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Ideas for
'Frege philosophy of mathematics', 'Space and Time' and 'Physics'
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10 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
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9790
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Geometry studies naturally occurring lines, but not as they occur in nature [Aristotle]
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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 / 3. Nature of Numbers / g. Real numbers
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22962
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Two is the least number, but there is no least magnitude, because it is always divisible [Aristotle]
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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 / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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18090
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Without infinity time has limits, magnitudes are indivisible, and numbers come to an end [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite
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22929
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Aristotle's infinity is a property of the counting process, that it has no natural limit [Aristotle, by Le Poidevin]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
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22930
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Lengths do not contain infinite parts; parts are created by acts of division [Aristotle, by Le Poidevin]
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18833
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A continuous line cannot be composed of indivisible points [Aristotle]
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