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'Frege philosophy of mathematics', 'Logic in Mathematics' and 'Reply to Hellman'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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To create order in mathematics we need a full system, guided by patterns of inference [Frege]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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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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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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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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We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
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