Combining Texts

All the ideas for 'fragments/reports', 'Set Theory and Its Philosophy' and 'The Mysterious Flame'

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23 ideas

1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
2546 Philosophy is a magnificent failure in its attempt to overstep the limits of our knowledge [McGinn]
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 / E. Structures of Logic / 1. Logical Form
2544 Thoughts have a dual aspect: as they seem to introspection, and their underlying logical reality [McGinn]
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]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
2539 Mental modules for language, social, action, theory, space, emotion [McGinn]
16. Persons / F. Free Will / 1. Nature of Free Will
2545 Free will is mental causation in action [McGinn]
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
2543 Brains aren't made of anything special, suggesting panpsychism [McGinn]
17. Mind and Body / D. Property Dualism / 6. Mysterianism
2540 Examining mind sees no brain; examining brain sees no mind [McGinn]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
2547 There is information if there are symbols which refer, and which can combine into a truth or falsehood [McGinn]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
26. Natural Theory / C. Causation / 4. Naturalised causation
2542 Causation in the material world is energy-transfer, of motion, electricity or gravity [McGinn]