(April 25, 2015 at 7:03 am)downbeatplumb Wrote: What is non-empirical about maths?
Maths are all about definition and proof without reference to the real world. (Of course something in the real world can motivate a mathematical definition, but the math process itself doesn't depend on experiment in any way. There are also schools of thought that say math is discovered, in opposition to the ones that say it's invented. But the principle of isomorphism says that mathematical truths are independent of the notation used to express them. Including physical counters from marbles to atomic nuclei.)
