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All the ideas for 'Thinking About Mathematics', 'Frege on Apriority (with ps)' and 'works'

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33 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
23027 Ideals and metaphysics are practical, not imaginative or speculative [Green,TH, by Muirhead]
3. Truth / D. Coherence Truth / 1. Coherence Truth
23030 Truth is a relation to a whole of organised knowledge in the collection of rational minds [Green,TH, by Muirhead]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
8729 Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
16901 The equivalent algebra model of geometry loses some essential spatial meaning [Burge]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
8763 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
18249 Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
8764 Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
16902 Peano arithmetic requires grasping 0 as a primitive number [Burge]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
8762 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
8760 Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
8761 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
8744 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
8749 Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
8750 Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
8752 Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
8753 Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
8731 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
8730 'Impredicative' definitions refer to the thing being described [Shapiro]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
23044 All knowledge rests on a fundamental unity between the knower and what is known [Green,TH, by Muirhead]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
16892 Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
23034 The ultimate test for truth is the systematic interdependence in nature [Green,TH, by Muirhead]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
23032 What is distinctive of human life is the desire for self-improvement [Green,TH, by Muirhead]
23. Ethics / A. Egoism / 2. Hedonism
23033 Hedonism offers no satisfaction, because what we desire is self-betterment [Green,TH, by Muirhead]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
23045 Politics is compromises, which seem supported by a social contract, but express the will of no one [Green,TH]
24. Political Theory / B. Nature of a State / 4. Citizenship
23050 The ideal is a society in which all citizens are ladies and gentlemen [Green,TH]
23052 Enfranchisement is an end in itself; it makes a person moral, and gives a basis for respect [Green,TH]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
23036 The good is identified by the capacities of its participants [Green,TH, by Muirhead]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
23039 A true state is only unified and stabilised by acknowledging individuality [Green,TH, by Muirhead]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
23038 People only develop their personality through co-operation with the social whole [Green,TH, by Muirhead]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
23040 If something develops, its true nature is embodied in its end [Green,TH]
28. God / A. Divine Nature / 1. God
23031 God is the ideal end of the mature mind's final development [Green,TH]
28. God / C. Attitudes to God / 4. God Reflects Humanity
23041 God is the realisation of the possibilities of each man's self [Green,TH]