One of the oldest philosophical debates is on the idea on the reality of the concepts of numbers. That seems awfully silly at first glance. Why are numbers illusions? We use them all the time, not to mention mathematics contains so many things that are, well, true. But one of the arguments, going all the way back to Ancient Greece, is whether they exist naturally. Sure, we’ve created mathematics and like many tools humans have invented, it has helped with many things. But do they exist naturally?
Think of the number 2.
You’re either thinking of the written number 2 or the doubling of an object, say, 2 apples.
The written number 2 is just a symbol we have created for two, but isn’t actually 2 itself. When you think of a wolf, you don’t imagine the word: “Wolf” itself, you think of an image of that wolf itself. Natural things have a depiction, ideas do not. There is no physical and natural manifestation of an idea like democracy because it is an artificially created concept by humans to define an advanced idea.
If you’re thinking of 2 apples, or some other doubling of an object, that doesn’t quite work either. You’re thinking of apples and there happens to be 2 of them, but it’s not the natural representation of “two-ness”, it’s just apples. Plus, what about something like 2 meters? That’s a form of “two-ness” that isn’t two objects but a measurement that can be applied to anything that matches, since we also invented measuring.
Not to mention math is a system made by humans TO work. So 2 + 2 only = 4 because we said so and because we want it too. If we switched 2 and 3 on the number line, 3 + 3 would = 4. If we used binary, 2 wouldn’t exist and would in fact be 10.
So when someone says it’s as natural, it’s really not. They’re using a language that was invented and taught to them. Animals may eat 2 apples but that doesn’t mean they’re, as far as we know, aware of the number 2 or using it for anything. If humans were never here, 2 would never have existed.
My final point is that ultimately, 2 is a value and is therefore even more artificial. All value is artificial because we are ranking something based on opinion or artificial ideas. “Best-ness” doesn’t exist naturally, “rich” doesn’t exist naturally, these are all words and phrases with relative meanings sure, but also real concepts. They’re just only real because we assigned artificial ideas to them. 2 is also a value, you’ve even likely equated numbers as a value in math class at one point.
But remember, the idea of 2 not being natural does not mean it isn’t real. Of course it is. I’ve typed it several times now. But it’s artificial just like language.