Do numbers exist?

[didymus]

Found this question on a YouTube channel called Numberphile. Do they absolutely exist even though you can’t point to them? Are they jsut names we attach to certain relationships? Or fictional they way some folk might claim the Bible is made up but still contains useful moral lessons.

I would say that mathematics exists and it is the language of God/Nature/the Universe. To understand reality through math we have to start math we have to start with numbers, so yeah, they exist.

 

[Bradski]

One way of looking at it would be to ask if nothing existed, that is, if there was nothing to count, would 1 and 2 and 3…have any meaning?

I’m not sure.

I remember a few years back having a long forum discussion about evil. My argument was (and still is) that someone would have to do evil for it exist. That you can’t call someone evil until he actually does something evil.

So maybe there are no numbers unless you have something to count.

 

[JuanFlorencio]

Found this question on a YouTube channel called Numberphile. Do they absolutely exist even though you can’t point to them? Are they jsut names we attach to certain relationships? Or fictional they way some folk might claim the Bible is made up but still contains useful moral lessons.

I would say that mathematics exists and it is the language of God/Nature/the Universe. To understand reality through math we have to start math we have to start with numbers, so yeah, they exist.

Usually, when an individual study numbers for the first time, he follows his teacher. He listens to him and he reads what he writes on the blackboard. So, oneday he will be able to say that numbers existed before he could realize it: They existed in his teacher’s mind. But is this what the Numberphile guys mean?

 

[JuanFlorencio]

“There is a wall in front of us”, says one. “There is no wall in front of us”, says the other. “Does it really exist or not?”, asks a third. “Try to cross it fast, you will find out”, says a fourth. “If it exists, something will happen which is independent of your fantasy and independent of your desires. If it doesn’t, you will be safe”.

In a similar manner we could ask: Are the relations that we can find between numbers independent of our wishes or are they dependent on them? They are independent. Do numbers rule over certain aspect of our intellectual life or does our intellectual life rule over numbers? Can something inexistent rule over something existent? Don’t numbers seem to preexist to us?

To respond to these questions, we need to define what do we mean with the word “existence”.

 

[GEddie]

Neuroscientists would say that number and quantification are bred into our head.

ICXC NIKA

 

[crenfro]

My mortgage company thinks so. (sorry, couldn’t resist )

 

[TomFromMD]

Numbers are typically adjectives, unless we’re talking about written or verbal descriptions of them. As a noun, 3 exists. <— It’s right there.

But if we’re talking about the numbers itself, they’re adjectives. They describe things. Does blue exist? Well, kind of. It exists in that things can be blue. And 3 exists in that there can be 3 little pigs. There are certainly rules about them that are true. 3+2=5, just as yellow+blue=green.

 

[Petaro]

If we didn’t teach our children numbers and left out maths at school, would they still exist? I am sure some little obnoxious kid would suddenly realise you had two lollies and he had none and he could divide them into one each for both of you. That is how wars started. Our culture went downhill from there until we reached statistics. Oh the pain!

 

[Aloysium]

Neuroscientists would say that number and quantification are bred into our head.

ICXC NIKA

If such a person did, he’d be speaking about stuff that is outside his pay grade. You take out a part of the left brain and these words that pop into my mind will all be gone. Their meaning as that of numbers does not reside in the biochemical processes involved in our existing in time and space.

My mortgage company thinks so. (sorry, couldn’t resist )

No reason to apologize or resist. It’s probably the most meaningful thing anyone will have to say.

 

[JuanFlorencio]

Neuroscientists would say that number and quantification are bred into our head.

ICXC NIKA

Would they identify numbers with our ability to count? If so, then, wouldn’t counting imply the previous existence of numbers, not as physical objects, but as a ruling reality?

 

[JuanFlorencio]

If we didn’t teach our children numbers and left out maths at school, would they still exist? I am sure some little obnoxious kid would suddenly realise you had two lollies and he had none and he could divide them into one each for both of you. That is how wars started. Our culture went downhill from there until we reached statistics. Oh the pain!

If the obnoxious kid didn’t do that, then a loving mother would realize one day that one of her two kids was missing, and she would look for him till she found him. And when she was gathering fruits for her family, she would gather at least as many pieces as kids she had. How fortunate she was, because numbers existed!

 

[Solmyr]

Number are abstractions, not actual objects. In the ancient times “counting” went: “one”, “two”, “many”. Some primitive tribes are still on that level. Conceptualizing “zero” and “negative integers” was HUGE achievement. It took thousands of years to achieve that. Fractions were not that hard, almost everyone was able to conceptualize “half” an apple.

But to answer the OP, yes, numbers exist, but only as abstractions, not as ontological entities. Just like other concepts, like literature. If, by some misfortune, the Sun went supernova and burned up the whole Solar System all the information about Hamlet, of the Ninth Symphony would be gone.

 

[John_Lazarus]

If we didn’t teach our children numbers and left out maths at school, would they still exist? I am sure some little obnoxious kid would suddenly realise you had two lollies and he had none and he could divide them into one each for both of you. That is how wars started. Our culture went downhill from there until we** reached statistics.** Oh the pain!

Yeah, but then you could tell the obnoxious kid, “Hey, statistically, we each have one lolly!”

 

[didymus]

Number are abstractions, not actual objects. In the ancient times “counting” went: “one”, “two”, “many”. Some primitive tribes are still on that level. Conceptualizing “zero” and “negative integers” was HUGE achievement. It took thousands of years to achieve that. Fractions were not that hard, almost everyone was able to conceptualize “half” an apple.

But to answer the OP, yes, numbers exist, but only as abstractions, not as ontological entities. Just like other concepts, like literature. If, by some misfortune, the Sun went supernova and burned up the whole Solar System all the information about Hamlet, of the Ninth Symphony would be gone.

Maybe the first math humans did was division, sharing out resources among members of hunter-gatherer bands. Also, humans used mathematical relationships long before they could be described (facial recognition, how hard & what angle to throw a spear).
So I’d say the numbers exist and we discover them to explain our existence.

Last thought; circles have always had circumferences, diameters and a ratio between the two. Can you really say that pi didn’t exist until some human came along and calculated it?

 

[Bahman]

Found this question on a YouTube channel called Numberphile. Do they absolutely exist even though you can’t point to them? Are they jsut names we attach to certain relationships? Or fictional they way some folk might claim the Bible is made up but still contains useful moral lessons.

I would say that mathematics exists and it is the language of God/Nature/the Universe. To understand reality through math we have to start math we have to start with numbers, so yeah, they exist.

Numbers are not objective entities but of course subjective.

 

[ProdglArchitect]

How we identify numbers is subjective, but the reality those identifications relate is absolute. 1 + 1 will always be 2, no matter how we identify 1.

I’d say that numbers are a tangible representation of an intangible truth about reality.

 

[JurisPrudens]

Found this question on a YouTube channel called Numberphile. Do they absolutely exist even though you can’t point to them? Are they jsut names we attach to certain relationships? Or fictional they way some folk might claim the Bible is made up but still contains useful moral lessons.

I would say that mathematics exists and it is the language of God/Nature/the Universe. To understand reality through math we have to start math we have to start with numbers, so yeah, they exist.

That’s an old controversy among serious mathematicians. Where do mathematical laws come from? Where do natural numbers, like Pi, come from?

Well, personally I cannot answer that question.

What I know is that Christian mathematicians tended to be Realists - believing that numbers are objective reality and exist outside of our mind.

 

[hazcompat]

From Five Fingers to Infinity: A Journey Through the History of Mathematics Paperback – August 1, 1994

amazon.com/Five-Fingers-Infinity-Journey-Mathematics/dp/0812691946

Peace

 

[Solmyr]

So I’d say the numbers exist and we discover them to explain our existence.

Where do they “exist”? What does the word “exist” mean in this context? There are some philosophers who assert the “existence” of so-called “abstract objects”, and they say that these “objects” are not “created”, rather they are “discovered”. So, contemplate it. Numbers are merely a subset of these abstract objects. Do you really think that Hamlet was “discovered” and not created by Shakespeare? That every translation of Hamlet is a newly “discovered” abstract object? Or every edition with a misspelled word in it reflects a brand new “discovery” of a brand new abstract object? Do you really think that the rules of the game called “chess” or “bridge” were actually discovered, and not simply “made up”?

Last thought; circles have always had circumferences, diameters and a ratio between the two. Can you really say that pi didn’t exist until some human came along and calculated it?

Yes. There was no concept of “pi” before the ratio of circumference vs. diameter was thought of. Mind you, if there would be a “circle” and its “diameter” in objective reality, their ratio would be approximating the value of “pi”. But numbers, circles, lines, points (zero dimensional dots) do not “exist”, except as concepts. What about the square root of minus one (usually designated by the letter “i”)? Or multi-dimensional spaces? We literally “make them up” because they are fun and useful.

Existence can be subdivided into physical existence and conceptual existence. Concept only exist as “imaginary” entities. If all the humans and their creations would disappear in a cataclysm, all our creations; literature, music, mathematics… etc. would simply cease to exist.

If some hypothetical intelligence could emerge somewhere in the universe, they could create their own mathematics and geometry, which might or might not be similar to ours, but the other “abstract objects” like Hamlet, or the Ninth Symphony would be lost forever.

 

[JuanFlorencio]

Where do they “exist”? What does the word “exist” mean in this context? There are some philosophers who assert the “existence” of so-called “abstract objects”, and they say that these “objects” are not “created”, rather they are “discovered”. So, contemplate it. Numbers are merely a subset of these abstract objects. Do you really think that Hamlet was “discovered” and not created by Shakespeare? That every translation of Hamlet is a newly “discovered” abstract object? Or every edition with a misspelled word in it reflects a brand new “discovery” of a brand new abstract object? Do you really think that the rules of the game called “chess” or “bridge” were actually discovered, and not simply “made up”?

Yes. There was no concept of “pi” before the ratio of circumference vs. diameter was thought of. Mind you, if there would be a “circle” and its “diameter” in objective reality, their ratio would be approximating the value of “pi”. But numbers, circles, lines, points (zero dimensional dots) do not “exist”, except as concepts. What about the square root of minus one (usually designated by the letter “i”)? Or multi-dimensional spaces? We literally “make them up” because they are fun and useful.

Existence can be subdivided into physical existence and conceptual existence. Concept only exist as “imaginary” entities. If all the humans and their creations would disappear in a cataclysm, all our creations; literature, music, mathematics… etc. would simply cease to exist.

If some hypothetical intelligence could emerge somewhere in the universe, they could create their own mathematics and geometry, which might or might not be similar to ours, but the other “abstract objects” like Hamlet, or the Ninth Symphony would be lost forever.

But “made up” in what sense? Do you think that you can make up a different “Pi”, with different properties than the “Pi” we know? Or, on the contrary, are we authorized to say -in case you come up with a different “Pi”- that you are wrong?