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All the ideas for 'fragments/reports', 'Grundgesetze der Arithmetik 1 (Basic Laws)' and 'Against Structural Universals'

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28 ideas

5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers are ratios of quantities, such as lengths or masses [Frege]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
My Basic Law V is a law of pure logic [Frege]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
If you think universals are immanent, you must believe them to be sparse, and not every related predicate [Lewis]
8. Modes of Existence / B. Properties / 5. Natural Properties
I assume there could be natural properties that are not instantiated in our world [Lewis]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
Tropes are particular properties, which cannot recur, but can be exact duplicates [Lewis]
8. Modes of Existence / D. Universals / 2. Need for Universals
Universals are meant to give an account of resemblance [Lewis]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
We can add a primitive natural/unnatural distinction to class nominalism [Lewis]
9. Objects / C. Structure of Objects / 1. Structure of an Object
The 'magical' view of structural universals says they are atoms, even though they have parts [Lewis]
If 'methane' is an atomic structural universal, it has nothing to connect it to its carbon universals [Lewis]
The 'pictorial' view of structural universals says they are wholes made of universals as parts [Lewis]
The structural universal 'methane' needs the universal 'hydrogen' four times over [Lewis]
Butane and Isobutane have the same atoms, but different structures [Lewis]
Structural universals have a necessary connection to the universals forming its parts [Lewis]
We can't get rid of structural universals if there are no simple universals [Lewis]
9. Objects / C. Structure of Objects / 5. Composition of an Object
Composition is not just making new things from old; there are too many counterexamples [Lewis]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
A whole is distinct from its parts, but is not a further addition in ontology [Lewis]
Different things (a toy house and toy car) can be made of the same parts at different times [Lewis]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Maybe abstraction is just mereological subtraction [Lewis]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett]
Frege took the study of concepts to be part of logic [Frege, by Shapiro]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Mathematicians abstract by equivalence classes, but that doesn't turn a many into one [Lewis]
25. Social Practice / E. Policies / 5. Education / b. Education principles
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
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]