Combining Philosophers
Ideas for Aristotle, Rayo,A/Uzquiasno,G and Thales
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32 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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12377
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Mathematics is concerned with forms, not with superficial properties [Aristotle]
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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 / 2. Geometry
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9790
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Geometry studies naturally occurring lines, but not as they occur in nature [Aristotle]
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12372
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The essence of a triangle comes from the line, mentioned in any account of triangles [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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1729
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We perceive number by the denial of continuity [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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11044
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One is prior to two, because its existence is implied by two [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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22962
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Two is the least number, but there is no least magnitude, because it is always divisible [Aristotle]
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11042
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Parts of a line join at a point, so it is continuous [Aristotle]
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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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17859
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Units came about when the unequals were equalised [Aristotle]
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17844
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The unit is stipulated to be indivisible [Aristotle]
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12273
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Unit is the starting point of number [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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12369
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A unit is what is quantitatively indivisible [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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18090
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Without infinity time has limits, magnitudes are indivisible, and numbers come to an end [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite
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22929
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Aristotle's infinity is a property of the counting process, that it has no natural limit [Aristotle, by Le Poidevin]
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13212
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Infinity is only potential, never actual [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
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22930
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Lengths do not contain infinite parts; parts are created by acts of division [Aristotle, by Le Poidevin]
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18833
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A continuous line cannot be composed of indivisible points [Aristotle]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
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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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11041
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Some quantities are discrete, like number, and others continuous, like lines, time and space [Aristotle]
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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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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 / 4. Mathematical Empiricism / a. Mathematical empiricism
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9974
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Ten sheep and ten dogs are the same numerically, but it is not the same ten [Aristotle]
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