Combining Texts

All the ideas for 'On Being (frags)', 'A Plea for Substitutional Quantification' and 'Knowledge and the Philosophy of Number'

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11 ideas

4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic

9470	Modal logic is not an extensional language [Parsons,C]

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]

5. Theory of Logic / G. Quantification / 4. Substitutional Quantification

9469	Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C]

9468	On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C]

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]