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All the ideas for 'Thinking About Mathematics', 'The Idea of Justice' and 'works'

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46 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophy attains its goal if one person feels perfect accord between their system and experience [Fichte]
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 / A. Nature of Reason / 7. Status of Reason
For Fichte there is no God outside the ego, and 'our religion is reason' [Fichte, by Feuerbach]
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 / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Fichte believed in things-in-themselves [Fichte, by Moore,AW]
We can deduce experience from self-consciousness, without the thing-in-itself [Fichte]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
The absolute I divides into consciousness, and a world which is not-I [Fichte, by Bowie]
Reason arises from freedom, so philosophy starts from the self, and not from the laws of nature [Fichte]
Abandon the thing-in-itself; things only exist in relation to our thinking [Fichte]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
16. Persons / F. Free Will / 4. For Free Will
Spinoza could not actually believe his determinism, because living requires free will [Fichte]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Rationality is conformity to reasons that can be sustained even after scrutiny [Sen]
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]