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All the ideas for 'fragments/reports', 'Set Theory and Its Philosophy' and 'Metaphysical Dependence'

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25 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
14092 Philosophers are often too fussy about words, dismissing perfectly useful ordinary terms [Rosen]
2. Reason / D. Definition / 1. Definitions
14100 Figuring in the definition of a thing doesn't make it a part of that thing [Rosen]
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]
5. Theory of Logic / K. Features of Logics / 10. Monotonicity
14096 Explanations fail to be monotonic [Rosen]
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]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
14097 Things could be true 'in virtue of' others as relations between truths, or between truths and items [Rosen]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
14095 Facts are structures of worldly items, rather like sentences, individuated by their ingredients [Rosen]
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]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
14093 An 'intrinsic' property is one that depends on a thing and its parts, and not on its relations [Rosen]
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 / 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]
10. Modality / A. Necessity / 5. Metaphysical Necessity
14094 The excellent notion of metaphysical 'necessity' cannot be defined [Rosen]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
14101 Are necessary truths rooted in essences, or also in basic grounding laws? [Rosen]
19. Language / E. Analyticity / 1. Analytic Propositions
14099 'Bachelor' consists in or reduces to 'unmarried' male, but not the other way around [Rosen]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
27. Natural Reality / F. Chemistry / 1. Chemistry
14098 An acid is just a proton donor [Rosen]