Combining Texts

All the ideas for 'The Roots of Reference', 'Knowledge and the Philosophy of Number' and 'Whitehead and the Rise of Modern Logic'

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11 ideas

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 / A. Overview of Logic / 7. Second-Order Logic
13639 Quine says higher-order items are intensional, and lack a clearly defined identity relation [Quine, by Shapiro]
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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
21557 Russell confused use and mention, and reduced classes to properties, not to language [Quine, by Lackey]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
14296 Dispositions are physical states of mechanism; when known, these replace the old disposition term [Quine]