Combining Texts

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

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29 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 / a. Individuation
12132 Indiscernibility is a necessary and sufficient condition for identity [Brody]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
15834 Brody bases sortal essentialism on properties required throughout something's existence [Brody, by Mackie,P]
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 / 2. Hylomorphism / a. Hylomorphism
12140 Modern emphasis is on properties had essentially; traditional emphasis is on sort-defining properties [Brody]
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 / 5. Essence as Kind
11895 A sortal essence is a property which once possessed always possessed [Brody, by Mackie,P]
12141 Maybe essential properties are those which determine a natural kind? [Brody]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
12137 De re essentialism standardly says all possible objects identical with a have a's essential properties [Brody]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
12142 Essentially, a has P, always had P, must have had P, and has never had a future without P [Brody]
12143 An object having a property essentially is equivalent to its having it necessarily [Brody]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
12144 Essentialism is justified if the essential properties of things explain their other properties [Brody]
9. Objects / D. Essence of Objects / 12. Essential Parts
12139 Mereological essentialism says that every part that ensures the existence is essential [Brody]
9. Objects / E. Objects over Time / 12. Origin as Essential
12135 Interrupted objects have two first moments of existence, which could be two beginnings [Brody]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
12130 a and b share all properties; so they share being-identical-with-a; so a = b [Brody]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
12138 Identity across possible worlds is prior to rigid designation [Brody]
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]