Combining Philosophers

Ideas for Anaxarchus, Plato and Tyler Burge

expand these ideas     |    start again     |     choose another area for these philosophers

display all the ideas for this combination of philosophers

13 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
8726 Geometry can lead the mind upwards to truth and philosophy [Plato]
9867 It is absurd to define a circle, but not be able to recognise a real one [Plato]
16901 The equivalent algebra model of geometry loses some essential spatial meaning [Burge]
9159 You can't simply convert geometry into algebra, as some spatial content is lost [Burge]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
13155 If you add one to one, which one becomes two, or do they both become two? [Plato]
9865 Daily arithmetic counts unequal things, but pure arithmetic equalises them [Plato]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
16902 Peano arithmetic requires grasping 0 as a primitive number [Burge]
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]
10216 We master arithmetic by knowing all the numbers in our soul [Plato]
16150 One is, so numbers exist, so endless numbers exist, and each one must partake of being [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]