Ideas from 'Russell's Mathematical Logic' by Kurt Gödel [1944], by Theme Structure

[found in 'Philosophy of Mathematics: readings (2nd)' (ed/tr Benacerraf/Putnam) [CUP 1983,0-521-29648-x]].

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2. Reason / D. Definition / 8. Impredicative Definition

10041

Impredicative Definitions refer to the totality to which the object itself belongs

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility

21716

In simple type theory the axiom of Separation is better than Reducibility [Linsky,B]

5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics

10035

Mathematical Logic is a non-numerical branch of mathematics, and the supreme science

5. Theory of Logic / G. Quantification / 2. Domain of Quantification

10042

Reference to a totality need not refer to a conjunction of all its elements

5. Theory of Logic / K. Features of Logics / 8. Enumerability

10038

A logical system needs a syntactical survey of all possible expressions

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis

10046

The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

10039

Some arithmetical problems require assumptions which transcend arithmetic

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

10043

Mathematical objects are as essential as physical objects are for perception

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism

10045

Impredicative definitions are admitted into ordinary mathematics