Combining Texts

All the ideas for 'Thinking About Mathematics', 'On Husserl' and 'A Short History of Ethics'

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29 ideas

1. Philosophy / B. History of Ideas / 4. Early European Thought
8013 In the Reformation, morality became unconditional but irrational, individually autonomous, and secular [MacIntyre]
1. Philosophy / B. History of Ideas / 5. Later European Thought
8021 The Levellers and the Diggers mark a turning point in the history of morality [MacIntyre]
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 / 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 / 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 / 4. Solipsism
21227 The Cogito demands a bridge to the world, and ends in isolating the ego [Velarde-Mayol]
12. Knowledge Sources / B. Perception / 3. Representation
21215 The representation may not be a likeness [Velarde-Mayol]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
8006 When Aristotle speaks of soul he means something like personality [MacIntyre]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
8002 Sophists don't distinguish a person outside one social order from someone outside all order [MacIntyre]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
8012 The value/fact logical gulf is misleading, because social facts involve values [MacIntyre]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
8005 'Happiness' is a bad translation of 'eudaimonia', which includes both behaving and faring well [MacIntyre]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
8001 'Dikaiosune' is justice, but also fairness and personal integrity [MacIntyre]
23. Ethics / D. Deontological Ethics / 2. Duty
8023 My duties depend on my identity, which depends on my social relations [MacIntyre]
24. Political Theory / A. Basis of a State / 3. Natural Values / a. Natural freedom
8022 I am naturally free if I am not tied to anyone by a contract [MacIntyre]
25. Social Practice / C. Rights / 1. Basis of Rights
8031 Fans of natural rights or laws can't agree on what the actual rights or laws are [MacIntyre]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
21219 Find the essence by varying an object, to see what remains invariable [Velarde-Mayol]
29. Religion / B. Monotheistic Religion / 5. Bible
8008 The Bible is a story about God in which humans are incidental characters [MacIntyre]