Still Debating With Plato--Is Mathematics Discovered or Invented?(sciencenews.org)
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Still Debating With Plato--Is Mathematics Discovered or Invented?
http://www.sciencenews.org/view/generic/id/31392/title/Still_debating_with_Plato
1 comments
False Dichotomy.
This frustrates me. I want to respond to you, but you blipped out a two word response that could mean so many things. In what way is it a false dichotomy. Unless you are saying someone invented it and then now humans are discovering it. Or what? I mean I just don't even know where to begin given the lack of original explanation on your part.
Sorry. I just think it could also be neither.
To me, it doesn't seem to makes sense to say mathematics is out there, waiting to be discovered, because of godel's incompleteness. What would the structure of the mathematics that is waiting to be discovered be? For any of mathematical system, there is a true statement in that system that cannot be proven. If mathematics is out there waiting to be discovered, I don't understand how Godel's incompleteness would stand when applied.
I also don't think mathematics is some cultural artifact people invented.
To me, it doesn't seem to makes sense to say mathematics is out there, waiting to be discovered, because of godel's incompleteness. What would the structure of the mathematics that is waiting to be discovered be? For any of mathematical system, there is a true statement in that system that cannot be proven. If mathematics is out there waiting to be discovered, I don't understand how Godel's incompleteness would stand when applied.
I also don't think mathematics is some cultural artifact people invented.