Combining Texts
Ideas for
'Metaphysics', 'Letters to Leibniz' and 'The Nature of Mathematical Knowledge'
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19 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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560
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Mathematical precision is only possible in immaterial things [Aristotle]
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9076
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Mathematics studies the domain of perceptible entities, but its subject-matter is not perceptible [Aristotle]
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6298
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Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik]
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12392
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Mathematical a priorism is conceptualist, constructivist or realist [Kitcher]
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18078
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The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher]
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12426
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The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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10958
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Perhaps numbers are substances? [Aristotle]
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13273
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Pluralities divide into discontinous countables; magnitudes divide into continuous things [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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12395
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Real numbers stand to measurement as natural numbers stand to counting [Kitcher]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / j. Complex numbers
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12425
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Complex numbers were only accepted when a geometrical model for them was found [Kitcher]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
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12074
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The one in number just is the particular [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
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17844
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The unit is stipulated to be indivisible [Aristotle]
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17845
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If only rectilinear figures existed, then unity would be the triangle [Aristotle]
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17859
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Units came about when the unequals were equalised [Aristotle]
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18071
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A one-operation is the segregation of a single object [Kitcher]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
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17861
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Two men do not make one thing, as well as themselves [Aristotle]
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646
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When we count, are we adding, or naming numbers? [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
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18066
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The old view is that mathematics is useful in the world because it describes the world [Kitcher]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
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18083
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With infinitesimals, you divide by the time, then set the time to zero [Kitcher]
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