Combining Texts
Ideas for
'Through the Looking Glass', 'Guidebook to Wittgenstein's Tractatus' and 'Nature and Meaning of Numbers'
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12 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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9823
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Numbers are free creations of the human mind, to understand differences [Dedekind]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
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10090
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Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman]
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17452
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Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck]
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7524
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Order, not quantity, is central to defining numbers [Dedekind, by Monk]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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14131
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Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
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14437
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Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell]
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18094
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Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
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9824
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In counting we see the human ability to relate, correspond and represent [Dedekind]
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23452
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Discriminating things for counting implies concepts of identity and distinctness [Morris,M]
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23460
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To count, we must distinguish things, and have a series with successors in it [Morris,M]
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23451
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Counting needs to distinguish things, and also needs the concept of a successor in a series [Morris,M]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
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9826
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A system S is said to be infinite when it is similar to a proper part of itself [Dedekind]
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