Combining Texts
Ideas for
'Metaphysics', 'Letters to Russell' and 'The Evolution of Logic'
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26 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 / e. Ordinal numbers
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13459
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The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD]
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13491
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The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD]
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13463
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There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD]
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13492
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Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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18253
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I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege]
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13446
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19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD]
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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 / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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13509
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We can establish truths about infinite numbers by means of induction [Hart,WD]
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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
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13474
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Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD]
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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 / 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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18166
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The loss of my Rule V seems to make foundations for arithmetic impossible [Frege]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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13471
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Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD]
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