Combining Texts

All the ideas for 'fragments/reports', 'The Metaphysic of Abstract Particulars' and 'On the Question of Absolute Undecidability'

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22 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
Relations need terms, so they must be second-order entities based on first-order tropes [Campbell,K]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Arithmetical undecidability is always settled at the next stage up [Koellner]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
Events are trope-sequences, in which tropes replace one another [Campbell,K]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
Two red cloths are separate instances of redness, because you can dye one of them blue [Campbell,K]
Red could only recur in a variety of objects if it was many, which makes them particulars [Campbell,K]
Tropes solve the Companionship Difficulty, since the resemblance is only between abstract particulars [Campbell,K]
Tropes solve the Imperfect Community problem, as they can only resemble in one respect [Campbell,K]
Trope theory makes space central to reality, as tropes must have a shape and size [Campbell,K]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
Nominalism has the problem that without humans nothing would resemble anything else [Campbell,K]
9. Objects / A. Existence of Objects / 1. Physical Objects
Tropes are basic particulars, so concrete particulars are collections of co-located tropes [Campbell,K]
Bundles must be unique, so the Identity of Indiscernibles is a necessity - which it isn't! [Campbell,K]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
Two pure spheres in non-absolute space are identical but indiscernible [Campbell,K]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
Abstractions come before the mind by concentrating on a part of what is presented [Campbell,K]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Davidson can't explain causation entirely by events, because conditions are also involved [Campbell,K]
Causal conditions are particular abstract instances of properties, which makes them tropes [Campbell,K]
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]