Combining Texts

All the ideas for 'Personal Identity', 'Set Theory and Its Philosophy' and 'The Structure of Empirical Knowledge'

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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 / 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]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
21506 A coherence theory of justification can combine with a correspondence theory of truth [Bonjour]
21509 There will always be a vast number of equally coherent but rival systems [Bonjour]
21503 Empirical coherence must attribute reliability to spontaneous experience [Bonjour]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
21511 A well written novel cannot possibly match a real belief system for coherence [Bonjour]
21510 The objection that a negated system is equally coherent assume that coherence is consistency [Bonjour]
21505 A coherent system can be justified with initial beliefs lacking all credibility [Bonjour]
21504 The best explanation of coherent observations is they are caused by and correspond to reality [Bonjour]
14. Science / A. Basis of Science / 5. Anomalies
21508 Anomalies challenge the claim that the basic explanations are actually basic [Bonjour]
16. Persons / B. Nature of the Self / 5. Self as Associations
3539 Personal identity is just causally related mental states [Parfit, by Maslin]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
1393 One of my future selves will not necessarily be me [Parfit]
16. Persons / D. Continuity of the Self / 4. Split Consciousness
1392 If we split like amoeba, we would be two people, neither of them being us [Parfit]
16. Persons / D. Continuity of the Self / 5. Concerns of the Self
1391 Concern for our own lives isn't the source of belief in identity, it is the result of it [Parfit]