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All the ideas for 'Thinking About Mathematics', 'The Idea of Justice' and 'What is Philosophy?'

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52 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Philosophy is in a perpetual state of digression [Deleuze/Guattari]
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy is a concept-creating discipline [Deleuze/Guattari]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophy aims at what is interesting, remarkable or important - not at knowledge or truth [Deleuze/Guattari]
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
The plague of philosophy is those who criticise without creating, and defend dead concepts [Deleuze/Guattari]
1. Philosophy / H. Continental Philosophy / 2. Phenomenology
Phenomenology needs art as logic needs science [Deleuze/Guattari]
2. Reason / A. Nature of Reason / 4. Aims of Reason
What justifies reliance on reason? Is it just a tool? Why is it better than blind belief? [Sen]
2. Reason / A. Nature of Reason / 5. Objectivity
In politics and ethics, scrutiny from different perspectives is essential for objectivity [Sen]
2. Reason / C. Styles of Reason / 3. Eristic
'Eris' is the divinity of conflict, the opposite of Philia, the god of friendship [Deleuze/Guattari]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic has an infantile idea of philosophy [Deleuze/Guattari]
Logic hates philosophy, and wishes to supplant it [Deleuze/Guattari]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
We cannot judge the Cogito. Must we begin? Must we start from certainty? Can 'I' relate to thought? [Deleuze/Guattari]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
14. Science / B. Scientific Theories / 4. Paradigm
Concepts are superior because they make us more aware, and change our thinking [Deleuze/Guattari]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / a. Other minds
Other people completely revise our perceptions, because they are possible worlds [Deleuze/Guattari]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Rationality is conformity to reasons that can be sustained even after scrutiny [Sen]
18. Thought / C. Content / 6. Broad Content
Phenomenology says thought is part of the world [Deleuze/Guattari]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
The logical attitude tries to turn concepts into functions, when they are really forms or forces [Deleuze/Guattari]
23. Ethics / B. Contract Ethics / 9. Contractualism
A human right is not plausible if public scrutiny might reject it [Sen]
24. Political Theory / A. Basis of a State / 4. Original Position / a. Original position
The original position insures that the agreements reached are fair [Sen]
24. Political Theory / A. Basis of a State / 4. Original Position / b. Veil of ignorance
The veil of ignorance encourages neutral interests, but not a wider view of values [Sen]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
A social contract limits the pursuit of justice to members of a single society [Sen]
24. Political Theory / B. Nature of a State / 4. Citizenship
A person's voice may count because of their interests, or because of their good sense [Sen]
24. Political Theory / C. Ruling a State / 2. Leaders / c. Despotism
Famines tend to be caused by authoritarian rule [Sen]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
Effective democracy needs tolerant values [Sen]
24. Political Theory / D. Ideologies / 5. Democracy / b. Consultation
Democracy as 'government by discussion' now has wide support [Sen]
Democracy needs more than some institutions; diverse sections of the people must be heard [Sen]
24. Political Theory / D. Ideologies / 13. Green Politics
Eradicating smallpox does not impoverish nature [Sen]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
Capabilities are part of freedom, involving real opportunities [Sen]
Freedom can involve capabilities, independence and non-interference [Sen]
25. Social Practice / B. Equalities / 1. Grounds of equality
The need for equality among people arises from impartiality and objectivity [Sen]
All modern theories of justice demand equality of something [Sen]
25. Social Practice / C. Rights / 1. Basis of Rights
Freedom from torture or terrorist attacks is independent of citizenship [Sen]
25. Social Practice / D. Justice / 1. Basis of justice
You don't need a complete theory of justice to see that slavery is wrong [Sen]
Practical justice concerns not only ideals, but ways to achieve them [Sen]
Our institutions should promote justice, rather than embodying it [Sen]
We must focus on removing manifest injustice, not just try to design a perfect society [Sen]
If justice needs public reasoning, which needs democracy, then justice and democracy are linked [Sen]
28. God / C. Attitudes to God / 5. Atheism
Atheism is the philosopher's serenity, and philosophy's achievement [Deleuze/Guattari]