Combining Texts
Ideas for
'Metaphysics', 'Persistence, Change and Explanation' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'
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21 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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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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18252
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Real numbers are ratios of quantities, such as lengths or masses [Frege]
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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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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 / B. Foundations for Mathematics / 1. Foundations for Mathematics
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18271
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We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
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17843
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The idea of 'one' is the foundation of number [Aristotle]
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17850
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Each many is just ones, and is measured by the one [Aristotle]
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17851
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Number is plurality measured by unity [Aristotle]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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10623
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Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
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9975
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Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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9793
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Mathematics studies abstracted relations, commensurability and proportion [Aristotle]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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13738
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It is a simple truth that the objects of mathematics have being, of some sort [Aristotle]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
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12339
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Aristotle removes ontology from mathematics, and replaces the true with the beautiful [Aristotle, by Badiou]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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18165
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My Basic Law V is a law of pure logic [Frege]
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