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BillTre replied to the thread Is mathematics invented or discovered?.These have only been observed indirectly (fossil footprints). It would seem to be more concrete to discuss things that are more directly... -
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Then at least some prime numbers are discovered--those that appear, for example, in the time periods of cicadas. -
BillTre reacted to PeterDonis's post in the thread Is mathematics invented or discovered? with
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I disagree. We conceptualize it in a particular way, but evolution does what it does whether humans conceptualize it or not, and what it... -
BillTre reacted to PeterDonis's post in the thread Is mathematics invented or discovered? with
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I don't think your usage is consistent with others in this thread--they appear to me to be using "group" in the direct mathematical... -
BillTre reacted to PeterDonis's post in the thread Is mathematics invented or discovered? with
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What about the ways prime numbers show up in "natural" settings? For example, there are 13-year and 17-year cicadas. It is not a... -
BillTre replied to the thread Is mathematics invented or discovered?.How are you defining a natural group? -
BillTre replied to the thread Is mathematics invented or discovered?.Not so for the biological sciences, where understanding the "whys" leads to a better understanding of the organisms involved. Why does...