand differences [Dedekind]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman]
Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck]
Order, not quantity, is central to defining numbers [Dedekind, by Monk]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
We want the essence of continuity, by showing its origin in arithmetic [Dedekind]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
A cut between rational numbers creates and defines an irrational number [Dedekind]
Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell]
Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock]
I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
In counting we see the human ability to relate, correspond and represent [Dedekind]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
A system S is said to be infinite when it is similar to a proper part of itself [Dedekind]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
If x changes by less and less, it must approach a limit [Dedekind]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K]
7. Existence / B. Change in Existence / 1. Nature of Change
Everything is changing, including yourself and the whole universe [Aurelius]
9. Objects / A. Existence of Objects / 3. Objects in Thought
A thing is completely determined by all that can be thought concerning it [Dedekind]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett]
We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind]
18. Thought / E. Abstraction / 8. Abstractionism Critique
Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
Nothing is evil which is according to nature [Aurelius]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
Justice has no virtue opposed to it, but pleasure has temperance opposed to it [Aurelius]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / b. Living naturally
The art of life is more like the wrestler's than the dancer's [Aurelius]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
We should respect the right of people to live in their own way, even if it is irrational [Swift]
24. Political Theory / A. Basis of a State / 1. A People / a. Human distinctiveness
Humans are naturally made for co-operation [Aurelius]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
Anti-colonial movements usually invoke the right of their 'people' to self-determination [Swift]
24. Political Theory / A. Basis of a State / 4. Original Position / a. Original position
Isn't it more rational to maximise the average position, but with a safety net? [Swift]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Hypothetical contracts have no binding force [Swift]
24. Political Theory / B. Nature of a State / 4. Citizenship
Cosmopolitans reject the right of different states to distribute resources in different ways [Swift]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
Democracy is bad, but the other systems are worse [Swift]
Since all opinions are treated as equal in democracy, it implies there are no right answers [Swift]
Design your democracy to treat citizens equally, or to produce better citizens? [Swift]
Design your democracy to yield political stability, or good decisions? [Swift]
24. Political Theory / D. Ideologies / 5. Democracy / c. Direct democracy
Teledemocracy omits debate and deliberation, which are important parts of good decisions [Swift]
24. Political Theory / D. Ideologies / 6. Liberalism / f. Multiculturalism
Multiculturalism is a barrier to the whole state being a community [Swift]
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
Liberals mistakenly think individuals choose their values, without reference to the community [Swift]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
The best way to build a cohesive community is to be involved in a war [Swift]
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
Membership and inclusion in a community implies non-membership and exclusion [Swift]
Liberals are concerned to protect individuals from too much community [Swift]
24. Political Theory / D. Ideologies / 8. Socialism
Redistributing wealth treats some people as means, rather than as ends [Swift]
24. Political Theory / D. Ideologies / 12. Feminism
Men have had the power to structure all of our social institutions [Swift]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
Maybe a freedom is from a restraint, and also in order to do something [Swift]
25. Social Practice / B. Equalities / 1. Grounds of equality
Opportunity should ignore extraneous factors, or foster competence, or ignore all disadvantages [Swift]
25. Social Practice / B. Equalities / 4. Economic equality
Inequalities are needed, as incentives to do the most important jobs [Swift]
A person can desire redistibution of wealth, without it being for reasons of equality [Swift]
25. Social Practice / C. Rights / 4. Property rights
You can't necessarily sell your legitimate right to something, even if you produced it [Swift]
Libertarians about property ignore the fact that private property is a denial of freedoms [Swift]
25. Social Practice / D. Justice / 1. Basis of justice
Justice can be seen as fairness or entitlement or desert [Swift]