Combining Texts

All the ideas for 'The Case for Closure', 'Knowledge and the Philosophy of Number' and 'The Rise of Analytic Philosophy 1879-1930'

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29 ideas

2. Reason / D. Definition / 8. Impredicative Definition
22285 Impredicative definitions are circular, but fine for picking out, rather than creating something [Potter]
3. Truth / A. Truth Problems / 2. Defining Truth
22301 The Identity Theory says a proposition is true if it coincides with what makes it true [Potter]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
22324 It has been unfortunate that externalism about truth is equated with correspondence [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naďve logical sets
23623 Predicativism says only predicated sets exist [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
23624 The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
23625 Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
22279 Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
22291 Deductivism can't explain how the world supports unconditional conclusions [Potter]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
23628 The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
23627 'Before' and 'after' are not two relations, but one relation with two orders [Hossack]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
22295 Modern logical truths are true under all interpretations of the non-logical words [Potter]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
23626 Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
23621 Numbers are properties, not sets (because numbers are magnitudes) [Hossack]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
23622 We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
22310 The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
22298 Why is fictional arithmetic applicable to the real world? [Potter]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
22287 If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete [Potter]
8. Modes of Existence / A. Relations / 4. Formal Relations / c. Ancestral relation
22284 'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers [Potter]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
22281 A material conditional cannot capture counterfactual reasoning [Potter]
11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty
19553 Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
19551 How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne]
19552 We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne]
19554 Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
22327 Knowledge from a drunken schoolteacher is from a reliable and unreliable process [Potter]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
22273 Traditionally there are twelve categories of judgement, in groups of three [Potter]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
22290 The phrase 'the concept "horse"' can't refer to a concept, because it is saturated [Potter]
19. Language / C. Assigning Meanings / 4. Compositionality
22283 Compositionality should rely on the parsing tree, which may contain more than sentence components [Potter]
22282 'Direct compositonality' says the components wholly explain a sentence meaning [Potter]
22296 Compositionality is more welcome in logic than in linguistics (which is more contextual) [Potter]