Combining Texts

All the ideas for 'fragments/reports', 'Set Theory and Its Philosophy' and 'Words without Objects'

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26 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 / E. Structures of Logic / 4. Variables in Logic
12797 If plural variables have 'some values', then non-count variables have 'some value' [Laycock]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
12794 Plurals are semantical but not ontological [Laycock]
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]
17694 Some non-count nouns can be used for counting, as in 'several wines' or 'fewer cheeses' [Laycock]
17695 Some apparent non-count words can take plural forms, such as 'snows' or 'waters' [Laycock]
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]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
12792 The category of stuff does not suit reference [Laycock]
12799 Descriptions of stuff are neither singular aggregates nor plural collections [Laycock]
7. Existence / C. Structure of Existence / 8. Stuff / b. Mixtures
12818 We shouldn't think some water retains its identity when it is mixed with air [Laycock]
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 / 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 / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
12795 Parts must be of the same very general type as the wholes [Laycock]
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]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
17696 'Humility is a virtue' has an abstract noun, but 'water is a liquid' has a generic concrete noun [Laycock]
19. Language / B. Reference / 1. Reference theories
12791 It is said that proper reference is our intellectual link with the world [Laycock]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]