Are Numbers Real?

[robvalue]

Or to use the example of PI, you could ask if that was discovered. But there are no perfect circles in nature. Presumably true of right angle triangles. Our mathematical descriptions are just approximations of them.

Take numbers. We think in terms of single objects. Like one or two oranges. But actually you don't have to think in this way. It's useful for every day situations but maybe an alien race would think entirely differently depending on how they evolved. Like part of a hive mind for example. Because we are making an arbitrary distinction between what is and is not an orange. That sounds like a daft statement but take humans and the debate about when life begins, is it at conception? When an egg is fertilised? When it is born etc? What about a bee? Is it a single object or part of a super organism? Why can't we say the same thing about a human? After all, there is never only one thing in existence, everything is part of a larger environment. The orange is part of a tree and part of its life cycle. But for convenience we talk about multiples of a single orange. Sometimes though it is not convenient to think in these terms.

But now I feel like we are getting away from the significance of the question in the first place. To follow your and Rob's skepticism any further, we may as well say "there are no such things as facts, because for there to be facts in the first place relies on a basic set of assumptions."

The hive mind aliens may not be able/willing to understand math the way we do, but this has no bearing on the fact that math is a real, objective thing. The hive mind aliens may have facets of their reality that are beyond our comprehension, but this does not necessarily indicate that those things are not objectively real. There may be a state of deep communication which all members of the hive mind enter into that we humans could never possibly fathom, but that does not mean that this state is devoid of objective and/or actual qualities.

What do you mean maths is a "real objective thing"? Real in what way? It’s a collection of abstract ideas. A lot of those ideas have useful practical applications. Any particular mathematical system is objective; further than that, I don’t know what you mean.

I think you’re conflating several things here. There are axiomatic truths, such as in mathematics; there are (presumably) truths about reality, and there are scientific facts which are our best attempt to model a perceived truth about reality.

I’m struggling to comprehend your terminology, both here and in the morality thread!

PS: I have no scepticism of mathematics, what I am saying is that it absolutely is true, beyond any doubt. It’s internally true. There is no element of doubt, only possible mistakes in logic. I don’t think numbers or maths are "real" in the same way physical objects are real. You can redefine "real" to make it fit, but I see no point in doing so.