Combining Texts

All the ideas for 'Defeasibility Theory', 'Why there isn't a ready-made world' and 'Elements of Set Theory'

expand these ideas     |    start again     |     specify just one area for these texts

20 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
13204 The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
13206 A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
13200 Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
13199 The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
13203 The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13202 Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13205 We can only define functions if Choice tells us which items are involved [Enderton]
7. Existence / D. Theories of Reality / 2. Realism
17644 Metaphysical realism is committed to there being one ultimate true theory [Putnam]
7. Existence / D. Theories of Reality / 4. Anti-realism
17648 It is an illusion to think there could be one good scientific theory of reality [Putnam]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
17643 Shape is essential relative to 'statue', but not essential relative to 'clay' [Putnam]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
19718 Indefeasibility does not imply infallibility [Grundmann]
12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data
17642 The old view that sense data are independent of mind is quite dotty [Putnam]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
19717 Can a defeater itself be defeated? [Grundmann]
19716 Simple reliabilism can't cope with defeaters of reliably produced beliefs [Grundmann]
19715 You can 'rebut' previous beliefs, 'undercut' the power of evidence, or 'reason-defeat' the truth [Grundmann]
19713 Defeasibility theory needs to exclude defeaters which are true but misleading [Grundmann]
19714 Knowledge requires that there are no facts which would defeat its justification [Grundmann]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
19719 'Moderate' foundationalism has basic justification which is defeasible [Grundmann]
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
17645 An alien might think oxygen was the main cause of a forest fire [Putnam]