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2 ideas
10216 | We master arithmetic by knowing all the numbers in our soul [Plato] |
Full Idea: It must surely be true that a man who has completely mastered arithmetic knows all numbers? Because there are pieces of knowledge covering all numbers in his soul. | |
From: Plato (Theaetetus [c.368 BCE], 198b) | |
A reaction: This clearly views numbers as objects. Expectation of knowing them all is a bit startling! They also appear to be innate in us, and hence they appear to be Forms. See Aristotle's comment in Idea 645. |
14248 | We could accept the integers as primitive, then use sets to construct the rest [Cohen] |
Full Idea: A very reasonable position would be to accept the integers as primitive entities and then use sets to form higher entities. | |
From: Paul J. Cohen (Set Theory and the Continuum Hypothesis [1966], 5.4), quoted by Oliver,A/Smiley,T - What are Sets and What are they For? | |
A reaction: I find this very appealing, and the authority of this major mathematician adds support. I would say, though, that the integers are not 'primitive', but pick out (in abstraction) consistent features of the natural world. |