Combining Texts

All the ideas for 'Set Theory and Its Philosophy', 'Human Nature' and 'Justified Belief as Responsible Belief'

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24 ideas

1. Philosophy / D. Nature of Philosophy / 8. Humour
6211 Laughter is a sudden glory in realising the infirmity of others, or our own formerly [Hobbes]
2. Reason / A. Nature of Reason / 6. Coherence
12801 Coherentists seek relations among beliefs that are simple, conservative and explanatory [Foley]
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 / A. Justification Problems / 3. Internal or External / c. Disjunctivism
12800 Externalists want to understand knowledge, Internalists want to understand justification [Foley]
13. Knowledge Criteria / B. Internal Justification / 2. Pragmatic justification
12802 We aren't directly pragmatic about belief, but pragmatic about the deliberation which precedes it [Foley]
12803 Justification comes from acceptable procedures, given practical constraints [Foley]
16. Persons / F. Free Will / 5. Against Free Will
6213 A man cannot will to will, or will to will to will, so the idea of a voluntary will is absurd [Hobbes]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
6208 Conceptions and apparitions are just motion in some internal substance of the head [Hobbes]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
6209 There is no absolute good, for even the goodness of God is goodness to us [Hobbes]
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
6210 Life has no end (not even happiness), because we have desires, which presuppose a further end [Hobbes]
25. Social Practice / F. Life Issues / 5. Sexual Morality
6212 Lust involves pleasure, and also the sense of power in pleasing others [Hobbes]