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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Precepts for Advancing Science and Arts' and 'An Outline of Philosophy'

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28 ideas

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]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
19392 I don't recommend universal doubt; we constantly seek reasons for things which are indubitable [Leibniz]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
21740 I doubt whether ethics is part of philosophy [Russell]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
21741 'You ought to do p' primarily has emotional content, expressing approval [Russell]
22. Metaethics / B. Value / 2. Values / g. Love
21746 Unlike hate, all desires can be satisfied by love [Russell]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
21747 Goodness is a combination of love and knowledge [Russell]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
21743 In wartime, happiness is hating the enemy, because it gives the war a purpose [Russell]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
21742 Originally virtue was obedience, to gods, government, or custom [Russell]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
21745 Act so as to produce harmonious rather than discordant desires [Russell]
25. Social Practice / D. Justice / 3. Punishment / d. Reform of offenders
21744 Legally curbing people's desires is inferior to improving their desires [Russell]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
22891 We could be aware of time if senses briefly vibrated, extending their experience of movement [Russell, by Bardon]