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All the ideas for 'fragments/reports', 'Structures and Structuralism in Phil of Maths' and 'De Re and De Dicto'

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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 / F. Referring in Logic / 1. Naming / a. Names
14650 Maybe proper names involve essentialism [Plantinga]
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
14648 Could I name all of the real numbers in one fell swoop? Call them all 'Charley'? [Plantinga]
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]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
14647 Surely self-identity is essential to Socrates? [Plantinga]
9. Objects / D. Essence of Objects / 9. Essence and Properties
14646 An object has a property essentially if it couldn't conceivably have lacked it [Plantinga]
10. Modality / A. Necessity / 4. De re / De dicto modality
14649 Can we find an appropriate 'de dicto' paraphrase for any 'de re' proposition? [Plantinga]
14642 Expressing modality about a statement is 'de dicto'; expressing it of property-possession is 'de re' [Plantinga]
14643 'De dicto' true and 'de re' false is possible, and so is 'de dicto' false and 'de re' true [Plantinga]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
14651 What Socrates could have been, and could have become, are different? [Plantinga]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]