Combining Texts

All the ideas for 'fragments/reports', 'Set Theory and Its Philosophy' and 'Essence, Necessity and Explanation'

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25 ideas

2. Reason / D. Definition / 4. Real Definition
15118 A successful Aristotelian 'definition' is what sciences produces after an investigation [Koslicki]
2. Reason / D. Definition / 6. Definition by Essence
15116 Essences cause necessary features, and definitions describe those necessary features [Koslicki]
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 / 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]
9. Objects / D. Essence of Objects / 1. Essences of Objects
15110 An essence and what merely follow from it are distinct [Koslicki]
9. Objects / D. Essence of Objects / 3. Individual Essences
15113 Individuals are perceived, but demonstration and definition require universals [Koslicki]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / c. Essentials are necessary
15112 If an object exists, then its essential properties are necessary [Koslicki]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
14. Science / A. Basis of Science / 2. Demonstration
15111 In demonstration, the explanatory order must mirror the causal order of the phenomena [Koslicki]
15115 In a demonstration the middle term explains, by being part of the definition [Koslicki]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
15117 Greek uses the same word for 'cause' and 'explanation' [Koslicki]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
15114 Discovering the Aristotelian essence of thunder will tell us why thunder occurs [Koslicki]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 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
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]