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Do numbers exist?

Not the visual or verbal symbols for numbers, but numbers themselves?

Are You a Numerist or an Anumerist?

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  • 5 votes
skado 9 Dec 19

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Numerals, the “visual or verbal symbols for numbers” do exist. As with anything that facilitates understanding, in this case they represent the idea/concept of “quantity”, so that humans may communicate effectively. I suspect that many animals also have a concept of quantity, else how do animal mothers keep track of their offspring…e.g. the mother duck, whose duckling falls down the drain and lingers nearby, or the mother cat or dog who relocates her kittens or puppies.


The question sounds like another question "Do I exist?".

The mere fact that one can ask the "do I exist?" question proves the person exists. The mere fact that a person can count proves numbers exist.


Define "exist" ?

“objective evidence?”

@bbyrd009 Define "objective" and "evidence" please.


I don’t care!


I'm not certain I understand the concept behind the question. But numbers exist as one of something is identifiable from two of the thing from three of the thing.


Numerals exist. Define "number".


I remember getting very upset in 4th grade when the teacher tried to explain geometric points. I had a notion of atoms, but points seemed confusing. Points may exist conceptually, but aren't tangible nor material. Numbers are the same.


Numbers are an abstraction, like all of math.
If I write a one on a piece of paper billions of carbon atoms make up that one, there's no one there.
Concepts aren't real in the physical sense, only in the abstract sense.
Like my identity, which brain cell does it reside in? All of them, it's a neural network, so it's not the neurons it's the connections between the neurons. I as a personality I do not physically exist.
There are no souls, there are no numbers.

More like Schroeder's cat. Numbers do exist as a usable and needed concept and when they are used to build or design something or allow a brain or computer or analog machine to work out a solution to some problem. Like building a pyramid. And, they don't exist because they are an abstraction.

@Beowulfsfriend Right like i the "imaginary number" which is the square root of -1. It works, but it's not real, it's even named imaginary, which is cool, all numbers are. Regardless of how concrete the concept is.

I disagree. All of our communication is conceptual. Some of it is imaginary but a good deal of it represents things that are real. The fact that our communications here implies numbers in that the terms used represent more than one of whatever we are taking about indicates something about the number of things discussed. My dog is real enough, but the fact is I have two dogs. How is it that numbers don't exist when my two dogs are very real verses one dog? If I only feed one because there are no numbers, the other one suffers.

All of language is conceptual. Will we say language doesn't exist? I would agree the sounds we use to represent real things is arbitrary just as the letters we use to write with, but here we all are using them to communicate concepts to one another using language. I don't see numbers as being different in this way.

@RussRAB I write software for a living, you're not thinking this through clearly. We use language to communicate and numbers to help us model the universe in our minds. Animals that can't do that like worms still find food and still live. A great many not "real" concepts are hard to see for what they are. Like Pi... 3.14159265358979 if you use it it must be accurate to the resolution required, but you can't point to Pi in the world. I am not my name, nor my sense of identity. It's all accurate and conclusively unreal. So I answer to my name, and I think I exist because I think, and I use Pi. This isn't hard, I have a murder of crows that can't count and have no idea there's 35 of them but they interreact and if one dies they hold a funeral. Before humans and mathematics the world did well, without math. If numbers are real then so is God, and in the same way. But numbers aren't real and neither is God.

@RussRAB Numbers are concepts that exist in our mind to help us understand various phenomena or things in the universe or the universe itself. You can't see a number 2 walking along a road.

@Willow_Wisp - I understand the conceptual nature of numbers and I agree that certain numerical concepts are abstractions we can't readily see or observe. I do think we can see numbers, however, since I can see two of some thing - persons, dogs, creatures, etc - walking down the street as opposed to seeing one or three of whatever it is. First grade arithmetic was taught by repeatedly drawing the number of things - typically apples and oranges - as separate quantities added together to result in a another combined quantity. My wife taught Montessori preschool kids by the same method only using real objects instead of drawings.

@RussRAB Seeing something is just applying the number concept to what you're looking at. The same way my Ex could hear me drop change and tell me exactly how much money I had in coins. I apply numbers to everything I look at as well, we all do, but that's because we were trained to apply it.
What was language to Hellen Keller before she was introduced to sign language?
What was numbers and mathematics to someone never introduced to those concepts.
She compared it to finding God, but she certainly had no concept of any of these concepts that we intuitively consider "real", just imagine the concepts we'll find in the future that will be so useful that we'll think are real that we simply have no concept of now.

@Willow_Wisp - I not going to argue farther except to say that I believe my dogs can observe 2 balls when they are tossed. They may each chase a separate ball or both chase the same one, but they observe both whether or not they apply a learned application to how many were tossed.

The teaching or learning of the conceptual representation of what is observed is separate from what is observed. The number of things can be observed and reacted to whether or not a conceptual representation exists to describe what the number is.

When I look up “exist” the dictionary says:
to have actual being.

When I look up “being” it says:
that which has actuality either materially or in idea.

@RussRAB You have a dog, and then you have another dog. The word, "two" is an abstraction which represents the idea of an object 🐶 and then another object in the same category. Yet even that is a further layer of abstraction, because the idea of category, is also a mathematical or mental abstraction used by our brains to model the world outside.

Yet at the same time those models do indeed exist as real things in themselves, in a sense similar to that of a physical model. Such as if I build a model railway, the model railway exists as an object, even if it is not a real railway. The interesting thing is, that we know this in part, because we know that dogs themselves, understand both the concept of categories and of numbers, as do many other animals, so they are not just human cultural constructs.

@skado If you use those definitions then number exists as an idea but not materially. But that I do think answers your question.

@Beowulfsfriend Righto, whether they exist or not depends on your frame of reference. This leads to a circular argument when you try to pin it down(very quantum) The test of a theorem is it's utility not it's "truth"

Can some abstractions relate reliably or predictably to things that do exist in the material sense?


Numbers are ideas... and ideas exist. So, therefore numbers exist.

Jesus is an idea as well, so what will we do with that?

@Willow_Wisp Darth Vader, Batman, and Bugs Bunny are all ideas too.

@Charles1971 Right and all of those represent billions of dollars in the entertainment industry just as Jesus represents billions of dollars of political control and social manipulation. Yet not one of them exist any more than numbers exist.

@Willow_Wisp Yet I've watched Darth Vader, Batman, and Bugs Bunny on TV and in theaters. So, what I saw did not exist? Ideas don't exist?

If that is true then philosophy doesn't exist, mathamatics doesn't exist, religion doesn't exist, theories don't exist, theoretical physics doesn't exist, stories don't exist, dreams don't exist, thought doesn't exist, nor does anything intangible.

So, please explain to me what the requisites are for something to exist?

@Charles1971 Only things exist, and things take up space and time. Nothing conceptual exist, but I have no way of handing off this abstraction. It's like trying to explain why C squared is a big deal and relevant in E=MC squared. Or why a proportional integral derivative loop (PID) works to someone unfamiliar with the concept. It is a human failing to confuse concept with items we describe using those concepts. Like variable in software. The variable isn't the value contained in the variable. The value is real, the variable isn't real beyond being a concept we created to locate that value in the code.

@Willow_Wisp The answer is that a thing may exist and not exist, both at the same time, in three levels at least. Money in my bank account only exists as an idea, yet I can draw it out as cash and translate it into a physical object, called coins and notes, yet the physical objects themselves only stand for the abstract idea of values, yet I can buy a dog with both those coins or a non material bank transfer, and thereby exchange that abstraction of value for a physical object, also worth so many pounds.

That's true, but when we start saying that our abstract concepts we use to understand the universe are real we run a serious danger.
If any abstract concept can be considered real then all abstract concepts can be considered real.
God is an abstract concept, therefore God is real, and so is magic and all the rest of the superstitious crap humans have made up.
That slope is too slippery for me to brave.
This is why Christians are convinced that there's sin, and objective morality, and salvation because they have imagined them as we have imagined mathematics so therefore it's all real to them and they can't be more wrong then they are.
You have to distinguish between real and the abstractions we use to define that reality.
Numbers aren't real.

@Willow_Wisp Yes I agree with you and also try to keep a bound between the world of abstract ideas, and real physical things. Human language especially can, because it is just a scrap heap of old historic accidents, so easily mislead. I had not long ago a common example on this very site. One of the really common language based falacies. When I had to explain to a member that there is no such thing as cold or dark, in real terms, only a lack of heat and light. He replied that there must be such a thing as dark, since it is what exists before light reaches you. I think that I finally got through to him when I asked if anyone had ever detected a particle of dark. See also my reply to RussRAB above.

@Fernapple In the Navy I knew a guy that claimed that batteries in his flashlight didn't store electricity they held darkness. When he turned on the flashlight it sucked up the darkness and stored it in the batteries. When the batteries were dead it was because they were plum full of dark.

@Willow_Wisp Phlogiston theory reborn. lol

@Fernapple My grandmother still believed in Phlogiston theory as late as 1966 even though the theory was antiquated by the discovery of oxygen in 1830. Science news traveled slowly in the American South apparently.

It seems we aren't on the same page with this. Feels like we've been debating semantics. As I see it, something can be real (such as Peter Pan or Godzilla or Zeus) yet also fictional. To me, those to concepts are not contradictory.

What Willow_Wisp seems to be discussing are concepts that have no exact definition. "SD1" could be the term referring to the exact and current contents of my sock drawer, but I don't even know how many socks are in my sock drawer, much less the amount of dust, air, or other minuscule particles that might be inside my sock drawer. So, SD1 isn't real, yet my socks are indeed real.

@Charles1971 Ideas, which are things of the imagination, are fictional attemps our brains make to model the world without, sometimes things which are without, and sometimes things which only exist in that imagination. Those ideas, can be represented in their turn by physical objects, so that money as an idea of value, can be represented by a coin, and Batman as a fictional hero, can be represented by physical ink stains on the page of a comic book. But we are still creating a fiction when we imbue those coins or ink stains with the power to represent, even though they physically exist.

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