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'fragments/reports', 'Russell's Metaphysical Logic' and 'Principles of Arithmetic, by a new method'
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11 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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13949
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All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
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18113
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PA concerns any entities which satisfy the axioms [Peano, by Bostock]
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17634
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Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
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15653
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We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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17635
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Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
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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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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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