Only if our definitions of geographical locations are ill-defined.
They are. They were invented by non mathematicians to facilitate communication about objects in the real world through human language -- in a non-mathematical field.
we must explicitly state our axioms re. messy stuff like biology and morality.
Sounds good, but it's kind of hard to do perfectly. Lots of geniuses have been at least peripherally aware of and have been wrestling with precisely this problem for millennia! But if you have it solved, please blog about it and show us the way! Also, don't be surprised when people start poking holes in what you write.
They are. They were invented by non mathematicians to facilitate communication about objects in the real world through human language -- in a non-mathematical field.
we must explicitly state our axioms re. messy stuff like biology and morality.
Sounds good, but it's kind of hard to do perfectly. Lots of geniuses have been at least peripherally aware of and have been wrestling with precisely this problem for millennia! But if you have it solved, please blog about it and show us the way! Also, don't be surprised when people start poking holes in what you write.