Mathematics, discovered or invented?
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July 8th, 2013 (6:14 PM).
I'd say it's fairly obvious that the answer is both, just depending on how one looks at it. I would presume that most "debate" about the issue is a result of equivocal notions of "mathematics."
Mathematics is, at heart, a language used to describe quantities and the relationships between them. That language is man-made - "2" only became "2" when the number was conceived and shared. But the quantity that we represent with the numeral "2" has always existed. We certainly didn't create that. There were 2 planets between the Earth and the Sun LONG before life even appeared on the Earth. The ability of man to conceptualize "2" and create a symbol to represent it had no effect whatsoever on the quantity of planets between the Earth and the Sun. That was a (relatively) fixed aspect of our solar system - we just created a symbol to represent and communicate it.
Similarly, there has ALWAYS been a ratio, and the exact same one, between the radius and the circumference of a circle. We didn't create that - it already existed. We simply discovered it. It's only the language by which it's defined to be 3.14159265... that we created.
And so on. The underlying principles of mathematics are part and parcel of reality. If one starts with a specific quantity of some things and adds some specific amount more of them, one ends up with a specific greater quantity of them. Those quantities would be exactly what they would be and the relationships between them would be exactly what they would be, regardless of whether we had a language with which to describe them or not. The creation of the language didn't create the quantities or alter them - it merely gave us a way to describe them and describe the ways in which the interrelate.
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