Combining Texts

All the ideas for 'Reals by Abstraction', 'Plural Quantification Exposed' and 'Intuitionism: an Introduction'

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7 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension

10779

A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo]

5. Theory of Logic / A. Overview of Logic / 4. Pure Logic

10781

A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo]

5. Theory of Logic / G. Quantification / 6. Plural Quantification

10783

Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo]

10778

Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

10632

The real numbers may be introduced by abstraction as ratios of quantities [Hale, by Hale/Wright]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

8754	Logic is dependent on mathematics, not the other way round [Heyting, by Shapiro]

9. Objects / A. Existence of Objects / 1. Physical Objects

10782

The modern concept of an object is rooted in quantificational logic [Linnebo]