It may be literally controversial[0], but I don't think it's wrong.
Yes, maths is an interesting (and open) question. But also, the rules of maths are the result of some set of axioms — it's not clear to me[1] that the axioms we have are necessarily the ones we must have, even though ours are clearly a really useful set.
We put labels onto the world to make it easier to deal with, but every time I look closer at any concept which has a physical reality associated with it, I find that it's unclear where the boundary should be.
What's a "word"? Does hyphenation or concatenation modify the boundary? What if it was concatenated in a different language and the meaning of the concatenation was loaned separately to the parts, e.g. "schadenfreude"? Was "Brexit" still a word before it was coined — and if yes then what else is, and if no then when did it become a word?
What's a "fish"? Dolphins are mammals, jellyfish have no CNS, molluscs glue themselves to a rock and digest their own brain.
What's a "species"? Not all mules are sterile.
Where's the cut-off between a fertilised human egg and a person? And on the other end, when does death happen?
What counts as "one" anglerfish, given the reproductive cycle has males attaching to and dissolving into the females?
There's only a smooth gradient with no sudden cut-offs going from dust to asteroids to minor planets to rocky planets to gas giants to brown dwarf stars.
There aren't really seven colours in the rainbow, and we have a lot more than five senses — there's not really a good reason to group "pain" and "gentle pressure" as both "touch", except to make it five.
[0] giving rise or likely to give rise to public disagreement
[1] however this is quite possibly due to me being wildly oblivious; the example I'd use is that one of Euclid's axioms turned out to be unnecessary, but so far as I am aware all the others are considered unavoidable?
Yes, maths is an interesting (and open) question. But also, the rules of maths are the result of some set of axioms — it's not clear to me[1] that the axioms we have are necessarily the ones we must have, even though ours are clearly a really useful set.
We put labels onto the world to make it easier to deal with, but every time I look closer at any concept which has a physical reality associated with it, I find that it's unclear where the boundary should be.
What's a "word"? Does hyphenation or concatenation modify the boundary? What if it was concatenated in a different language and the meaning of the concatenation was loaned separately to the parts, e.g. "schadenfreude"? Was "Brexit" still a word before it was coined — and if yes then what else is, and if no then when did it become a word?
What's a "fish"? Dolphins are mammals, jellyfish have no CNS, molluscs glue themselves to a rock and digest their own brain.
What's a "species"? Not all mules are sterile.
Where's the cut-off between a fertilised human egg and a person? And on the other end, when does death happen?
What counts as "one" anglerfish, given the reproductive cycle has males attaching to and dissolving into the females?
There's only a smooth gradient with no sudden cut-offs going from dust to asteroids to minor planets to rocky planets to gas giants to brown dwarf stars.
There aren't really seven colours in the rainbow, and we have a lot more than five senses — there's not really a good reason to group "pain" and "gentle pressure" as both "touch", except to make it five.
[0] giving rise or likely to give rise to public disagreement
[1] however this is quite possibly due to me being wildly oblivious; the example I'd use is that one of Euclid's axioms turned out to be unnecessary, but so far as I am aware all the others are considered unavoidable?