### All the ideas for Michael Burke, Alan McMichael and Michael Potter

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27 ideas

###### 4. Formal Logic / F. Set Theory ST / 1. Set Theory
 10702 Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
###### 4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
 10713 Usually the only reason given for accepting the empty set is convenience [Potter]
###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
 13044 Infinity: There is at least one limit level [Potter]
###### 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
 10708 Nowadays we derive our conception of collections from the dependence between them [Potter]
###### 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
 13546 The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
###### 4. Formal Logic / G. Formal Mereology / 1. Mereology
 10707 Mereology elides the distinction between the cards in a pack and the suits [Potter]
###### 5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
 10704 We can formalize second-order formation rules, but not inference rules [Potter]
###### 5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
 10703 Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
###### 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
 10712 If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
###### 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
 17882 It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
###### 8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
 13043 A relation is a set consisting entirely of ordered pairs [Potter]
###### 9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
 16235 Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley]
 14753 The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider]
###### 9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
 16072 'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman]
###### 9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
 13042 If dependence is well-founded, with no infinite backward chains, this implies substances [Potter]
###### 9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
 14751 Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider]
###### 9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
 16071 Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman]
 16234 Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley]
 13278 Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki]
###### 9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
 14750 Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider]
###### 9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
 13041 Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
###### 9. Objects / D. Essence of Objects / 3. Individual Essences
 14637 Only individuals have essences, so numbers (as a higher type based on classes) lack them [McMichael]
###### 9. Objects / D. Essence of Objects / 9. Essence and Properties
 14636 Essences are the interesting necessary properties resulting from a thing's own peculiar nature [McMichael]
 14640 Maybe essential properties have to be intrinsic, as well as necessary? [McMichael]
###### 9. Objects / D. Essence of Objects / 15. Against Essentialism
 14638 Essentialism is false, because it implies the existence of necessary singular propositions [McMichael]
###### 10. Modality / A. Necessity / 1. Types of Modality
 10709 Priority is a modality, arising from collections and members [Potter]
###### 26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
 14639 Individuals enter into laws only through their general qualities and relations [McMichael]