Combining Texts

All the ideas for 'No Understanding without Explanation', 'Some Puzzles of Ground' and 'Knowledge and the Philosophy of Number'

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13 ideas

4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
14263 Strong Kleene disjunction just needs one true disjunct; Weak needs the other to have some value [Fine,K]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve 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 / 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]
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]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
14262 Formal grounding needs transitivity of grounding, no self-grounding, and the existence of both parties [Fine,K]
11. Knowledge Aims / A. Knowledge / 2. Understanding
14365 Scientific understanding is always the grasping of a correct explanation [Strevens]
14368 We may 'understand that' the cat is on the mat, but not at all 'understand why' it is there [Strevens]
14369 Understanding is a precondition, comes in degrees, is active, and holistic - unlike explanation [Strevens]