Combining Texts

All the ideas for 'Review of Bob Hale's 'Abstract Objects'', 'Infinitism not solution to regress problem' and 'Knowledge and the Philosophy of Number'

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12 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
9184 We can't presume that all interesting concepts can be analysed [Williamson]
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
9183 Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist [Williamson]
23622 We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
8836 Must all justification be inferential? [Ginet]
8837 Inference cannot originate justification, it can only transfer it from premises to conclusion [Ginet]