Combining Texts
Ideas for
'Metaphysics', 'The Philosophy of Mathematics' and 'Constructibility and Mathematical Existence'
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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 / c. Priority of numbers
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9191
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Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
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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 / 5. Definitions of Number / b. Greek arithmetic
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17851
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Number is plurality measured by unity [Aristotle]
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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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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 / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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9192
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The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
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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 / b. Type theory
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10265
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Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]
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8759
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We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
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10264
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Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]
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