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Posted By: AngusI'm cool with it as long as we clearly understand the difference between real and real.
Posted By: BigOilRepPosted By: AngusI'm cool with it as long as we clearly understand the difference between real and real.
Bigot.
Posted By: AngusSome of my best friends are real !
Posted By: AngusWhat you miss is that our discovery.of interesting things in mathematics, solely on the basis of proving them consistent with the rest of the structure, very often turns out much later to be a useful way to describe or predict material reality. And often not, as well.
It is just not right to think that mathematics is fundamentally the outcome of attempts to describe the world. It's much bigger.
Posted By: AngusI concede your first point pending developments. Since I won't likely be around long enough to experience the discovery that nature disagrees with mathematics (should that ever happen), it's a safe concession.
I don't understand the second point. The surprise was that the system based on a sort of aesthetic mental consistency should work on something we found in the road - i.e. external reality.
Taking that surprise as evidence of something significant leads me to my sense that mathemarics has an existence of its own and we are discovering it much as we discover other aspects of nature. It's all one big universe.
Posted By: AngusGödel had something to say about when Mathematics would be complete.
If we have invented mathematics ourselves to take care of our sheep business, then presumably we would have had the option of inventing some other system to take care of our sheep business. I know of no other system than numbers with which to count sheep. If there is only one way to invent mathematics that works, I would call its "invention" a discovery. It implies the existence of a "way that works" which we call mathematics.
As you know I am a Platonist on the matter. To me the existence of mathematics independent of anybody to think it up is a given. If there were no people would there be three of anything?
Other than that, we seem to be closer than the continuing argument would imply.