Combining Texts
Ideas for
'Mahaprajnaparamitashastra', 'Mathematical logic and theory of types' and 'Frege philosophy of mathematics'
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14 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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9896
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A prime number is one which is measured by a unit alone [Dummett]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
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18255
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Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
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9895
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A number is a multitude composed of units [Dummett]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
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9852
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We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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9829
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The identity of a number may be fixed by something outside structure - by counting [Dummett]
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9828
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Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
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10418
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Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell]
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10047
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Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave]
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23478
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Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
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21718
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Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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9876
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Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
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18126
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A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock]
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18128
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Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock]
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18124
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Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock]
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