Would you say math was discovered or invented?

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  • #26
Hurkyl
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In reality (that is to say that ontologically speaking) the universe never displays an absolute negative quantitative property.
:rolleyes:

At least you've not ranting about zero this time. I'd respond in full, but I don't want to hijack the topic. You might want to check out some of the history of the cubic and quartic formulas, though, which forced the mainstream acceptance of negative and complex numbers.
 
  • #27
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Les Sleeth said:
Absolutely, it is one of my favorite subjects. I think, however, you've chosen the wrong subject to be skeptical about. Order in this universe is likely more confirmed than any other single property.
Order != mathematics.
 
  • #28
MathematicalPhysicist
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vinter said:
Is Math a language?

The fact that we write 33 as 33 and not as "-, is due to maths as a language. But the fact that 33 + 33 = 66 is a law of the universe.



Basically, I'm getting confused.
yes maths is a language and the fact that some use it as a tool in other empiricial disciplines doesnt change the fact it's a language.

now those pure mathematicians and metamathematicians are those who actually expand the vocabulary in maths on general and practical maths with physics,biology and so on are those who are using maths to describe nature.

it seems to be a big problem (especially from americans who want everything to be practical) nowadays that people only categorize maths as describing nature solely.
 
  • #29
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Hurkyl said:
:rolleyes:

At least you've not ranting about zero this time. I'd respond in full, but I don't want to hijack the topic. You might want to check out some of the history of the cubic and quartic formulas, though, which forced the mainstream acceptance of negative and complex numbers.
I fully accept the notion of negative numbers and imaginary numbers. I use them all the time. I just recognize that they aren't absolute or distinct ideas of quantity. They are always relative relationships between quantities. Yet the mathematical community has defined them as absolute or "stand-alone' concept. Like it's perfectly acceptable to talk about an absolute negative number. Like as if that concept has merit without any relation to anything else. That is simply incorrect. By that I mean it is ontologically incorrect. No quantity in the universe can have an absolute property of negativity. It just doesn't make any sense. It's a relative property between sets, it's not an absolute property of a set.

So in this sense modern mathematical formalism simply has it incorrect. They idea that sets (or numbers) can have an absolute property of negatively is simply an axiomatic invention. This concept has not been "discovered" it has been incorrectly "invented" out of thin air.

If I give you 3 apples that represents -3 apples to me, but to you it's +3 apples. Do you see my point? The very same apples are both negative and positive at the same time depending on the point of view. The number 3 is absolute, but the property of negativity is not. So why did the mathematical community decide to invent the idea that -3's can somehow be said to exist as absolute mathematical numbers? It's simply ontologically['i] incorrect with respect to the observed behavior of the quantitative properties of the universe. (i.e. It's wrong!)

The same thing goes for imaginary numbers, but that's a little more complex (if you'll forgive the pun) so I won't bother confusing things by speaking to it.

I fully understand and use negative numbers, imaginary numbers, and even zero. But mathematical formalism has all of these concepts incorrectly defined with respect to the ontology of the universe.

I refer back to my previous conditional statement which I firmly believe,…

IF mathematical formalism is supposed to correctly represent the ontological quantitative nature of our universe, THEN our current modern mathematical formalism is ontologically incorrect.

That doesn't necessarily meant that mathematics is logically flawed within it's own system of axioms (which I happen to also believe is true none-the-less), but it simply means that mathematics does not correctly represent the ontological quantitative nature of our universe.

That also doesn't meant that I can't used negative numbers, or imaginary numbers, or zero. It simply means that I can recognize the real meaning of these concepts (where I'm using real here to simply mean ontologically correct) in spite of their incorrect arbitrarily invented mathematical definitions.

Zero, for example, is not a number or quantity. It's the absence of a number or quantity. There is a difference! And it's actually quite significant. Especially when considering other more advanced concepts such as transfinite numbers, irrational numbers, and even the number of points that can exist in a finite line segment. How you view these higher-level concepts, and therefore what conclusions you draw from them, is dependent on how you view the notion of zero.

Mathematics has zero incorrectly defined. Where I'm using "incorrect" here to mean "ontologically incorrect".
 
  • #30
Les Sleeth
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NeutronStar said:
I fully accept the notion of negative numbers and imaginary numbers. I use them all the time. I just recognize that they aren't absolute or distinct ideas of quantity. They are always relative relationships between quantities. Yet the mathematical community has defined them as absolute or "stand-alone' concept. Like it's perfectly acceptable to talk about an absolute negative number. Like as if that concept has merit without any relation to anything else. That is simply incorrect. By that I mean it is ontologically incorrect. No quantity in the universe can have an absolute property of negativity. It just doesn't make any sense. It's a relative property between sets, it's not an absolute property of a set. . . . Zero, for example, is not a number or quantity. . . Mathematics has zero incorrectly defined. Where I'm using "incorrect" here to mean "ontologically incorrect".
Interesting observations, but I would be surprised if those relying on math to do science don't understand your points. I can see how such views might develop if one only works with numbers, and never has to verify predictions.
 
  • #31
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Les Sleeth said:
I can see how such views might develop if one only works with numbers, and never has to verify predictions.
I too fully understand where the pure mathematicians are coming from. However, I also firmly believe that pure mathematics could be both, logically abstract, and ontologically correct. So I don't understand why mathematicians don't strive to make it both logically abstract, and ontologically correct.

Well, actually, I do understand why the mathematical community historically went down this path. I just disagree with the direction that they have chosen to take. What I don't understand is why the scientific community isn't in an uproar about it.

Who is at the helm of the mathematical community? Any why have they chosen to completely ignore the original historical foundation of mathematics? (i.e. The observed ontological quantitative properties exhibited by the universe?)

To answer my own question, I believe it was their thirst for some idealized logical purity that is disconnected from physical reality. Personally I think that notion is absurd. The quantitative properties of our universe exist because the physical universe exists. Any attempt to try sweep that under the carpet is nothing short of silliness.

It's just plain silly. It really is!

More importantly, as we continue down this path we will get further and further away from ontological truths. All aliens will recognize numbers like π and e because these quantitative relationships arise from ontological situations.

But will all aliens agree with the axiom of the existence of an empty set? No. Why not? Because that's strictly a human invention that is actually quite ontologically incorrect. Aliens would laugh at such a notion as being a display of our ignorance. The aliens will, however, understand the concept of a set itself, because that is ontological. They will just have to explain to us that we don't fully understand the concept of sets, and then show us why it is ontologically incorrect to claim that an empty set can exist.

I'm not even an alien and I know that much! :biggrin:

In fact, whenever we ask whether we are inventing a concept, or discovering it, I think it is a good test to think in terms of extraterrestrials. Would they come to the same conclusions? If so then it must be a discovery. Or might they think up something else? If so, then we must be inventing an arbitrary concept.
 
  • #32
Hurkyl
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My response here.
 
  • #33
Icebreaker
If aliens may not agree with some axoims, then it's possible that some theorems as well and, from there, our entire math structure. Meaning that they might have a different math system than ours, and therefore, math is invented, not discovered -- for it to be discovered, it must be universal.
 
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  • #34
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Icebreaker said:
If aliens may not agree with some axoims, then it's possible that some theorems as well and, from there, our entire math structure. Meaning that they might have a different math system than hours, and therefore, math is invented, not discovered -- for it to be discovered, it must be universal.
Not so, just because the medieval Europeans didn't know about the New World didn't mean it wasn't there, nor that the geography they did no was wrong. Just because mathematicians have only discussed certain systems and there are other systems yet unkown to us doesn't invalidate the systems we know. Mathematicians are continually dealing with aliens who discover different systems and new perspectives on old ones. It's called the younger generation.
 
  • #35
Icebreaker
Exactly, it is not invented because one of the two must be "wrong", and therefore there must be a true and universal answer.
 

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