Combining Philosophers
Ideas for Galen, Bernard Linsky and Peter Geach
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8 ideas
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
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12154
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Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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10735
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Abstraction from objects won't reveal an operation's being performed 'so many times' [Geach]
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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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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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