Combining Texts

All the ideas for 'fragments/reports', 'Set Theory and Its Philosophy' and 'The Central Questions of Philosophy'

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29 ideas

2. Reason / E. Argument / 3. Analogy
5331 You can't infer that because you have a hidden birth-mark, everybody else does [Ayer]
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 / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
2611 It is currently held that quantifying over something implies belief in its existence [Ayer]
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]
9. Objects / D. Essence of Objects / 3. Individual Essences
16520 We see properties necessary for a kind (in the definition), but not for an individual [Ayer]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
2613 The theory of other minds has no rival [Ayer]
5328 Originally I combined a mentalistic view of introspection with a behaviouristic view of other minds [Ayer]
5330 Physicalism undercuts the other mind problem, by equating experience with 'public' brain events [Ayer]
16. Persons / B. Nature of the Self / 5. Self as Associations
5326 Qualia must be united by a subject, because they lead to concepts and judgements [Ayer]
5325 Is something an 'experience' because it relates to other experiences, or because it relates to a subject? [Ayer]
16. Persons / B. Nature of the Self / 7. Self and Body / a. Self needs body
5324 Bodily identity and memory work together to establish personal identity [Ayer]
16. Persons / C. Self-Awareness / 2. Knowing the Self
5322 Self-consciousness is not basic, because experiences are not instrinsically marked with ownership [Ayer]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / c. Inadequacy of mental continuity
5327 Temporal gaps in the consciousness of a spirit could not be bridged by memories [Ayer]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
5329 Why shouldn't we say brain depends on mind? Better explanation! [Ayer]
19. Language / D. Propositions / 6. Propositions Critique
2610 Talk of propositions is just shorthand for talking about equivalent sentences [Ayer]
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]