Combining Texts

All the ideas for 'Set Theory and Its Philosophy', 'talk' and 'Anthropological Studies of Classification'

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38 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 / E. Structures of Logic / 5. Functions in Logic
15105 F(x) walked into a bar. The barman said.. [Sommers,W]
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 / 3. Being / d. Non-being
12408 Sartre to Waitress: Coffee with no cream, please... [Sommers,W]
7. Existence / D. Theories of Reality / 4. Anti-realism
12397 Said Plato: 'The things that we feel... [Sommers,W]
7. Existence / E. Categories / 1. Categories
10496 Monothetic categories have fixed defining features, and polythetic categories do not [Ellen]
10497 In symbolic classification, the categories are linked to rules [Ellen]
7. Existence / E. Categories / 5. Category Anti-Realism
10495 Continuous experience sometimes needs imposition of boundaries to create categories [Ellen]
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]
11. Knowledge Aims / B. Certain Knowledge / 5. Cogito Critique
12407 Barman to Descartes: Would you like another drink?... [Sommers,W]
12399 There was a young student called Fred... [Sommers,W]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
20963 A philosopher and his wife are out for a drive... [Sommers,W]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / c. Empirical idealism
12404 Dear Sir, Your astonishment's odd.... [Sommers,W]
12403 There once was a man who said: 'God... [Sommers,W]
12402 ..But if he's a student of Berkeley... [Sommers,W]
12409 The philosopher Berkeley once said.. [Sommers,W]
12. Knowledge Sources / B. Perception / 1. Perception
14694 "My dog's got synaesthesia." How does he smell? ..... [Sommers,W]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
12401 A toper who spies in the distance... [Sommers,W]
13. Knowledge Criteria / E. Relativism / 4. Cultural relativism
10498 Classification is no longer held to be rooted in social institutions [Ellen]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
12410 There once was a man who said 'Damn!... [Sommers,W]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
9392 How do behaviourists greet each other? [Sommers,W]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
12405 'If you're aristocratic,' said Nietzsche... [Sommers,W]
24. Political Theory / D. Ideologies / 2. Anarchism
9391 Why do anarchists drink herbal tea? [Sommers,W]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
12400 Cries the maid: 'You must marry me Hume!'... [Sommers,W]
16527 Causation - we all thought we knew it/ Till Hume came along and saw through it/…. [Sommers,W]
27. Natural Reality / D. Time / 1. Nature of Time / c. Idealist time
17592 The barman called 'Time!', and Augustine said..... [Sommers,W]
27. Natural Reality / D. Time / 2. Passage of Time / c. Tenses and time
15208 The past, present and future walked into a bar.... [Sommers,W]