Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Russell's Mathematical Logic' and 'The Rise of Analytic Philosophy 1879-1930'

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32 ideas

2. Reason / D. Definition / 8. Impredicative Definition
10041 Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
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 / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21716 In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
10035 Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
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 / G. Quantification / 2. Domain of Quantification
10042 Reference to a totality need not refer to a conjunction of all its elements [Gödel]
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]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10038 A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10046 The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10039 Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10043 Mathematical objects are as essential as physical objects are for perception [Gödel]
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]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
10045 Impredicative definitions are admitted into ordinary mathematics [Gödel]
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]
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]