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Mathematics, discovered or invented?

CrowSvenson

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I'm too right-brained for this. But I'll say it was invented. Like logic itself, it's something WE made, and doesn't "exist" outside of our grey matter.
 
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Whilst I am on the same side as you in this debate Crow, I have to disagree with your arguments. Logic is far from a human concept. We are possibly the most illogical being to exist or that ever will exist, even more so because we can recognise logical actions and decisions and then voluntarily take a different one. Further more, who is to say that aliens on some far off planet aren't highly logical beings? We didn't create logic, it (like the principals we describe with mathematics) is just something we can identify and imitate or explain.

Sorry for that rather off-topic bit guys :)
 
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That is interesting you bring it up though Crow, logic is a key defining aspect of math and I think it should be considered.

I agree that logic was created, someone/thing must have specifically gone out of their way to deem something logical. But what is logical? Newtonian physics is logical, quantum physics is most definitely not. But who's to say that if quantum physics was discovered first it would remain illogical.
Maintaining my stance in the original debate, I think logic is independent of whether or not math was created, because it itself had to be defined before we could claim anything was logical or not.
 
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I'm pretty new to debate but I now finally had the courage to try and say what I can because I know that PC is one of the friendliest communities around I have ever seen (right? :D). This is a complicated subject and I tried my best to express my opinion about this topic (Gosh this took so long for me to write):

I think whatever in math was right has been discovered and whatever is incorrect in math has been invented because our world functions through those concepts that work. We count and the theory of counting is right in its own sense. Our most common style of counting, which is the foundation of maths everywhere (1,2,3,4), has been invented. There are other styles of counting such as by Base 13, when numbers are counted as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, and C. It's like counting with 13 fingers instead of 10. And we may switch the numbers up into characters or random symbols and they can still represent a correct counting system. Counting is true, that's a known fact. If that wasn't true math, there would be a whole set of assumptions because there is nothing for them to stand on and develop into ideas that represent truth. (It would be so confusing without any numbers because we need them to explain lots of other phenomena)

If counting is true, shouldn't the mathematical operations be true (e.g. addition/multiplication)?
We can immediately apply it into our lives, but we can shift the symbols anyhow we want it to be. x can be c, and + may be switched around with -. But it is still true if the concept underlying the symbols are true.

We can attempt to explain the other theories of math by the use of the established theories proven to be facts (e.g. counting and arithmetic operations (+,-,x). Physics is another case. Just because the math is right doesn't make it true. Physics is the science of observation backed up by the absolute truth of mathematics. We try to explain physics phenomena rationally by math. The phenomena are right, but how did they happen? That is the question we want to answer by observation followed by math. But just because the thought is rational and the math is right doesn't make it true. We might have observed and applied math at the wrong place.

For ex.: Gravity is true. It is a known fact. Humanity saw things falling to the ground and attempted to explain it. But gravity is a really complicated and the theories and hypothesis made to explain it may be either true or false due to wrong scope (wrong scope = focusing on assumptions/ wrong area // And assuming that the math concepts behind it is perfect), but it doesn't change the fact that gravity is true and a fact of life.

I heard someone mentioned a cube and square. We can find the area and volume of a cube/square by various formulas but the style of those may be different. But it works, so shouldn't it be true because volume and areas exist in every kind of 2-D and 3-D shapes imaginable?

Humanity has discovered the right areas of mathematics and invented the false theories of mathematics because our world cannot function through wrong theories about math. Math is the order of life. Our world functions cannot exist without math.
 
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I think whatever in math was right has been discovered and whatever is incorrect in math has been invented...

I heard someone mentioned a cube and square. We can find the area and volume of a cube/square by various formulas but the style of those may be different. But it works, so shouldn't it be true because volume and areas exist in every kind of 2-D and 3-D shapes imaginable?

This entire post.
I've quoted here because I want to point out we were discussing assuming as if it was all correct, but I like your ideas. :)

The cube/square scenario was describing perspective, so if you look at a cube face on it looks like a square right? But if you have had and can not have any other view of the cube other than face on you would assume it was simply a square and had no evidence to prove otherwise :).
 
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Math as a language was invented, but the concepts that language explains existed long before we were able to codify them. It's not like special relativity existed only after Einstein told us all about it. ;p
 
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@Livewire - Exactly! I couldn't have put it better myself.

@Quopol - That is an interesting perspective that has yet to appear and it is indeed well thought out but I must continue to respectfully disagree. The issue with your view isn't correct vs incorrect, it is that it still views mathematics and the principals it describes as the same thing.

Incorrect maths is invented just as you said and pretty much for the reasons you said. I'll give you that one. But correct mathematics was also invented - correct mathematics just means we are using the language of mathematics to accurately describe a discovered principal. In this sense correct mathematics is the equivalent of writing a non-fiction book whilst incorrect mathematics is more like writing a narrative.

It is as Livewire, myself and a few others on here have said. You are all viewing mathematics as though the formula we use to calculate gravity is the same thing as the actual force of gravity.
 
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@Livewire - Exactly! I couldn't have put it better myself.

@Quopol - That is an interesting perspective that has yet to appear and it is indeed well thought out but I must continue to respectfully disagree. The issue with your view isn't correct vs incorrect, it is that it still views mathematics and the principals it describes as the same thing.

Incorrect maths is invented just as you said and pretty much for the reasons you said. I'll give you that one. But correct mathematics was also invented - correct mathematics just means we are using the language of mathematics to accurately describe a discovered principal. In this sense correct mathematics is the equivalent of writing a non-fiction book whilst incorrect mathematics is more like writing a narrative.

It is as Livewire, myself and a few others on here have said. You are all viewing mathematics as though the formula we use to calculate gravity is the same thing as the actual force of gravity.

I agree with your idea that we try our best to understand gravity with our formulas, but it doesn't make them equivalent. The formulas aren't what makes math beautiful. It's our world that makes it so.
EDIT: I forgot to mention... Sorry that I sent the wrong message. I agreed with your idea while I was writing my post. I'm not so great at writing and I'm open for constructive criticism. How can I make it so that these kind of incidences don't happen again? Thank you for taking your time to answer my question (if you do so).
 
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I'd say it's fairly obvious that the answer is both, just depending on how one looks at it. I would presume that most "debate" about the issue is a result of equivocal notions of "mathematics."

Mathematics is, at heart, a language used to describe quantities and the relationships between them. That language is man-made - "2" only became "2" when the number was conceived and shared. But the quantity that we represent with the numeral "2" has always existed. We certainly didn't create that. There were 2 planets between the Earth and the Sun LONG before life even appeared on the Earth. The ability of man to conceptualize "2" and create a symbol to represent it had no effect whatsoever on the quantity of planets between the Earth and the Sun. That was a (relatively) fixed aspect of our solar system - we just created a symbol to represent and communicate it.

Similarly, there has ALWAYS been a ratio, and the exact same one, between the radius and the circumference of a circle. We didn't create that - it already existed. We simply discovered it. It's only the language by which it's defined to be 3.14159265... that we created.

And so on. The underlying principles of mathematics are part and parcel of reality. If one starts with a specific quantity of some things and adds some specific amount more of them, one ends up with a specific greater quantity of them. Those quantities would be exactly what they would be and the relationships between them would be exactly what they would be, regardless of whether we had a language with which to describe them or not. The creation of the language didn't create the quantities or alter them - it merely gave us a way to describe them and describe the ways in which the interrelate.
 
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Very interesting question!

Math as a language was invented, but the concepts that language explains existed long before we were able to codify them. It's not like special relativity existed only after Einstein told us all about it. ;p
This is the perfect answer, I'd say. Mathematics as a language is something that we invented to try to understand our universe in a way that we can manipulate, but the ratios and equations taking place in every day life have always been there. It's entirely possible that our view on the universe (from a mathematical standpoint) is entirely wrong and we've been miscalculating everything (and it's possible that things simply can't be calculated), but given that we're able to understand, evaluate and manipulate the world in the ways that we do, I think it's a safe bet that we've got this down haha. It's interesting to consider an unquantifiable world in which all maths we took to be law is revealed to be false, but from the limited knowledge that we have, it seems likely that'll never happen.

Though 'likely' is a probability, so perhaps we're imagining that too? ;)
 
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Maths is a perfect self-contained system. We represent it with an invented language and numeracy system to model things that we perceive and concepts we've invented, but maths itself is not invented.
 

Omicron

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Definitely not invented, discovered. Math exists in nature and many examples can be made, like fibonacci's series in plants or nautilus. As Livewire stated above, the way we express math was invented, but math itself was just discovered.
 
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The problem with that, as I have said before, is that you are all confusing mathematics with what it describes. Mathematics is a language the patterns and principals that occur naturally throughout the universe were discovered - but mathematics itself is a language just like English or Spanish that we have invented.

What you guys are doing is the same as saying that an apple is the same thing as the word "apple" when in reality one is an object and the other is the word we use to describe that object.
 
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What you guys are doing is the same as saying that an apple is the same thing as the word "apple" when in reality one is an object and the other is the word we use to describe that object.

Precisely. The Apple exists and has its properties regardless of whether we choose to describe or label it. The words and labels have been invented, but the reality they describe is discovered.

What do you all think about the notion that maths, being perfect a perfect system (100% consistent, no issues, contradictions, etc) cannot be man-made?
 
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It feels like mathematics is something invented because you can do things in math that have no correspondence in the real world. Where do negative numbers exist in nature? Imaginary numbers? (Serious question - I'm not a math person.) Like language, we can create words (and conceptions) of things that don't or can't exist.

Feels to me like mathematics is an interpretation of nature. Nature is discovered, but nature is not math. Math is the language we use to understand nature. In that sense it feelss like it's more communication than anything, a worldview or conception. I think there are several ways of understanding nature, math being just one of them.

What do you all think about the notion that maths, being perfect a perfect system (100% consistent, no issues, contradictions, etc) cannot be man-made?

I'd say first: Is math perfect? How can we know? Is it complete, growing, changing? Then I'd say: why can't humanity create or conceive of something perfect?
 
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It feels like mathematics is something invented because you can do things in math that have no correspondence in the real world. Where do negative numbers exist in nature? Imaginary numbers? (Serious question - I'm not a math person.) Like language, we can create words (and conceptions) of things that don't or can't exist.

Imaginary numbers are used a lot in engineering principles and such. I did a course on them in my final year of university but a lot of the stuff I covered escapes me now haha. As for negative numbers, think about opposing forces. So you're driving your car and you have a forward driving force and the backwards force is the resistance. This backwards force can be considered as a negative number to represent a force acting in the opposite direction to the driving force - it all depends on how you choose to label your diagram when you do these kinds of calculations.

Feels to me like mathematics is an interpretation of nature. Nature is discovered, but nature is not math. Math is the language we use to understand nature. In that sense it feelss like it's more communication than anything, a worldview or conception. I think there are several ways of understanding nature, math being just one of them.

My response is in red and I agree with what you say in your second paragraph, except for the double s on the word 'feels' :p
 
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The problem with that, as I have said before, is that you are all confusing mathematics with what it describes.
Who are you responding to?

I can't see even one post since your last one - not a single one - that doesn't in fact very deliberately and pointedly distinguish between those two things.
 
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@Arlo - I was responding to Omicron and Archer, but really it applies to anyone who is trying to say that the naturally occurring patterns and "rules" that we describe through mathematics is the same as the language. They, and everyone else, are of course entitled to their opinions but I, as you may have noticed, disagree to a rather large degree.

Sorry about being unclear as to who that was directed at.
 
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@Arlo - I was responding to Omicron and Archer, but really it applies to anyone who is trying to say that the naturally occurring patterns and "rules" that we describe through mathematics is the same as the language. They, and everyone else, are of course entitled to their opinions but I, as you may have noticed, disagree to a rather large degree.

Sorry about being unclear as to who that was directed at.

Maths is a perfect self-contained system. We represent it with an invented language and numeracy system to model things that we perceive and concepts we've invented, but maths itself is not invented.

Definitely not invented, discovered. Math exists in nature and many examples can be made, like fibonacci's series in plants or nautilus. As Livewire stated above, the way we express math was invented, but math itself was just discovered.

As I already noted, both of those responses, along with all the other responses at least since your last one, very explicitly point out the distinction between the two things. They very pointedly do NOT claim that "the naturally occurring patterns and "rules" that we describe through mathematics is the same as the language." In fact, at least in the past three weeks or so (I haven't bothered to read back further than that), NOBODY has made that claim.

??
 

Trev

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Math was invented.

You could argue that the world was set up to have math in mind but honestly, that doesn't make sense. Humans didn't know how to explain things so they made up stuff for it. Do you honestly think that the symbol for 8 was passed down from the beginning of time, when there was nothing? No, humans made it up because they wanted to know what "eight" would look like. They also invented "eight", mind you. If math hadn't been invented, I could easily just point to the edge of my laptop and call that an octaganoganatriclogon and everyone would believe me no matter how ridiculous it sounds because it explains something that people otherwise couldn't explain.

Here's a good example: a human measures the distance between two trees and says that it's a yard. People believe it because it explains what the distance between the trees is, thus making the yard measurement permanently written in the human mind. In reality, it's just two trees far apart with an indiscernible distance between them, and it's never really known if it's a yard, an inch, a mile, or if everyone is just crazy for giving a random name to something because they didn't understand it.
 
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