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All the ideas for 'works', 'Quine on Quantifying In' and 'Structures and Structuralism in Phil of Maths'

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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 / E. Structures of Logic / 1. Logical Form
12220 Is it the sentence-token or the sentence-type that has a logical form? [Fine,K]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
12222 Substitutional quantification is referential quantification over expressions [Fine,K]
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]
12. Knowledge Sources / B. Perception / 1. Perception
22167 Our images of bodies are not produced by the bodies, but by our own minds [Augustine, by Aquinas]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
22117 Our minds grasp reality by direct illumination (rather than abstraction from experience) [Augustine, by Matthews]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
22118 Augustine created the modern concept of the will [Augustine, by Matthews]
22. Metaethics / B. Value / 2. Values / g. Love
4348 Love, and do what you will [Augustine]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
7821 Pagans produced three hundred definitions of the highest good [Augustine, by Grayling]
23. Ethics / D. Deontological Ethics / 2. Duty
22119 Augustine said (unusually) that 'ought' does not imply 'can' [Augustine, by Matthews]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
22116 Augustine identified Donatism, Pelagianism and Manicheism as the main heresies [Augustine, by Matthews]
29. Religion / D. Religious Issues / 3. Problem of Evil / b. Human Evil
19338 Augustine said evil does not really exist, and evil is a limitation in goodness [Augustine, by Perkins]