Combining Philosophers
Ideas for Luitzen E.J. Brouwer, J.L. Austin and Gottfried Leibniz
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15 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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18119
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Mathematics is a mental activity which does not use language [Brouwer, by Bostock]
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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 / 3. Nature of Numbers / h. Reals from Cauchy
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18247
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Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
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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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12920
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There is no multiplicity without true 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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12451
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Scientific laws largely rest on the results of counting and measuring [Brouwer]
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18118
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Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
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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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