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All the ideas for 'Structures and Structuralism in Phil of Maths', 'The Principles of Science' and 'The Concept of Mind'

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30 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
18005 Philosophy aims to become more disciplined about categories [Ryle]
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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8628 I hold that algebra and number are developments of logic [Jevons]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / e. Dispositions as potential
14297 A dispositional property is not a state, but a liability to be in some state, given a condition [Ryle]
8. Modes of Existence / C. Powers and Dispositions / 7. Against Powers
14300 No physical scientist now believes in an occult force-exerting agency [Ryle]
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 / A. Nature of Mind / 3. Mental Causation
2622 Can one movement have a mental and physical cause? [Ryle]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
1353 Reporting on myself has the same problems as reporting on you [Ryle]
1354 We cannot introspect states of anger or panic [Ryle]
16. Persons / F. Free Will / 5. Against Free Will
2624 I cannot prepare myself for the next thought I am going to think [Ryle]
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
2620 Dualism is a category mistake [Ryle]
17. Mind and Body / B. Behaviourism / 2. Potential Behaviour
2388 Behaviour depends on desires as well as beliefs [Chalmers on Ryle]
3354 You can't explain mind as dispositions, if they aren't real [Benardete,JA on Ryle]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
2387 How can behaviour be the cause of behaviour? [Chalmers on Ryle]