Combining Texts

All the ideas for 'fragments/reports', 'Essays on Intellectual Powers 2: Senses' and 'Set Theory and Its Philosophy'

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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]
7. Existence / A. Nature of Existence / 1. Nature of Existence
23634 Accepting the existence of anything presupposes the notion of existence [Reid]
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]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
23635 Truths are self-evident to sensible persons who understand them clearly without prejudice [Reid]
12. Knowledge Sources / B. Perception / 1. Perception
7631 Sensation is not committed to any external object, but perception is [Reid]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / c. Primary qualities
23637 Primary qualities are the object of mathematics [Reid]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
23638 Secondary qualities conjure up, and are confused with, the sensations which produce them [Reid]
12. Knowledge Sources / B. Perception / 5. Interpretation
23639 It is unclear whether a toothache is in the mind or in the tooth, but the word has a single meaning [Reid]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
6492 Reid is seen as the main direct realist of the eighteenth century [Reid, by Robinson,H]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
23641 People dislike believing without evidence, and try to avoid it [Reid]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
23642 If non-rational evidence reaches us, it is reason which then makes use of it [Reid]
18. Thought / E. Abstraction / 2. Abstracta by Selection
23640 Only mature minds can distinguish the qualities of a body [Reid]
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]