Combining Texts
Ideas for
'Axiomatic Theories of Truth', 'Outline of a System of Utilitarianism' and 'Russell's Metaphysical Logic'
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10 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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16321
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The compactness theorem can prove nonstandard models of PA [Halbach]
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16343
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The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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16312
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To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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21723
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The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
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21721
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Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B]
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21703
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Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B]
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21714
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The ramified theory subdivides each type, according to the range of the variables [Linsky,B]
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16308
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Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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21713
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Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B]
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21715
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For those who abandon logicism, standard set theory is a rival option [Linsky,B]
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