Combining Texts

All the ideas for 'works', 'The Philosophy of Logic' and 'Plural Quantification Exposed'

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9 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 / D. Assumptions for Logic / 3. Contradiction

10121

Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal]

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 / 5. The Infinite / i. Cardinal infinity

18200

Very large sets should be studied in an 'if-then' spirit [Putnam]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics

18199

Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam]

8857	We must quantify over numbers for science; but that commits us to their existence [Putnam]

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

10782

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