Combining Texts
Ideas for
'Thinking About Mathematics', 'Frege philosophy of mathematics' and 'Modern Philosophy:introduction and survey'
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7 ideas
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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The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
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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 / 3. Nature of Numbers / h. Reals from Cauchy
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Cauchy gave a formal definition of a converging sequence. [Shapiro]
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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 / c. Counting procedure
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Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton]
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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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