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All the ideas for 'On the Question of Absolute Undecidability', 'Conspectus libelli (book outline)' and 'Definitions'

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22 ideas

2. Reason / D. Definition / 1. Definitions
11223 Definitions usually have a term, a 'definiendum' containing the term, and a defining 'definiens' [Gupta]
11215 Notable definitions have been of piety (Plato), God (Anselm), number (Frege), and truth (Tarski) [Gupta]
2. Reason / D. Definition / 2. Aims of Definition
11225 A definition needs to apply to the same object across possible worlds [Gupta]
11227 The 'revision theory' says that definitions are rules for improving output [Gupta]
2. Reason / D. Definition / 3. Types of Definition
11224 Traditional definitions are general identities, which are sentential and reductive [Gupta]
11226 Traditional definitions need: same category, mention of the term, and conservativeness and eliminability [Gupta]
11221 A definition can be 'extensionally', 'intensionally' or 'sense' adequate [Gupta]
2. Reason / D. Definition / 4. Real Definition
11217 Chemists aim at real definition of things; lexicographers aim at nominal definition of usage [Gupta]
2. Reason / D. Definition / 6. Definition by Essence
11216 If definitions aim at different ideals, then defining essence is not a unitary activity [Gupta]
2. Reason / D. Definition / 10. Stipulative Definition
11218 Stipulative definition assigns meaning to a term, ignoring prior meanings [Gupta]
2. Reason / D. Definition / 11. Ostensive Definition
11220 Ostensive definitions look simple, but are complex and barely explicable [Gupta]
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 / 6. Ordering in Sets
11222 The ordered pair <x,y> is defined as the set {{x},{x,y}}, capturing function, not meaning [Gupta]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
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
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
12699 A body would be endless disunited parts, if it did not have a unifying form or soul [Leibniz]
9. Objects / C. Structure of Objects / 2. Hylomorphism / d. Form as unifier
12700 Form or soul gives unity and duration; matter gives multiplicity and change [Leibniz]
10. Modality / D. Knowledge of Modality / 2. A Priori Contingent
12736 If we understand God and his choices, we have a priori knowledge of contingent truths [Leibniz, by Garber]
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
12698 Every body contains a kind of sense and appetite, or a soul [Leibniz]