Combining Philosophers
Ideas for Rescher,N/Oppenheim,P, Stephen Boulter and Gottfried Leibniz
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13 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
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13163
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Circles must be bounded, so cannot be infinite [Leibniz]
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13008
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Geometry, unlike sensation, lets us glimpse eternal truths and their necessity [Leibniz]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
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12920
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There is no multiplicity without true units [Leibniz]
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9147
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Number cannot be defined as addition of ones, since that needs the number; it is a single act of abstraction [Fine,K on Leibniz]
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12956
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Only whole numbers are multitudes of units [Leibniz]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
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19390
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Everything is subsumed under number, which is a metaphysical statics of the universe, revealing powers [Leibniz]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
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19406
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I strongly believe in the actual infinite, which indicates the perfections of its author [Leibniz]
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13190
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I don't admit infinite numbers, and consider infinitesimals to be useful fictions [Leibniz]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
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19375
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The continuum is not divided like sand, but folded like paper [Leibniz, by Arthur,R]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
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18081
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Nature uses the infinite everywhere [Leibniz]
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18080
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A tangent is a line connecting two points on a curve that are infinitely close together [Leibniz]
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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
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12937
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We shouldn't just accept Euclid's axioms, but try to demonstrate them [Leibniz]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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23026
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We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz]
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