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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Moral Realism and Moral Dilemma' and 'Substance and Individuation in Leibniz'

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31 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 / A. Relations / 1. Nature of Relations
13076 Scholastics treat relations as two separate predicates of the relata [Cover/O'Leary-Hawthorne]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
10173 A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
13102 If you individuate things by their origin, you still have to individuate the origins themselves [Cover/O'Leary-Hawthorne]
13103 Numerical difference is a symmetrical notion, unlike proper individuation [Cover/O'Leary-Hawthorne]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
13104 Haecceity as property, or as colourless thisness, or as singleton set [Cover/O'Leary-Hawthorne]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
13100 Maybe 'substance' is more of a mass-noun than a count-noun [Cover/O'Leary-Hawthorne]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
13068 We can ask for the nature of substance, about type of substance, and about individual substances [Cover/O'Leary-Hawthorne]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
13069 The general assumption is that substances cannot possibly be non-substances [Cover/O'Leary-Hawthorne]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
13072 Modern essences are sets of essential predicate-functions [Cover/O'Leary-Hawthorne]
17080 Modern essentialists express essence as functions from worlds to extensions for predicates [Cover/O'Leary-Hawthorne]
9. Objects / E. Objects over Time / 12. Origin as Essential
13101 Necessity-of-origin won't distinguish ex nihilo creations, or things sharing an origin [Cover/O'Leary-Hawthorne]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
13081 Even extreme modal realists might allow transworld identity for abstract objects [Cover/O'Leary-Hawthorne]
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
13071 We can go beyond mere causal explanations if we believe in an 'order of being' [Cover/O'Leary-Hawthorne]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
22456 Maybe virtues conflict with each other, if some virtue needs a vice for its achievement [Foot]