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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Conversations, with Glyn Daly' and 'On the Happy Life'

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32 ideas

1. Philosophy / A. Wisdom / 2. Wise People
13560 A wise man is not subservient to anything [Seneca]
1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / c. Eighteenth century philosophy
9777 Kant was the first philosopher [Zizek]
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
9778 There is no dialogue in philosophy [Zizek]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
9779 Philosophy is transcendental questioning (not supporting science or constructing ontology) [Zizek]
3. Truth / F. Semantic Truth / 2. Semantic Truth
10170 While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10166 ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10175 Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10165 'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
10174 Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10164 Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10172 Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10167 Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
10169 Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
10179 There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
10181 Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
10182 There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
10168 Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
10178 Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
10176 Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
10177 Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10171 The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
10173 A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / d. Purpose of consciousness
9780 Consciousness is a malfunction of evolution [Zizek]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
13558 The supreme good is harmony of spirit [Seneca]
22. Metaethics / B. Value / 2. Values / f. Altruism
9781 Tolerance and love are strategies to avoid encountering our neighbours [Zizek]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
13559 I seek virtue, because it is its own reward [Seneca]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
13561 Virtue is always moderate, so excess need not be feared [Seneca]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
13562 It is shameful to not even recognise your own slaves [Seneca]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
13564 There is far more scope for virtue if you are wealthy; poverty only allows endurance [Seneca]
13565 If wealth was a good, it would make men good [Seneca]
13563 Why does your wife wear in her ears the income of a wealthy house? [Seneca]
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
13557 Unfortunately the majority do not tend to favour what is best [Seneca]