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.

[GrandizerII]

Is it possible that people find it difficult to view morality as objective because people have varying attitudes with regards to what's right and wrong that this lack of clear consensus gives the impression (whether false or not) that morality is not objective but subjective? Whereas with mathematics, people don't tend to be conflicted about the truths of mathematical statements, therefore lending an aura of absoluteness and rigidity regarding these statements, which then gives the impression that mathematics is objective (or at least, more on the objective side than morality)?

[robvalue]

It’s more like every single person draws up their own moral (mathematical) system, and so what is true in one system is not true in another. It just so happens that certain mathematical systems are so incredibly useful that it’s highly practical to all use the same one in most applied tasks.

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Maths applied through science can give us data and predict outcomes, but it can’t tell us which outcomes are preferable without also including exact criteria for what "preferable" means. It can’t do the ethics for you.

[Little lunch]

Let's test it out. I'll provide you with a bank account number and you can transfer over the "made up" numbers from your paycheck. If they transfer, then we have evidence that numbers are not made up and should not be ignored.

... but if you like, we can retest biweekly and check our results.  

I don't think you could live on my salary.

Wrong thread.
I think you meant to put this in the 'We were so poor - First World Edition'.  :-)

[The Grand Nudger]

It’s more like every single person draws up their own moral (mathematical) system, and so what is true in one system is not true in another. It just so happens that certain mathematical systems are so incredibly useful that it’s highly practical to all use the same one in most applied tasks.

---

Maths applied through science can give us data and predict outcomes, but it can’t tell us which outcomes are preferable without also including exact criteria for what "preferable" means. It can’t do the ethics for you.

Science also depends on variable weighting....ergo maths can't do the science for you, either. 

[Angrboda]

I think it's worth pointing out that in some sense the question of whether numbers and math are real and exist is predicated on an ontological assumption that there is a world independent of our senses and that our sensory experience can provide us with direct evidence of that world. Our latest insights suggest that our mental concepts are all a product of a complex biological device and that any concepts about the external world are therefore necessarily constructs of the mind. One doesn't have to travel far to find examples of this. The example of a cricle was given earlier, and no such thing as a circle exists in the so-called real world. Our idea of a circle is an idealization that is largely a byproduct of the way our senses work, specifically with regard to granularity and sub-feature processing in the brain and eye. Until our ontologies catch up with the fact of the mental nature of "our world" then questions of the existence of things which may be based in the way the brain thinks about the world are likely to persist without any clear resolution. I'm not sure how to reconcile these two radically different ideas, that of the independent existence of an external world and the radically dependent nature of the mental one, but it's possible that such a reconciliation could dissolve such questions and render them non-questions.

[ignoramus]

Guys, is the subatomic lattice structure of eg: a diamond not proof that nature does and can create mathematically perfect objects at it core?

Ultimately, if we need to split hairs, we can argue that since the electron path of any particle of nature can only be approximated by probability, therefore everything at the nth degree will be fuzzy

[Neo-Scholastic]

The example of a cricle was given earlier, and no such thing as a circle exists in the so-called real world. Our idea of a circle is an idealization that is largely a byproduct of the way our senses work, specifically with regard to granularity and sub-feature processing in the brain and eye

If our concept of circularity is based on an idealization what is it an idealization of? Is the value of pi just a rough approximation based on empirical observation? Is there any possible universe in which the value of pi is different?

[ignoramus]

^ I would say no.
(by our definition of what a circle is, and its circumference relative to its radius.)

Those are fixed ratios in any universe, no?

[Fireball]

The definition of a circle is, via Euclid, "A circle is a plane figure bounded by one line, and such that all right lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its center."

That is already the ideal, we don't draw anything else from a simple definition.

Pi is simply the ratio of the diameter to the circumference; it just happens to be a transcendental number, which means that it is a decimal fraction that never repeats. It is not an approximation; we use approximate values for it depending on the required precision for what we are doing.