Combining Texts

Ideas for 'Logical Consequence', 'Recent Aesthetics in England and America' and 'The Republic'

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6 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

8726	Geometry can lead the mind upwards to truth and philosophy [Plato]

6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics

10692

Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

9863	We aim for elevated discussion of pure numbers, not attaching them to physical objects [Plato]

9864	In pure numbers, all ones are equal, with no internal parts [Plato]

8727	Geometry is not an activity, but the study of unchanging knowledge [Plato]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

9861	The same thing is both one and an unlimited number at the same time [Plato]